define logical thinking in education

• Onsite training

3,000,000+ delegates

15,000+ clients

1,000+ locations

• KnowledgePass
• Log a ticket

01344203999 Available 24/7

What is Logical Thinking? A Beginner's Guide 

What is Logical Thinking? A Beginner's Guide: Discover the essence of Logical Thinking in this detailed guide. Unveil its importance in problem-solving, decision-making, and analytical reasoning. Learn techniques to develop this crucial skill, understand common logical fallacies, and explore how Logical Thinking can be applied effectively in various aspects of life and work.

Exclusive 40% OFF

Training Outcomes Within Your Budget!

We ensure quality, budget-alignment, and timely delivery by our expert instructors.

Share this Resource

• Strategic Planning and Thinking Course
• Leadership Skills Training
• Practical Thinking Course
• Attention Management Training
• Introduction to Supervising a Team

Whether you're solving a complex problem, engaging in critical discussions, or just navigating your daily routines, Logical Thinking plays a pivotal role in ensuring that your thoughts and actions are rational and coherent. In this blog, we will discuss What is Logical Thinking in detail, its importance, and its components. You'll also learn about the various ways that make up Logical Thinking and how to develop this essential skill.    

Table of contents  

1)  Understanding Logical Thinking 

2)  Components of Logical Thinking 

3)  Why is Logical Thinking important? 

4)  What are Logical Thinking skills?   

5)  Developing Logical Thinking skills 

6)  Exercises to improve Logical Thinking 

7)  Conclusion 

Understanding Logical Thinking  

Logical Thinking is the capacity to employ reason and systematic processes to analyse information, establish connections, and reach well-founded conclusions. It entails a structured and rational approach to problem-solving and decision-making. 

For example, consider a scenario where you're presented with a puzzle. To logically think through it, you would assess the provided clues, break down the problem into smaller elements, and systematically find potential solutions. You'd avoid hasty or emotion-driven judgments and rely on evidence and sound reasoning to arrive at the correct answer, showcasing the essence of Logical Thinking in problem-solving.

C omponents of Logical Thinking  

After knowing What is Logic al Thinking, let’s move on to the key components of Logical Thinking. Logical Thinking comprises several key components that work together to facilitate reasoned analysis and problem-solving. Here are the following key components of Logical Thinking.  

1)  Deductive reasoning : Deductive reasoning involves drawing specific conclusions from general premises or facts. It's like moving from a broad idea to a more specific conclusion. For example, if all humans are mortal, and Socrates is a human, then you can logically conclude that Socrates is mortal. 

2)   I nductive reasoning : Inductive reasoning is the procedure of forming general conclusions based on specific observations or evidence. It's the opposite of deductive reasoning. For instance, if you observe that the sun has risen every day, you might inductively reason that the sun will rise again tomorrow.  

3)  Causal inference : Causal inference is the ability to identify cause-and-effect relationships between events, actions, or variables. It involves understanding that one event or action can lead to another event as a consequence . In essence, it's the recognition that a specific cause produces a particular effect.  

4)  Analogy : Analogical reasoning or analogy involves drawing similarities and making comparisons between two or more situations, objects, or concepts. It's a way of applying knowledge or understanding from one context to another by recognising shared features or characteristics. Analogical reasoning is powerful because it allows you to transfer what you know in one domain to another, making it easier to comprehend and solve new problems. 

Why is Logical Thinking Important?  

1)  Effective problem-solving : Logical Thinking equips individuals with the ability to dissect complex problems, identify patterns, and devise systematic solutions. Whether it's troubleshooting a technical issue or resolving personal dilemmas, Logical Thinking ensures that problems are approached with a structured and efficient methodology. 

2)  Enhanced decision-making : Making sound decisions is a cornerstone of success in both personal and professional life. Logical Thinking allows individuals to evaluate options, consider consequences, and choose the most rational course of action. This is particularly critical in high-stakes situations. 

3)   Critical thinking : Logical Thinking is at the core of critical thinking. It encourages individuals to question assumptions, seek evidence, and challenge existing beliefs. This capacity for critical analysis fosters a deeper understanding of complex issues and prevents the acceptance of unfounded or biased information. 

4)  Effective communication : In discussions and debates, Logical Thinking helps individuals express their ideas and viewpoints clearly and persuasively. It enables individuals to construct well-structured arguments, provide evidence, and counter opposing views, fostering productive and respectful communication. 

5)  Academic and professional success : Logical Thinking is highly valued in educational settings and the workplace. It allows students to excel academically by tackling challenging coursework and assignments. In the professional world, it's a key attribute for problem-solving, innovation, and career advancement. 

6)  Avoiding Logical fallacies : Logical Thinking equips individuals with the ability to recognise and avoid common logical fallacies such as circular reasoning, straw man arguments, and ad hominem attacks. This safeguards them from being deceived or manipulated by flawed or deceptive arguments. 

Supercharge Your Sales with our Sales Negotiation Skills Course . Check out now and close deals like a pro!  

What are Logical Thinking skills ?  

Logical Thinking skills are cognitive abilities that allow individuals to process information, analyse it systematically, and draw reasonable conclusions. These skills enable people to approach problems, decisions, and challenges with a structured and rational mindset .  

Developing Logical Thinking skills  

Developing strong Logical Thinking skills is essential for improved problem-solving, decision-making, and critical analysis. Here are some key strategies to help you enhance your Logical Thinking abilities.   

1)  Practice critical thinking : Engage in activities that require critical thinking, such as analysing articles, solving puzzles, or evaluating arguments. Regular practice sharpens your analytical skills.  

2)  L earn formal logic : Study the principles of formal logic, which provide a structured approach to reasoning. This can include topics like syllogisms, propositional logic, and predicate logic. 

3)  I dentify assumptions : When faced with a problem or argument, be aware of underlying assumptions. Question these assumptions and consider how they impact the overall reasoning. 

4)  B reak down problems : When tackling complex problems, break them down into smaller, more manageable components. Analyse each component individually before looking at the problem as a whole . 

5)   Seek diverse perspectives : Engage in discussions and debates with people who hold different viewpoints. This helps you consider a range of perspectives and strengthens your ability to construct and counter -arguments. 

6)  Read widely : Reading a variety of materials, from academic articles to literature, exposes you to different modes of reasoning and argumentation. This broadens your thinking and enhances your ability to connect ideas.  

7)  Solve puzzles and brain teasers : Engaging in puzzles, riddles, and brain teasers challenges your mind and encourages creative problem-solving. It's an enjoyable way to exercise your Logical Thinking. 

8)  Develop mathematical skills : Mathematics is a discipline that heavily relies on Logical Thinking. Learning and practising mathematical concepts and problem-solving techniques can significantly boost your logical reasoning skills. 

Unlock Your sales potential with our Soft Skills Training For Sales Professionals . Elevate your sales game today and boost your success – register now!  

Exercises to improve Logical Thinking  

Enhancing your Logical Thinking skills is achievable through various exercises and activities. Here are some practical exercises to help you strengthen your Logical Thinking abilities:  

1)   Sudoku puzzles : Solve Sudoku puzzles, as they require logical deduction to fill in the missing numbers.  

2)   Crossword puzzles : Crosswords challenge your vocabulary and logical word placement.  

3)  Brain teasers : Engage in brain teasers and riddles that encourage creative problem-solving.  

4)  Chess and board games : Play strategic board games like chess, checkers, or strategic video games that require forward thinking and planning.  

5)  Logical argumentation : Engage in debates or discussions where you must construct reasoned arguments and counter opposing viewpoints.  

6)  Coding and programming : Learn coding and programming languages which promote structured and Logical Thinking in problem-solving. 

7)  Mathematical challenges : Solve mathematical problems and equations, as mathematics is inherently logical.  

8)   Mensa puzzles : Work on Mensa puzzles, which are designed to test and strengthen Logical Thinking skills. 

9)  Logic games : Play logic-based games like Minesweeper or Mastermind.  

10)   Logical analogy exercises : Practice solving analogy exercises, which test your ability to find relationships between words or concepts.  

11)  Visual logic puzzles : Tackle visual logic puzzles like nonograms or logic grid puzzles. 

12)  Critical reading : Read books, articles, or academic papers and critically analyse the arguments and evidence presented. 

13)  Coding challenges : Participate in online coding challenges and competitions that require logical problem-solving in coding. 

14)  Scientific method : Conduct simple science experiments or projects, applying the scientific method to develop hypotheses and draw logical conclusions.  

15)   Poker or card games : Play card games like poker, where you must strategi se and make logical decisions based on probabilities and information. 

16)  Analyse real-world situations : Analyse real-world situations or news stories, evaluating the information, causes, and potential consequences. 

These exercises will help you practice and enhance your Logical Thinking skills in a fun and engaging way, making them an integral part of your problem-solving and decision-making toolkit. 

Take your sales to the next level! Elevate your skills with our Sales Training . Join us today!  

Concluson  

In this blog, we have discussed What is Logical Thinking, its importance, its components and ways to improve this skill. When you learn how to think logically, you start gathering each and every information as much as possible, analyse the facts, and methodically choose the best way to go forward with your decision. Logical Thinking is considered the most important tool in brainstorming ideas, assessing issues and finding solutions. 

Master the art of effective meetings. Elevate your Meeting Skills for success. Get started now!  

Frequently Asked Questions

Upcoming business skills resources batches & dates.

Fri 24th May 2024

Fri 28th Jun 2024

Fri 26th Jul 2024

Fri 23rd Aug 2024

Fri 27th Sep 2024

Fri 25th Oct 2024

Fri 22nd Nov 2024

Fri 27th Dec 2024

Get A Quote

WHO WILL BE FUNDING THE COURSE?

My employer

By submitting your details you agree to be contacted in order to respond to your enquiry

• Business Analysis
• Lean Six Sigma Certification

Share this course

Our biggest spring sale.

We cannot process your enquiry without contacting you, please tick to confirm your consent to us for contacting you about your enquiry.

By submitting your details you agree to be contacted in order to respond to your enquiry.

We may not have the course you’re looking for. If you enquire or give us a call on 01344203999 and speak to our training experts, we may still be able to help with your training requirements.

Or select from our popular topics

• ITIL® Certification
• Scrum Certification
• Change Management Certification
• Business Analysis Courses
• Microsoft Azure Certification
• Microsoft Excel Courses
• Microsoft Project
• Explore more courses

Press esc to close

Fill out your  contact details  below and our training experts will be in touch.

Fill out your   contact details   below

Thank you for your enquiry!

One of our training experts will be in touch shortly to go over your training requirements.

Back to Course Information

Fill out your contact details below so we can get in touch with you regarding your training requirements.

* WHO WILL BE FUNDING THE COURSE?

Preferred Contact Method

No preference

Back to course information

Fill out your  training details  below

Fill out your training details below so we have a better idea of what your training requirements are.

HOW MANY DELEGATES NEED TRAINING?

HOW DO YOU WANT THE COURSE DELIVERED?

Online Instructor-led

Online Self-paced

WHEN WOULD YOU LIKE TO TAKE THIS COURSE?

Next 2 - 4 months

WHAT IS YOUR REASON FOR ENQUIRING?

Looking for some information

Looking for a discount

I want to book but have questions

One of our training experts will be in touch shortly to go overy your training requirements.

Your privacy & cookies!

Like many websites we use cookies. We care about your data and experience, so to give you the best possible experience using our site, we store a very limited amount of your data. Continuing to use this site or clicking “Accept & close” means that you agree to our use of cookies. Learn more about our privacy policy and cookie policy cookie policy .

We use cookies that are essential for our site to work. Please visit our cookie policy for more information. To accept all cookies click 'Accept & close'.

Translate this page from English...

*Machine translated pages not guaranteed for accuracy. Click Here for our professional translations.

Defining Critical Thinking

Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Copyright Year: 2016

Publisher: Matthew J. Van Cleave

Language: English

Formats Available

Conditions of use.

Learn more about reviews.

Reviewed by "yusef" Alexander Hayes, Professor, North Shore Community College on 6/9/21

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness. read more

Comprehensiveness rating: 5 see less

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness.

Content Accuracy rating: 5

The book is accurate.

Relevance/Longevity rating: 5

While many modern examples are used, and they are helpful, they are not necessarily needed. The usefulness of logical principles and skills have proved themselves, and this text presents them clearly with many examples.

Clarity rating: 5

It is obvious that the author cares about their subject, audience, and students. The text is comprehensible and interesting.

Consistency rating: 5

The format is easy to understand and is consistent in framing.

Modularity rating: 5

This text would be easy to adapt.

Organization/Structure/Flow rating: 5

The organization is excellent, my one suggestion would be a concluding chapter.

Interface rating: 5

I accessed the PDF version and it would be easy to work with.

Grammatical Errors rating: 5

The writing is excellent.

Cultural Relevance rating: 5

This is not an offensive text.

Reviewed by Susan Rottmann, Part-time Lecturer, University of Southern Maine on 3/2/21

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it... read more

Comprehensiveness rating: 4 see less

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it fits better for a general critical thinking course than for a true logic course. I'm not sure that I'd agree. I have been using Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," and I think that book is a better introduction to critical thinking for non-philosophy majors. However, the latter is not open source so I will figure out how to get by without it in the future. Overall, the book seems comprehensive if the subject is logic. The index is on the short-side, but fine. However, one issue for me is that there are no page numbers on the table of contents, which is pretty annoying if you want to locate particular sections.

Content Accuracy rating: 4

I didn't find any errors. In general the book uses great examples. However, they are very much based in the American context, not for an international student audience. Some effort to broaden the chosen examples would make the book more widely applicable.

Relevance/Longevity rating: 4

I think the book will remain relevant because of the nature of the material that it addresses, however there will be a need to modify the examples in future editions and as the social and political context changes.

Clarity rating: 3

The text is lucid, but I think it would be difficult for introductory-level students who are not philosophy majors. For example, in Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," the sub-headings are very accessible, such as "Experts cannot rescue us, despite what they say" or "wishful thinking: perhaps the biggest single speed bump on the road to critical thinking." By contrast, Van Cleave's "Introduction to Logic and Critical Thinking" has more subheadings like this: "Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form" or "Propositional logic and the four basic truth functional connectives." If students are prepared very well for the subject, it would work fine, but for students who are newly being introduced to critical thinking, it is rather technical.

It seems to be very consistent in terms of its terminology and framework.

Modularity rating: 4

The book is divided into 4 chapters, each having many sub-chapters. In that sense, it is readily divisible and modular. However, as noted above, there are no page numbers on the table of contents, which would make assigning certain parts rather frustrating. Also, I'm not sure why the book is only four chapter and has so many subheadings (for instance 17 in Chapter 2) and a length of 242 pages. Wouldn't it make more sense to break up the book into shorter chapters? I think this would make it easier to read and to assign in specific blocks to students.

Organization/Structure/Flow rating: 4

The organization of the book is fine overall, although I think adding page numbers to the table of contents and breaking it up into more separate chapters would help it to be more easily navigable.

Interface rating: 4

The book is very simply presented. In my opinion it is actually too simple. There are few boxes or diagrams that highlight and explain important points.

The text seems fine grammatically. I didn't notice any errors.

The book is written with an American audience in mind, but I did not notice culturally insensitive or offensive parts.

Overall, this book is not for my course, but I think it could work well in a philosophy course.

Reviewed by Daniel Lee, Assistant Professor of Economics and Leadership, Sweet Briar College on 11/11/19

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument read more

Comprehensiveness rating: 3 see less

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument

To the best of my ability, I regard this content as accurate, error-free, and unbiased

The book is broadly relevant and up-to-date, with a few stray temporal references (sydney olympics, particular presidencies). I don't view these time-dated examples as problematic as the logical underpinnings are still there and easily assessed

Clarity rating: 4

My only pushback on clarity is I didn't find the distinction between argument and explanation particularly helpful/useful/easy to follow. However, this experience may have been unique to my class.

To the best of my ability, I regard this content as internally consistent

I found this text quite modular, and was easily able to integrate other texts into my lessons and disregard certain chapters or sub-sections

The book had a logical and consistent structure, but to the extent that there are only 4 chapters, there isn't much scope for alternative approaches here

No problems with the book's interface

The text is grammatically sound

Cultural Relevance rating: 4

Perhaps the text could have been more universal in its approach. While I didn't find the book insensitive per-se, logic can be tricky here because the point is to evaluate meaningful (non-trivial) arguments, but any argument with that sense of gravity can also be traumatic to students (abortion, death penalty, etc)

No additional comments

Reviewed by Lisa N. Thomas-Smith, Graduate Part-time Instructor, CU Boulder on 7/1/19

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text,... read more

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text, and the index is very thorough.

The content is excellent. The text is thorough and accurate with no errors that I could discern. The terminology and exercises cover the material nicely and without bias.

The text should easily stand the test of time. The exercises are excellent and would be very helpful for students to internalize correct critical thinking practices. Because of the logical arrangement of the text and the many sub-sections, additional material should be very easy to add.

The text is extremely clearly and simply written. I anticipate that a diligent student could learn all of the material in the text with little additional instruction. The examples are relevant and easy to follow.

The text did not confuse terms or use inconsistent terminology, which is very important in a logic text. The discipline often uses multiple terms for the same concept, but this text avoids that trap nicely.

The text is fairly easily divisible. Since there are only four chapters, those chapters include large blocks of information. However, the chapters themselves are very well delineated and could be easily broken up so that parts could be left out or covered in a different order from the text.

The flow of the text is excellent. All of the information is handled solidly in an order that allows the student to build on the information previously covered.

The PDF Table of Contents does not include links or page numbers which would be very helpful for navigation. Other than that, the text was very easy to navigate. All the images, charts, and graphs were very clear

I found no grammatical errors in the text.

Cultural Relevance rating: 3

The text including examples and exercises did not seem to be offensive or insensitive in any specific way. However, the examples included references to black and white people, but few others. Also, the text is very American specific with many examples from and for an American audience. More diversity, especially in the examples, would be appropriate and appreciated.

Reviewed by Leslie Aarons, Associate Professor of Philosophy, CUNY LaGuardia Community College on 5/16/19

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an... read more

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an argument and an explanation; validity; soundness; and the distinctions between an inductive and a deductive argument in accessible terms in the first chapter. It also does a good job introducing and discussing informal fallacies (Chapter 4). The incorporation of opportunities to evaluate real-world arguments is also very effective. Chapter 2 also covers a number of formal methods of evaluating arguments, such as Venn Diagrams and Propositional logic and the four basic truth functional connectives, but to my mind, it is much more thorough in its treatment of Informal Logic and Critical Thinking skills, than it is of formal logic. I also appreciated that Van Cleave’s book includes exercises with answers and an index, but there is no glossary; which I personally do not find detracts from the book's comprehensiveness.

Overall, Van Cleave's book is error-free and unbiased. The language used is accessible and engaging. There were no glaring inaccuracies that I was able to detect.

Van Cleave's Textbook uses relevant, contemporary content that will stand the test of time, at least for the next few years. Although some examples use certain subjects like former President Obama, it does so in a useful manner that inspires the use of critical thinking skills. There are an abundance of examples that inspire students to look at issues from many different political viewpoints, challenging students to practice evaluating arguments, and identifying fallacies. Many of these exercises encourage students to critique issues, and recognize their own inherent reader-biases and challenge their own beliefs--hallmarks of critical thinking.

As mentioned previously, the author has an accessible style that makes the content relatively easy to read and engaging. He also does a suitable job explaining jargon/technical language that is introduced in the textbook.

Van Cleave uses terminology consistently and the chapters flow well. The textbook orients the reader by offering effective introductions to new material, step-by-step explanations of the material, as well as offering clear summaries of each lesson.

This textbook's modularity is really quite good. Its language and structure are not overly convoluted or too-lengthy, making it convenient for individual instructors to adapt the materials to suit their methodological preferences.

The topics in the textbook are presented in a logical and clear fashion. The structure of the chapters are such that it is not necessary to have to follow the chapters in their sequential order, and coverage of material can be adapted to individual instructor's preferences.

The textbook is free of any problematic interface issues. Topics, sections and specific content are accessible and easy to navigate. Overall it is user-friendly.

I did not find any significant grammatical issues with the textbook.

The textbook is not culturally insensitive, making use of a diversity of inclusive examples. Materials are especially effective for first-year critical thinking/logic students.

I intend to adopt Van Cleave's textbook for a Critical Thinking class I am teaching at the Community College level. I believe that it will help me facilitate student-learning, and will be a good resource to build additional classroom activities from the materials it provides.

Reviewed by Jennie Harrop, Chair, Department of Professional Studies, George Fox University on 3/27/18

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters... read more

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters that are dense with statistical analyses and critical vocabulary. These topics are likely better broached in manageable snippets rather than hefty single chapters.

The ideas addressed in Introduction to Logic and Critical Thinking are accurate but at times notably political. While politics are effectively used to exemplify key concepts, some students may be distracted by distinct political leanings.

The terms and definitions included are relevant, but the examples are specific to the current political, cultural, and social climates, which could make the materials seem dated in a few years without intentional and consistent updates.

While the reasoning is accurate, the author tends to complicate rather than simplify -- perhaps in an effort to cover a spectrum of related concepts. Beginning readers are likely to be overwhelmed and under-encouraged by his approach.

Consistency rating: 3

The four chapters are somewhat consistent in their play of definition, explanation, and example, but the structure of each chapter varies according to the concepts covered. In the third chapter, for example, key ideas are divided into sub-topics numbering from 3.1 to 3.10. In the fourth chapter, the sub-divisions are further divided into sub-sections numbered 4.1.1-4.1.5, 4.2.1-4.2.2, and 4.3.1 to 4.3.6. Readers who are working quickly to master new concepts may find themselves mired in similarly numbered subheadings, longing for a grounded concepts on which to hinge other key principles.

Modularity rating: 3

The book's four chapters make it mostly self-referential. The author would do well to beak this text down into additional subsections, easing readers' accessibility.

The content of the book flows logically and well, but the information needs to be better sub-divided within each larger chapter, easing the student experience.

The book's interface is effective, allowing readers to move from one section to the next with a single click. Additional sub-sections would ease this interplay even further.

Grammatical Errors rating: 4

Some minor errors throughout.

For the most part, the book is culturally neutral, avoiding direct cultural references in an effort to remain relevant.

Reviewed by Yoichi Ishida, Assistant Professor of Philosophy, Ohio University on 2/1/18

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic,... read more

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic, this textbook does not cover suppositional arguments, such as conditional proof and reductio ad absurdum. But other standard argument forms are covered. Chapter 3 covers inductive logic, and here this textbook introduces probability and its relationship with cognitive biases, which are rarely discussed in other textbooks. Chapter 4 introduces common informal fallacies. The answers to all the exercises are given at the end. However, the last set of exercises is in Chapter 3, Section 5. There are no exercises in the rest of the chapter. Chapter 4 has no exercises either. There is index, but no glossary.

The textbook is accurate.

The content of this textbook will not become obsolete soon.

The textbook is written clearly.

The textbook is internally consistent.

The textbook is fairly modular. For example, Chapter 3, together with a few sections from Chapter 1, can be used as a short introduction to inductive logic.

The textbook is well-organized.

There are no interface issues.

I did not find any grammatical errors.

This textbook is relevant to a first semester logic or critical thinking course.

Reviewed by Payal Doctor, Associate Professro, LaGuardia Community College on 2/1/18

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner... read more

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner book, but seems to be a good text for a course that needs a foundation for arguments. There are exercises on creating truth tables and proofs, so it could work as a logic primer in short sessions or with the addition of other course content.

The books is accurate in the information it presents. It does not contain errors and is unbiased. It covers the essential vocabulary clearly and givens ample examples and exercises to ensure the student understands the concepts

The content of the book is up to date and can be easily updated. Some examples are very current for analyzing the argument structure in a speech, but for this sort of text understandable examples are important and the author uses good examples.

The book is clear and easy to read. In particular, this is a good text for community college students who often have difficulty with reading comprehension. The language is straightforward and concepts are well explained.

The book is consistent in terminology, formatting, and examples. It flows well from one topic to the next, but it is also possible to jump around the text without loosing the voice of the text.

The books is broken down into sub units that make it easy to assign short blocks of content at a time. Later in the text, it does refer to a few concepts that appear early in that text, but these are all basic concepts that must be used to create a clear and understandable text. No sections are too long and each section stays on topic and relates the topic to those that have come before when necessary.

The flow of the text is logical and clear. It begins with the basic building blocks of arguments, and practice identifying more and more complex arguments is offered. Each chapter builds up from the previous chapter in introducing propositional logic, truth tables, and logical arguments. A select number of fallacies are presented at the end of the text, but these are related to topics that were presented before, so it makes sense to have these last.

The text is free if interface issues. I used the PDF and it worked fine on various devices without loosing formatting.

1. The book contains no grammatical errors.

The text is culturally sensitive, but examples used are a bit odd and may be objectionable to some students. For instance, President Obama's speech on Syria is used to evaluate an extended argument. This is an excellent example and it is explained well, but some who disagree with Obama's policies may have trouble moving beyond their own politics. However, other examples look at issues from all political viewpoints and ask students to evaluate the argument, fallacy, etc. and work towards looking past their own beliefs. Overall this book does use a variety of examples that most students can understand and evaluate.

My favorite part of this book is that it seems to be written for community college students. My students have trouble understanding readings in the New York Times, so it is nice to see a logic and critical thinking text use real language that students can understand and follow without the constant need of a dictionary.

Reviewed by Rebecca Owen, Adjunct Professor, Writing, Chemeketa Community College on 6/20/17

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current... read more

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current events, funny scenarios, or other interesting ways to evaluate argument structure and validity. The third section, which deals with logical fallacies, is very clear and comprehensive. My only critique of the material included in the book is that the middle section may be a bit dense and math-oriented for learners who appreciate the more informal, informative style of the first and third section. Also, the book ends rather abruptly--it moves from a description of a logical fallacy to the answers for the exercises earlier in the text.

The content is very reader-friendly, and the author writes with authority and clarity throughout the text. There are a few surface-level typos (Starbuck's instead of Starbucks, etc.). None of these small errors detract from the quality of the content, though.

One thing I really liked about this text was the author's wide variety of examples. To demonstrate different facets of logic, he used examples from current media, movies, literature, and many other concepts that students would recognize from their daily lives. The exercises in this text also included these types of pop-culture references, and I think students will enjoy the familiarity--as well as being able to see the logical structures behind these types of references. I don't think the text will need to be updated to reflect new instances and occurrences; the author did a fine job at picking examples that are relatively timeless. As far as the subject matter itself, I don't think it will become obsolete any time soon.

The author writes in a very conversational, easy-to-read manner. The examples used are quite helpful. The third section on logical fallacies is quite easy to read, follow, and understand. A student in an argument writing class could benefit from this section of the book. The middle section is less clear, though. A student learning about the basics of logic might have a hard time digesting all of the information contained in chapter two. This material might be better in two separate chapters. I think the author loses the balance of a conversational, helpful tone and focuses too heavily on equations.

Consistency rating: 4

Terminology in this book is quite consistent--the key words are highlighted in bold. Chapters 1 and 3 follow a similar organizational pattern, but chapter 2 is where the material becomes more dense and equation-heavy. I also would have liked a closing passage--something to indicate to the reader that we've reached the end of the chapter as well as the book.

I liked the overall structure of this book. If I'm teaching an argumentative writing class, I could easily point the students to the chapters where they can identify and practice identifying fallacies, for instance. The opening chapter is clear in defining the necessary terms, and it gives the students an understanding of the toolbox available to them in assessing and evaluating arguments. Even though I found the middle section to be dense, smaller portions could be assigned.

The author does a fine job connecting each defined term to the next. He provides examples of how each defined term works in a sentence or in an argument, and then he provides practice activities for students to try. The answers for each question are listed in the final pages of the book. The middle section feels like the heaviest part of the whole book--it would take the longest time for a student to digest if assigned the whole chapter. Even though this middle section is a bit heavy, it does fit the overall structure and flow of the book. New material builds on previous chapters and sub-chapters. It ends abruptly--I didn't realize that it had ended, and all of a sudden I found myself in the answer section for those earlier exercises.

The simple layout is quite helpful! There is nothing distracting, image-wise, in this text. The table of contents is clearly arranged, and each topic is easy to find.

Tiny edits could be made (Starbuck's/Starbucks, for one). Otherwise, it is free of distracting grammatical errors.

This text is quite culturally relevant. For instance, there is one example that mentions the rumors of Barack Obama's birthplace as somewhere other than the United States. This example is used to explain how to analyze an argument for validity. The more "sensational" examples (like the Obama one above) are helpful in showing argument structure, and they can also help students see how rumors like this might gain traction--as well as help to show students how to debunk them with their newfound understanding of argument and logic.

The writing style is excellent for the subject matter, especially in the third section explaining logical fallacies. Thank you for the opportunity to read and review this text!

Reviewed by Laurel Panser, Instructor, Riverland Community College on 6/20/17

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as... read more

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as the 13th edition with the same title. Lori Watson is the second author on the 13th edition.

Competing with Hurley is difficult with respect to comprehensiveness. For example, Van Cleave’s book is comprehensive to the extent that it probably covers at least two-thirds or more of what is dealt with in most introductory, one-semester logic courses. Van Cleave’s chapter 1 provides an overview of argumentation including discerning non-arguments from arguments, premises versus conclusions, deductive from inductive arguments, validity, soundness and more. Much of Van Cleave’s chapter 1 parallel’s Hurley’s chapter 1. Hurley’s chapter 3 regarding informal fallacies is comprehensive while Van Cleave’s chapter 4 on this topic is less extensive. Categorical propositions are a topic in Van Cleave’s chapter 2; Hurley’s chapters 4 and 5 provide more instruction on this, however. Propositional logic is another topic in Van Cleave’s chapter 2; Hurley’s chapters 6 and 7 provide more information on this, though. Van Cleave did discuss messy issues of language meaning briefly in his chapter 1; that is the topic of Hurley’s chapter 2.

Van Cleave’s book includes exercises with answers and an index. A glossary was not included.

Reviews of open source textbooks typically include criteria besides comprehensiveness. These include comments on accuracy of the information, whether the book will become obsolete soon, jargon-free clarity to the extent that is possible, organization, navigation ease, freedom from grammar errors and cultural relevance; Van Cleave’s book is fine in all of these areas. Further criteria for open source books includes modularity and consistency of terminology. Modularity is defined as including blocks of learning material that are easy to assign to students. Hurley’s book has a greater degree of modularity than Van Cleave’s textbook. The prose Van Cleave used is consistent.

Van Cleave’s book will not become obsolete soon.

Van Cleave’s book has accessible prose.

Van Cleave used terminology consistently.

Van Cleave’s book has a reasonable degree of modularity.

Van Cleave’s book is organized. The structure and flow of his book is fine.

Problems with navigation are not present.

Grammar problems were not present.

Van Cleave’s book is culturally relevant.

Van Cleave’s book is appropriate for some first semester logic courses.

Table of Contents

Chapter 1: Reconstructing and analyzing arguments

• 1.1 What is an argument?
• 1.2 Identifying arguments
• 1.3 Arguments vs. explanations
• 1.4 More complex argument structures
• 1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form
• 1.6 Validity
• 1.7 Soundness
• 1.8 Deductive vs. inductive arguments
• 1.9 Arguments with missing premises
• 1.10 Assuring, guarding, and discounting
• 1.11 Evaluative language
• 1.12 Evaluating a real-life argument

Chapter 2: Formal methods of evaluating arguments

• 2.1 What is a formal method of evaluation and why do we need them?
• 2.2 Propositional logic and the four basic truth functional connectives
• 2.3 Negation and disjunction
• 2.4 Using parentheses to translate complex sentences
• 2.5 “Not both” and “neither nor”
• 2.6 The truth table test of validity
• 2.7 Conditionals
• 2.8 “Unless”
• 2.9 Material equivalence
• 2.10 Tautologies, contradictions, and contingent statements
• 2.11 Proofs and the 8 valid forms of inference
• 2.12 How to construct proofs
• 2.13 Short review of propositional logic
• 2.14 Categorical logic
• 2.15 The Venn test of validity for immediate categorical inferences
• 2.16 Universal statements and existential commitment
• 2.17 Venn validity for categorical syllogisms

Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies

• 3.1 Inductive arguments and statistical generalizations
• 3.2 Inference to the best explanation and the seven explanatory virtues
• 3.3 Analogical arguments
• 3.4 Causal arguments
• 3.5 Probability
• 3.6 The conjunction fallacy
• 3.7 The base rate fallacy
• 3.8 The small numbers fallacy
• 3.9 Regression to the mean fallacy
• 3.10 Gambler's fallacy

Chapter 4: Informal fallacies

• 4.1 Formal vs. informal fallacies
• 4.1.1 Composition fallacy
• 4.1.2 Division fallacy
• 4.1.3 Begging the question fallacy
• 4.1.4 False dichotomy
• 4.1.5 Equivocation
• 4.2 Slippery slope fallacies
• 4.2.1 Conceptual slippery slope
• 4.2.2 Causal slippery slope
• 4.3 Fallacies of relevance
• 4.3.1 Ad hominem
• 4.3.2 Straw man
• 4.3.3 Tu quoque
• 4.3.4 Genetic
• 4.3.5 Appeal to consequences
• 4.3.6 Appeal to authority

Answers to exercises Glossary/Index

Ancillary Material

About the book.

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.”

About the Contributors

Matthew Van Cleave ,   PhD, Philosophy, University of Cincinnati, 2007.  VAP at Concordia College (Moorhead), 2008-2012.  Assistant Professor at Lansing Community College, 2012-2016. Professor at Lansing Community College, 2016-

Contribute to this Page

• Programs & Services
• Delphi Center

Ideas to Action (i2a)

• What is Critical Thinking?

The ability to think critically calls for a higher-order thinking than simply the ability to recall information.

Definitions of critical thinking, its elements, and its associated activities fill the educational literature of the past forty years. Critical thinking has been described as an ability to question; to acknowledge and test previously held assumptions; to recognize ambiguity; to examine, interpret, evaluate, reason, and reflect; to make informed judgments and decisions; and to clarify, articulate, and justify positions (Hullfish & Smith, 1961; Ennis, 1962; Ruggiero, 1975; Scriven, 1976; Hallet, 1984; Kitchener, 1986; Pascarella & Terenzini, 1991; Mines et al., 1990; Halpern, 1996; Paul & Elder, 2001; Petress, 2004; Holyoak & Morrison, 2005; among others).

After a careful review of the mountainous body of literature defining critical thinking and its elements, UofL has chosen to adopt the language of Michael Scriven and Richard Paul (2003) as a comprehensive, concise operating definition:

Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.

Paul and Scriven go on to suggest that critical thinking is based on: "universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness. It entails the examination of those structures or elements of thought implicit in all reasoning: purpose, problem, or question-at-issue, assumptions, concepts, empirical grounding; reasoning leading to conclusions, implication and consequences, objections from alternative viewpoints, and frame of reference. Critical thinking - in being responsive to variable subject matter, issues, and purposes - is incorporated in a family of interwoven modes of thinking, among them: scientific thinking, mathematical thinking, historical thinking, anthropological thinking, economic thinking, moral thinking, and philosophical thinking."

This conceptualization of critical thinking has been refined and developed further by Richard Paul and Linder Elder into the Paul-Elder framework of critical thinking. Currently, this approach is one of the most widely published and cited frameworks in the critical thinking literature. According to the Paul-Elder framework, critical thinking is the:

• Analysis of thinking by focusing on the parts or structures of thinking ("the Elements of Thought")
• Evaluation of thinking by focusing on the quality ("the Universal Intellectual Standards")
• Improvement of thinking by using what you have learned ("the Intellectual Traits")

Selection of a Critical Thinking Framework

The University of Louisville chose the Paul-Elder model of Critical Thinking as the approach to guide our efforts in developing and enhancing our critical thinking curriculum. The Paul-Elder framework was selected based on criteria adapted from the characteristics of a good model of critical thinking developed at Surry Community College. The Paul-Elder critical thinking framework is comprehensive, uses discipline-neutral terminology, is applicable to all disciplines, defines specific cognitive skills including metacognition, and offers high quality resources.

Why the selection of a single critical thinking framework?

The use of a single critical thinking framework is an important aspect of institution-wide critical thinking initiatives (Paul and Nosich, 1993; Paul, 2004). According to this view, critical thinking instruction should not be relegated to one or two disciplines or departments with discipline specific language and conceptualizations. Rather, critical thinking instruction should be explicitly infused in all courses so that critical thinking skills can be developed and reinforced in student learning across the curriculum. The use of a common approach with a common language allows for a central organizer and for the development of critical thinking skill sets in all courses.

• SACS & QEP
• Planning and Implementation
• Why Focus on Critical Thinking?
• Paul-Elder Critical Thinking Framework
• Culminating Undergraduate Experience
• Community Engagement
• Frequently Asked Questions
• What is i2a?

Copyright © 2012 - University of Louisville , Delphi Center

Created by the Great Schools Partnership , the GLOSSARY OF EDUCATION REFORM is a comprehensive online resource that describes widely used school-improvement terms, concepts, and strategies for journalists, parents, and community members. | Learn more »

Critical Thinking

Critical thinking is a term used by educators to describe forms of learning, thought, and analysis that go beyond the memorization and recall of information and facts. In common usage, critical thinking is an umbrella term that may be applied to many different forms of learning acquisition or to a wide variety of thought processes. In its most basic expression, critical thinking occurs when students are analyzing, evaluating, interpreting, or synthesizing information and applying creative thought to form an argument, solve a problem, or reach a conclusion.

Critical thinking entails many kinds of intellectual skills, including the following representative examples:

• Developing well-reasoned, persuasive arguments and evaluating and responding to counterarguments
• Examining concepts or situations from multiple perspectives, including different cultural perspectives
• Questioning evidence and assumptions to reach novel conclusions
• Devising imaginative ways to solve problems, especially unfamiliar or complex problems
• Formulating and articulating thoughtful, penetrating questions
• Identifying themes or patterns and making abstract connections across subjects

Critical thinking is a central concept in educational reforms that call for schools to place a greater emphasis on skills that are used in all subject areas and that students can apply in all educational, career, and civic settings throughout their lives. It’s also a central concept in reforms that question how teachers have traditionally taught and what students should be learning—notably, the 21st century skills movement, which broadly calls on schools to create academic programs and learning experiences that equip students with the most essential and in-demand knowledge, skills, and dispositions they will need to be successful in higher-education programs and modern workplaces. As higher education and job requirements become competitive, complex, and technical, proponents argue, students will need skills such as critical thinking to successfully navigate the modern world, excel in challenging careers, and process increasingly complex information.

Critical thinking also intersects with debates about assessment and how schools should measure learning acquisition. For example, multiple-choice testing formats have been common in standardized testing for decades, yet the heavy use of such testing formats emphasizes—and may reinforce the importance of—factual retention and recall over other skills. If schools largely test and award grades for factual recall, teachers will therefore stress memorization and recall in their teaching, possibly at the expense of skills such as critical thinking that are vitally important for students to possess but far more challenging to measure accurately.

Alphabetical Search

• Partnerships

The development of the reasoning brain and how to foster logical reasoning skills

Early childhood development / Effective lifelong learning / Learning mathematics

Executive summary

Learning to reason logically is necessary for the growth of critical and scientific thinking in children. Yet, both psychological and neural evidence indicates that logical reasoning is hard even for educated adults. Here, we examine the factors that scaffold the emergence of logical reasoning in children. Evidence suggests that the development of reasoning with concrete information can be accounted for by the development of both world knowledge and self-regulation. The transition from concrete to abstract reasoning, however, is a challenge for children. Children’s development of reasoning may be supported by encouraging both divergent thinking and reasoning at levels of abstraction that are just above reasoners’ current levels, alongside activities in which children reason with others.

Introduction

It is often argued that one of the most fundamental goals of education is to nurture critical thinking, that is, to teach children to employ good reasoning skills when developing their beliefs. Therefore, fostering logical reasoning should be an important goal for education: Children should learn to provide logical reasons for their opinions and should be able to distinguish between good and bad arguments. This is likely to be important for their effective exercise of citizenship as adults. For example, logical reasoning could tell you that it is unwarranted to conclude “All Muslims are terrorists” from the assertions “All the 9/11 perpetrators are Muslims” and “All the 9/11 perpetrators are terrorists.” Yet, many educated adults still draw such a conclusion, most likely because fear and bias can overcome rational thinking. This suggests that logical reasoning is hard even for educated adults, a conclusion that is supported by a wealth of psychological studies. Perhaps the most striking demonstration of the difficulty of logical reasoning was discovered by the psychologist Peter Wason in 1966 1 . Wason designed a task in which he presented participants with four playing cards, each with a letter on one side and a number on the other side. For example, the cards could be as follow:

A         B         2          3

Participants were then shown the conditional rule “If a card has the letter A on one side, then it has the number 2 on the other side.” The task consisted of selecting those cards that had to be turned over to discover whether the rule was true or false. Since Wason’s study, that task has been performed many times, and the results are always the same. Most people select either the A card alone or sometimes both the cards A and 2. However, very few adults, even highly educated, typically choose the 3 card. This is despite the fact that discovering what is on the other side of the 3 card is necessary to evaluate whether the rule is true or false (i.e., if there is an A on the other side of the 3, the rule is false). This reasoning failure has puzzled psychologists for decades because it questions the long-standing assumption that human beings are inherently rational. Why is it so hard for participants to select the 3 card? Neuroscience research suggests that it is because it is much more difficult for the brain to focus on the elements that are absent from the rule (e.g., 3) than on the elements that are present (e.g., A) 2 . Thus, selecting the 3 card requires much more extensive brain activation in several brain regions (primarily involved in attention and concentration) to overcome that tendency (see Figure 1). So, how can we get people to activate more of their reasoning brain and act more rationally on this task? One of the first ideas that comes to mind would be to teach them logic. Cheng and colleagues 3 have tested this. The researchers presented the Wason selection task to college students before and after they took a whole-semester introductory class in logic (about 40 hours of lectures). Surprisingly, they found no difference in the students’ poor performance between the beginning and the end of the semester. In other words, a whole semester of learning about logic did not help students make any less error on the task! What, then, can train the reasoning brain? To answer that question, it is interesting to turn to what we know about the development of logical reasoning in children.

Figure 1. The reasoning brain. Location of the brain regions (in red, blue, and white) that are activated when participants reason with elements that are not present in the rule in the Wason card task. Activations are displayed on pictures of the brain taken using a magnetic resonance imaging scanner. (Reproduced from Ref. 2 )

The development of concrete logical reasoning in children

It is clear that even young children can use some logical reasoning when concrete information is involved. For instance, most 6-year-olds can draw the conclusion “The person is hurt” from the statements “If the person breaks his arm, the person will be hurt” and “The person breaks his arm.” However, the reasoning abilities of young children are limited. For example, many 6-year-olds would also draw the conclusion “The person broke his arm” from the statements “If the person breaks his arm, the person will be hurt” and “The person is hurt.” This, however, is an invalid conclusion because there may be many other reasons why a person could be hurt. Children will progressively understand this and will make this type of reasoning error less and less as they get older. By the time they reach the end of elementary school, most children are able to refrain from concluding “The person broke his arm” from the statements “If the person breaks his arm, the person will be hurt” and “The person is hurt” 4 . Critically, this increased reasoning ability is mirrored by an increase in the ability to think about alternate causes for a given consequence. For example, older children are much more able than younger children to think about the many other reasons why someone would be hurt, like getting sick, breaking a leg, cutting a finger, etc. In other words, better reasoning ability with age is associated with a better ability to consider alternatives from stored knowledge. Clearly, however, children differ in terms of what they know about the world. This predicts that those who have better world knowledge and can think about more alternatives should be better reasoners than the others. And this is exactly what has been shown in several studies 4 .

Interestingly, the importance of world knowledge for reasoning has a paradoxical effect: It can make children poorer reasoners on some occasions. For example, children who can think about a lot of alternatives would be less inclined to draw the logically valid conclusion “The person will be tired” from the statements “If a person goes to sleep late, then he will be tired” and “The person goes to sleep late.” This is because a child with significant world knowledge can think of several circumstances that would make the conclusion unwarranted, such as waking up later the next day. Thus, more world knowledge needs to be associated with more ability to suppress the alternatives that might come to mind if the task requires it. This self-regulation ability relies on a part of the brain that also massively develops during childhood, i.e., the prefrontal cortex (see Figure 2). Overall, then, the development of concrete logical reasoning in children can be largely accounted for by the development of both world knowledge and self-regulation skills that are associated with the frontal cortex.

Figure 2. The prefrontal cortex. Location of the prefrontal cortex on a 3D rendering of the human brain. Polygon data were generated by Database Center for Life Science(DBCLS),  distributed under a CC-BY-SA-2.1-jp license.

From concrete to abstract reasoning

There is, however, an important difference between the reasoning skills described above and the task developed by Peter Wason about the four cards. What we just described relates to reasoning with very concrete information, whereas the card task involves reasoning with purely abstract information. Abstract reasoning is difficult because it requires one to manipulate information without any referent in the real world. Knowledge is of no help. In fact, neuroscience research indicates that abstract and concrete reasoning rely on two different parts of the brain 5 (see Figure 3). The ability to reason logically with an abstract premise is generally only found during late adolescence 4 . Transitioning from concrete to abstract reasoning may require extensive practice with concrete reasoning. With mastery, children may extract from the reasoning process abstract strategies that could be applied to abstract information. A recent study, however, suggests a trick to help facilitate this transition in children 6 . The researchers discovered that abstract reasoning in 12- to 15-year-olds is much improved when these adolescents are previously engaged in a task in which they have to reason with information that is concrete but empirically false, such as “If a shirt is rubbed with mud, then the shirt will be clean.” No such effect was observed when adolescents are asked to reason with concrete information that is empirically true, such as “If a shirt is washed with detergent, then the shirt will be clean.” Therefore, reasoning with information that contradicts what we know about the world might constitute an intermediary step in transitioning from concrete to abstract reasoning.

Figure 3. Brain regions activated when reasoning with concrete (left) and abstract (right) information. Activations are displayed on pictures of the brain taken using a magnetic resonance imaging scanner. (Reproduced from Ref. 5 )

What can we do to foster logical reasoning skills?

What, then, can we do to help foster the development of logical reasoning skills in children? The research described above suggests several potentially fruitful ways. First, it is clear that the development of concrete reasoning—the very first type of reasoning children can engage in—relies on an increased ability to think about counter-examples for a given statement. This implies that knowledge about the world is critical to the emergence of logical reasoning in children, at least when concrete information is involved. Therefore, all activities that would expand such world knowledge (e.g., reading informational books, learning new vocabulary, exploring new environments and places) are likely to be beneficial to the development of children’s reasoning skills. Second, it is important to consider that the more world knowledge a child possesses, the more he/she will need to juggle with this knowledge. For example, generating counter-examples when solving a reasoning problem will require maintaining pieces of information in memory for a short period of time, a type of memory called working memory . World knowledge can also sometimes be detrimental to reasoning and needs to be inhibited , such as when recognizing that the conclusion “The person will be tired” logically follows from the statements “If a person goes to sleep late, then he will be tired” and “The person goes to sleep late” (even if one might think of several conditions that would make the conclusion untrue based on what we know about the world). Fostering these types of self-regulation skills (working memory and inhibition) should thus be beneficial to the development of logical reasoning. Several studies suggest that these functions could be promoted by targeting children’s emotional and social development, such as in curricula involving social pretend play (requiring children to act out of character and adjusting to improvisation of others), self-discipline, orderliness, and meditation exercises 7 . Studies also indicate positive effects of various physical activities emphasizing self-control and mindfulness, such as yoga or traditional martial arts 7 . Third, studies indicate that the transition from concrete to abstract reasoning occurring around adolescence is challenging. Although more research is needed in this domain, one promising way to help this transition is by encouraging children’s thinking about alternatives with content that contradicts what they know about the world (e.g., “If a shirt is rubbed with mud, then the shirt will be clean”). In sum, as stated by Henry Markovits, “the best way to encourage the development of more abstract ways of logical reasoning is to gradually encourage both divergent thinking and reasoning at levels of abstraction that are just above reasoners’ current levels” 4 .

Fostering the development of logical reasoning should be an important goal of education. Yet, studies indicate that logical reasoning is hard even for educated adults and relies on the activation of an extensive network of brain regions. Neuroscience studies also demonstrate that reasoning with concrete information involves brain regions that qualitatively differ from those involved in reasoning with more abstract information, explaining why transitioning from concrete to abstract reasoning is challenging for children. We nonetheless reviewed here the more recent research on the development of reasoning skills and suggest several important factors that scaffold children’s reasoning abilities, such as world knowledge and self-regulation functions. On a final note, it is important to consider that logical reasoning is not something that we always do on our own, isolated from our peers. In fact, some have argued that the very function of reasoning is to argue with our peers (i.e., to find the best arguments to convince others and to evaluate arguments made by others) 8 . This idea is interesting from an educational point of view because it suggests that reasoning with others might be easier than reasoning in isolation—a hypothesis validated by several studies. For example, performance on the card task developed by Peter Wason is much higher when participants solve it as a group rather than alone 8 . Therefore, encouraging activities in which children reason with others might also be a fruitful avenue for stimulating the reasoning brain.

• Wason, P. C. Reasoning. In New Horizons in Psychology (ed. Foss, B. M.). (Penguin: Harmondsworth, 1966).
• Prado, J., & Noveck, I. A. Overcoming perceptual features in logical reasoning: A parametric functional magnetic resonance imaging study. J Cogn Neurosci . 19(4): 642-57 (2007).
• Cheng, P. W. et al. Pragmatic versus syntactic approaches to training deductive reasoning. Cogn Psychol . 18(3): 293-328 (1986).
• Markovits, H. How to develop a logical reasoner. In The Developmental Psychology of Reasoning and Decision-Making (ed. Markovits, H.) 148-164. (Psychology Press: Hove, UK, 2014).
• Goel, V. Anatomy of deductive reasoning. Trends Cogn. Sci. (Reg. Ed.) 11(10): 435-41 (2007).
• Markovits, H., & Lortie-Forgues, H. Conditional reasoning with false premises facilitates the transition between familiar and abstract reasoning. Child Development 82(2): 646-660 (2011).
• Diamond, A., & Lee, K. Interventions shown to aid executive function development in children 4 to 12 years old. Science 333(6045): 959-964 (2011).
• Mercier, H., & Sperber, D. Why do humans reason? Arguments for an argumentative theory. Behav Brain Sci . 34(2): 57-74; discussion 74-111 (2011).

All Courses

• Interview Questions
• Career Guide
• Success Stories
• PGP in Data Science and Business Analytics
• PG Program in Data Science and Business Analytics Classroom
• PGP in Data Science and Engineering (Data Science Specialization)
• PGP in Data Science and Engineering (Bootcamp)
• PGP in Data Science & Engineering (Data Engineering Specialization)
• Master of Data Science (Global) – Deakin University
• MIT Data Science and Machine Learning Course Online
• Master’s (MS) in Data Science Online Degree Programme
• MTech in Data Science & Machine Learning by PES University
• Data Analytics Essentials by UT Austin
• Data Science & Business Analytics Program by McCombs School of Business
• MTech In Big Data Analytics by SRM
• M.Tech in Data Engineering Specialization by SRM University
• M.Tech in Big Data Analytics by SRM University
• PG in AI & Machine Learning Course
• Weekend Classroom PG Program For AI & ML
• AI for Leaders & Managers (PG Certificate Course)
• Artificial Intelligence Course for School Students
• IIIT Delhi: PG Diploma in Artificial Intelligence
• Machine Learning PG Program
• MIT No-Code AI and Machine Learning Course
• Study Abroad: Masters Programs
• MS in Information Science: Machine Learning From University of Arizon
• SRM M Tech in AI and ML for Working Professionals Program
• UT Austin Artificial Intelligence (AI) for Leaders & Managers
• UT Austin Artificial Intelligence and Machine Learning Program Online
• MS in Machine Learning
• IIT Roorkee Full Stack Developer Course
• IIT Madras Blockchain Course (Online Software Engineering)
• IIIT Hyderabad Software Engg for Data Science Course (Comprehensive)
• IIIT Hyderabad Software Engg for Data Science Course (Accelerated)
• IIT Bombay UX Design Course – Online PG Certificate Program
• Online MCA Degree Course by JAIN (Deemed-to-be University)
• Cybersecurity PG Course
• Online Post Graduate Executive Management Program
• Product Management Course Online in India
• NUS Future Leadership Program for Business Managers and Leaders
• PES Executive MBA Degree Program for Working Professionals
• Online BBA Degree Course by JAIN (Deemed-to-be University)
• MBA in Digital Marketing or Data Science by JAIN (Deemed-to-be University)
• Master of Business Administration- Shiva Nadar University
• Post Graduate Diploma in Management (Online) by Great Lakes
• Online MBA Programs
• Cloud Computing PG Program by Great Lakes
• University Programs
• Stanford Design Thinking Course Online
• Design Thinking : From Insights to Viability
• PGP In Strategic Digital Marketing
• Post Graduate Diploma in Management
• Master of Business Administration Degree Program
• MS in Business Analytics in USA
• MS in Machine Learning in USA
• Study MBA in Germany at FOM University
• M.Sc in Big Data & Business Analytics in Germany
• Study MBA in USA at Walsh College
• MS Data Analytics
• MS Artificial Intelligence and Machine Learning
• MS in Data Analytics
• Master of Business Administration (MBA)
• MS in Information Science: Machine Learning
• MS in Machine Learning Online
• MIT Data Science Program
• AI For Leaders Course
• Data Science and Business Analytics Course
• Cyber Security Course
• PG Program Online Artificial Intelligence Machine Learning
• PG Program Online Cloud Computing Course
• Data Analytics Essentials Online Course
• MIT Programa Ciencia De Dados Machine Learning
• MIT Programa Ciencia De Datos Aprendizaje Automatico
• Program PG Ciencia Datos Analitica Empresarial Curso Online
• Mit Programa Ciencia De Datos Aprendizaje Automatico
• Online Data Science Business Analytics Course
• Online Ai Machine Learning Course
• Online Full Stack Software Development Course
• Online Cloud Computing Course
• Cybersecurity Course Online
• Online Data Analytics Essentials Course
• Ai for Business Leaders Course
• Mit Data Science Program
• No Code Artificial Intelligence Machine Learning Program
• MS Information Science Machine Learning University Arizona
• Wharton Online Advanced Digital Marketing Program
• What is logical thinking?
• How can you build logical thinking skills?

What is Logical thinking?

Logical thinking can also be defined as the act of analysing a situation and coming up with a sensible solution. It is similar to critical thinking. Logical thinking uses reasoning skills to objectively study any problem, which helps make a rational conclusion about how to proceed. For example, you are facing a problem in the office, to address that, you use the available facts, you are using logical reasoning skills.

In this write-up, we will explore tips on how you can improve your logical thinking skills and the reasons why logical thinking can help you be a stronger professional.

Now the question arises in our mind, why are logical thinking skills important?

Also Read – What is Empathy in Design Thinking?

Logical thinking skills play a very important and necessary role in developing your career because they can help you reason through important decisions, solve problems, generate creative ideas, and set goals. Whether you want to advance your career or have just entered the industry, you will encounter challenges daily that require logical reasoning skills. The stronger your logical thinking skills are, the more easily you will be able to come up with solutions and plans that can benefit you and your workplace.

There are many ways in which you can strengthen logical thinking in your daily work.

Methods that help you in developing your logical thinking skills are :

• Spend time on creative hobbies.
• Practice questioning.
• Socializing with others.
• Learn a new skill.

1. Spending time on creative hobbies

It has been observed that creative hobbies like drawing, painting, writing, or playing music can stimulate the brain and help promote logical thinking. Creative thinking, in a way, naturally develops problem-solving abilities that can help you become a better performer at your workplace.

Let’s talk about one more example, learning a new instrument requires deep thought and concentration. The logical thinking skills that you will gain from the process of learning a new instrument can help you approach your work more intently, developing your ability to solve problems with more flexibility and ease.

In addition to this, creative hobbies also help reduce stress. When your stress levels are manageable, you will have an easier time focusing and making logical decisions wherever required. There are many different ways in which you can handle stress, but developing a creative mind is especially productive and can help you bolster both personal and professional life.

2. Practice questioning

Another best way to strengthen your logical thinking skills is to question things that you typically accept as fact. When you regularly ask the question, it helps you view situations more completely and intricately, allowing you to approach problems at work more logically and creatively.

Asking more and more questions often leads to discoveries about topics you had not considered before, which may encourage you to explore further. This method can be used anywhere, especially at work. Let us take an example of a department at your workplace you are not familiar with. Create a list of questions where you need clarity or understanding. This will help you understand its purpose.

Let us take an example. If you work in the sales-marketing department and want to know more about search engine optimization skills , consider asking someone in that department for an overview to learn more about their current projects and processes. This will help you think more critically about the role you would be taking at work as it relates to that team.

3. Socialize with others

Socializing and building relationships with others help you broaden your perspective, giving you more opportunities to develop your logical thinking skills. When you get to know the point of view of other people, it helps you approach problems at work in a new and different way.

There are many ways in which you can invest time in building relationships. It can be from participating in an activity to simply eating lunch or meeting over coffee together regularly. It is truly said that the more logically you can handle problems at work, the more easily you will be able to advance in your career.

4. Learn a new skill

Learning a new skill can also help in sharpening logical skills.

If you take the opportunity to learn as often as possible, you apply the same level of thinking to your job, making you successful.

For example, suppose you decide to start learning a new coding language. This process will require careful thinking and planning. Practicing every day will help to put you in the mindset of thoughtfully approaching problems at work and will also help you develop a new skill that will help you advance your career.

5. Anticipating the outcome of your decisions

When you are working to strengthen your logical thinking skills, it is helpful for you to consider what impact your decisions might have in the future. The closer you pay attention to the results of your decisions and analyze them, the easier the process will become.

Whenever you come up with a solution to a problem at the workplace, try to think about what the outcome may be. Slowly and eventually, you will find it easier to think of your decisions’ immediate and long-term results. This is an important aspect of logical thinking.

Logical skills can be easily strengthened with daily practice. When you start applying these exercises regularly, and by learn more from professional courses you will observe yourself start to naturally approach everyday decisions at work with a more logical perspective.

Top Free Courses

How to Answer ‘Reason for a Job Change’

Best Career Options After 12th Commerce

Career Options after 12th Arts

WES Evaluation for Indian Students: A Complete Guide

Top 25 Highest Paying Jobs In India

Career Objective for Resume for Freshers (with Examples)

Leave a comment cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Table of contents

Teaching Logic to Elementary Students – The Why and How

Logic is the beginning of wisdom, not the end – Leonard Nimoy

Logic, can it be taught? Or is it something that is naturally instilled? Actually, it can be taught! Breathe a sigh of relief. It is one of the most important skills to teach in elementary grades because it is a foundational critical thinking skill.  Teaching logic to elementary students requires the use of reasoning and deduction to study a problem objectively, thereby allowing you to make a rational conclusion. As a teacher, you use logic all the time when you analyze the facts to address a problem. Logic prepares students for life. It equips them with the reasoning skills needed to navigate the sticky situations of life. And it starts right in your classroom.

What is logic? What are its benefits?

In a nutshell, logic is the science of reasoning that allows you to determine a possible outcome or best choice. Not only is it a crucial skill for real-life application, but it is equally important inside the classroom. There are many benefits to teaching logic to elementary students. First, logic empowers and enables students with the ability to take what information they are given and build upon it. Second, it is the cornerstone of math. Lastly, logical reasoning encourages students to think for themselves, experiment, and even ask the big, out-of-the-box questions.

Activities for the Classroom

The best part of teaching logic in the classroom is that it doesn’t have to be boring! There are so many interactive puzzles, games , and activities to keep students engaged and plugged in. Some of my personal favorites include Magic Squares, Sudoku, analogies, matrix logic puzzles, and Which One Doesn’t Belong? puzzlers. Students love solving these types of puzzles and don’t even realize they are creating and forming new reasoning skills.  There are a few tips I have for incorporating logic into your instruction.

• Ask “why?” frequently. Teach your students to think for themselves, and not always accept everything they hear at face value. Help them learn how to apply reasoning and proof to their thinking. Answering “why” questions will help students think through the logic they used to solve a problem or come to a conclusion. Help them learn to justify their answers.
• Use a structured, intentional approach.  Make it a part of your daily schedule and make it FUN! Students need time to practice it. Help your students to understand the power of thinking and want to get better at it.
• Play games that encourage the use of strategy and logical thinking. There are a plethora of fun games that will help kids develop their logical reasoning skills. Remember the game Battleship we all played as kids? These activities may be used with the whole group in the morning as a daily challenge, in small groups, or in a math center. They are great for early finishers!

How to incorporate it into Classroom Instruction  

While logic is an important foundational math skill, it can be taught across any subject. Logical reasoning can be incorporated into ELA, Science, or even Social Studies. It can become a part of morning meetings where you project a logic puzzle.  For example, you can give the kiddos a picture of four things, like a football, a baseball, a basketball, and a tennis ball.  Ask them “ Which One Doesn’t Belong?”  Now the fun begins, because there is no one right answer.  A football is the only ball that isn’t round, and a baseball is the only one that is not filled with air.  What’s really cool is that your kids might create reasons you hadn’t even thought of.

These types of puzzles make for great discussions. To even bump it up a bit more, you can use four seemingly unrelated objects like a pencil, a shovel, a blow dryer, and a stuffed animal.  You will be surprised at the reasoning the kids use to decide which one doesn’t belong.  The key here is that the reasoning determines whether or not the answer is correct. If the reasoning is logical, the answer is correct.   

Although there are many types of logic puzzles, the important thing is to present them in a way that challenges your kids and keeps them engaged. You can have your students work independently or in pairs when teaching logic to elementary students. Logic puzzles are also a great alternative activity for your early finishers.

My Favorite Logic Resources

I love incorporating critical thinking into any season or event. I’ve created logic puzzles to keep your students engaged and thinking every season.

 First, w ith these Winter Logic Puzzles , students can strengthen and develop problem-solving skills as well as making inferences, drawing conclusions, and even comparing and contrasting. Use during centers, as morning warm-up activities, or assign to fast finishers. There is also a Digital Version for those who are teaching remotely. This puzzle resource is perfect for grades K-2. For other winter lessons, check out this blog post . 

Second, your students will love catching a leprechaun using this St. Patrick’s Day Logic Puzzle Resource. Students will strengthen both reading and math skills as well as develop logical thinking. Print and laminate for fun themed centers! Available in both color and black and white. I digital version will be added in February. 

Lastly, for students finishing early or those who have previously mastered basic and addition and subtraction, these Spring Themed Math Puzzles are on target! This resource contains 24 addition and subtraction logic puzzle task cards to help your students become effective problem solvers by combining math with deductive reasoning. Challenge your students in an interactive way! They will love it.

Critical Thinking is Essential in the Classroom

Critical thinking Activities can be easily strengthened with daily practice. When you teach students how to apply these exercises regularly, you will start to witness how they naturally approach everyday decisions with a more logical perspective. When students grow up and face real-world problems, they will be better equipped to solve them if they have strong critical thinking and problem-solving skills. They will be ready to think outside the box . Which activity will you choose?! 

You can get a sample freebie logic activity when you subscribe to my email list below. If you do not want to miss any of the upcoming lessons! You can join my email list to be notified of all the interactive lessons coming up! By joining the email list, you will also receive freebies for exclusive email subscribers!  

PIN IT FOR LATER

• Read more about: Critical Thinking , Math , Student Achievement , Thinking Skills

You might also like...

4 Engaging Reading Interventions All Your Students Will Love

 7 Captivating Poem of the Week Activities that Build Fluency and Comprehension

Math Menus: 4 Powerful Ways to Marry Creativity and Math

Search the Blog

Browse by category.

Logic and Teaching–Learning Strategy

• First Online: 17 July 2018

Cite this chapter

• Siddheshwar Rameshwar Bhatt 2  

284 Accesses

This chapter deals with logic and teaching–learning strategy. It emphasizes the role of logical order in teaching and learning. It expounds different issues relating to logic in the field of education. It highlights the role of logical operations in teaching–learning strategy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as EPUB and PDF
• Read on any device
• Instant download
• Own it forever
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Komisar, B. P. (1966). Needs and the needs-curriculum. In B. O. Smith & R. H. Ennis (Eds.), Language and concepts in education . Chicago: Rand McNally.

Google Scholar  

Peters, R. S. (1967). The concept of education . London: Routledge and Kegan Paul.

Scheffler, I. (1960). The language of education . Springfield, IL: Thomas.

Smith, B. O., & Ennis, R. H. (Eds.). (1966). Language and concepts in education . Rand McNally, Chicago.

Download references

Author information

Authors and affiliations.

Indian Council of Philosophical Research, Ministry of Human Resource Development, New Delhi, Delhi, India

Siddheshwar Rameshwar Bhatt ( Chairman )

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Siddheshwar Rameshwar Bhatt .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Bhatt, S.R. (2018). Logic and Teaching–Learning Strategy. In: Philosophical Foundations of Education. Springer, Singapore. https://doi.org/10.1007/978-981-13-0442-2_6

Download citation

DOI : https://doi.org/10.1007/978-981-13-0442-2_6

Published : 17 July 2018

Publisher Name : Springer, Singapore

Print ISBN : 978-981-13-0441-5

Online ISBN : 978-981-13-0442-2

eBook Packages : Education Education (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

What Is Logical Thinking? 6 Types; 4 Exercises to Improve It

• Cognitive Skills and Study Methods
• Susan du Plessis
• May 21, 2023

You have four blocks in front of you, a black one, a red one, a white one and a green one. You must remove two of them. You may not take away the red, the black and the white blocks simultaneously. You may not take away the white, the green and the red ones simultaneously. Which two blocks may be removed? To answer this puzzle, you will need to think logically.

What is logical thinking.

Logical thinking is the process in which one uses reasoning consistently to come to a conclusion. Synonyms are logical reasoning, reasoning skills and reasoning ability.

Problems or situations involving logical thinking call for structure, relationships between facts, and chains of reasoning that “make sense.”

In his book Brain Building , Dr. Karl Albrecht says that the basis of all logical thinking is sequential thought . This process involves taking the important ideas, facts, and conclusions in a problem and arranging them in a chain-like progression that takes on a meaning in and of itself. To think logically is to think in steps.

6 Types of logical thinking

In logic, there are two broad methods of concluding: deductive reasoning  and  inductive reasoning.

• Deductive reasoning  begins with a broad truth (the major premise), such as the statement that all men are mortal. This is followed by the minor premise, a more specific statement, such as that Socrates is a man. A conclusion follows: Socrates is mortal. . The conclusion cannot be false if both the major and minor premises are true. .
• In  inductive reasoning , broad conclusions are drawn from specific observations; data leads to conclusions. If the data shows a tangible pattern, it will support a hypothesis. For example, having seen ten white swans, we could use inductive reasoning to conclude that all swans are white. . This hypothesis is easier to disprove than to prove, and the premises are not necessarily true, but they are true given the existing evidence and given that one cannot find a situation in which it is not true. .
• Linear reasoning is a systematic and analytical thought process that follows a known step-by-step progression similar to a straight line. Linear reasoning is the thinking traditionally linked to intelligence and is present when you solve mathematical problems. It is typical for learning at school. .
• Conditional reasoning  uses if-then statements that are true to form a true conclusion. The conclusion can be either valid or invalid, even though the premises are true. .
• Cause-and-effect reasoning generally occurs when people naturally want to know the reasons behind anything that happened. This search often results in cause-and-effect reasoning, which asserts or denies that one thing causes another, or that one thing is caused by another. .
• Analogical reasoning can be defined as a specific way of thinking based on the idea that because two or more things are similar in some respecs, they are probably also similar in some further respect. . A strong analogy has nontrivial ,  causally connected , or otherwise relevant  similarities between its  source and target domains . For example ( Study.com ): str

Eating too much refined sugar is analogous to smoking cigarettes. Just like cigarettes, refined sugar is unnecessary for optimal functioning and eventually leads to poorer health outcomes. This analogy is nontrivial because refined sugar differs from cigarettes in many respects. The conclusion “leads to poorer health outcomes” is relevant because the same mechanism (consumption of either sugar or cigarettes) is what causes the outcome. .

Importance of logical thinking for students

Logical thinking skills allow learners to understand what they have read or been shown and build upon that knowledge without incremental guidance. Logical thinking teaches students that knowledge is fluid and builds upon itself.

The relationship between logical reasoning and reading is well established in the literature. It has been said that “there is no reading without reasoning,” and even that reading is  reasoning.

Logical reasoning is also an important foundational skill of math .“Learning mathematics is a highly sequential process,” says Dr. Albrecht. “If you don’t grasp a certain concept, fact, or procedure, you can never hope to grasp others that come later, which depend upon it. For example, to understand fractions, you must first understand division. Likewise, understanding simple algebra equations requires that you understand fractions. Solving word problems depends on knowing how to set up and manipulate equations, and so on.”

A study by  Bhat  (2016) examined the contribution of six components of reasoning ability (inductive reasoning, deductive reasoning, linear reasoning, conditional reasoning, cause-and-effect reasoning, and analogical reasoning) to explain the variation in the academic achievement of 598 class 10th students. The predictive power of various components of reasoning ability for academic achievement was 31.5%.

It has been proven that specific training in logical reasoning can make people “smarter.” Logical thinking allows a child to reject quick answers, such as “I don’t know,” or “this is too difficult,” by empowering them to delve deeper into their thinking processes and understand better the methods used to arrive at a solution and even the solution itself.

Training in logical thinking encourages learners to think for themselves, to question hypotheses, to develop alternative hypotheses, and to test those hypotheses against known facts.

A learned mental process

Reasoning ability is not a magical process or a matter of genetic endowment but a learned mental process. Training in logical thinking encourages students to think for themselves, question hypotheses, develop alternative hypotheses, and test those hypotheses against known facts.

When doing cognitive skills training, it is essential to note that such training should be  multi-cognitive.  In physical training, a balanced workout is vital as overtraining one part of the body can cause deformity, such as Popeye syndrome when overtraining the biceps.

The brain is no different. For example, in  Maguire et al.’s experiment with London taxi drivers , growth in the posterior hippocampi seems to have come at a cost, as they had reduced  anterior  hippocampal gray matter volume compared with bus drivers, with anterior volume decreasing with more navigation experience ( Maguire et al., 2006 ).

One should also consider the role of  mutualism.  A mutualistic view suggests that cognitive abilities mutually facilitate growth. For example, better reasoning skills allow individuals to improve their vocabulary more quickly, and better vocabulary is associated with faster improvement in reasoning ability ( Kievit et al., 2017 ).

Therefore, in addition to doing Edublox’s  Development Tutor program four to five times a week for 15-20 minutes per session, the following exercise can be done for 4-5 minutes: .

• Logical thinking exercise with objects .
• Logical thinking exercise with letters .
• Logical thinking exercise with numbers .
• Logical thinking exercises for advanced learners . .

Aside from food, water, and shelter, the one thing that a person will most need in life is an education. Of those four necessities, education is the only one that can help ensure a person’s consistent ability to provide himself or herself with the other three. Unfortunately, the importance of logical thinking skills is underestimated in education, and training in reasoning ability is therefore grossly neglected. .

. Edublox offers cognitive training and live online tutoring to students with dyslexia, dysgraphia, dyscalculia, and other learning disabilities. Our students are in the United States, Canada, Australia, and elsewhere.  Book a free consultation  to discuss your child’s learning needs. .

• Products & Pricing
• Testimonials
• Privacy Policy

• Table of Contents
• Random Entry
• Chronological
• Editorial Information
• About the SEP
• Editorial Board
• How to Cite the SEP
• Special Characters
• Advanced Tools
• Support the SEP
• PDFs for SEP Friends
• Make a Donation
• SEPIA for Libraries
• Entry Contents

Bibliography

Academic tools.

• Friends PDF Preview
• Author and Citation Info
• Back to Top

Logical Empiricism

Logical empiricism is a philosophic movement rather than a set of doctrines, and it flourished in the 1920s and 30s in several centers in Europe and in the 40s and 50s in the United States. It had several different leaders whose views changed considerably over time. Moreover, these thinkers differed from one another, often sharply. Because logical empiricism is here construed as a movement rather than as doctrine, there is probably no important position that all logical empiricists shared—including, surprisingly enough, empiricism. And while most participants in the movement were empiricists of one form or another, they disagreed on what the best form of empiricism was and on the cognitive status of empiricism. What held the group together was a common concern for scientific methodology and the important role that science could play in reshaping society. Within that scientific methodology the logical empiricists wanted to find a natural and important role for logic and mathematics and to find an understanding of philosophy according to which it was part of the scientific enterprise.

The following discussion of logical empiricism is organized under five headings:

1. Mapping the Movement

2. background, 3. some major participants in the movement, 4.1 empiricism, verificationism, and anti-metaphysics, 4.2 analyticity, 4.3 unity of science and reduction, 4.4 probability, other internet resources, related entries.

The term ‘logical empiricism’ has no very precise boundaries and still less that distinguishes it from ‘logical positivism’. It is therefore hard to map. ‘Logical empiricism’ here includes three groups: (1) the Vienna Circle, here taken broadly to include those who were part of various private discussion groups, especially that around Moritz Schlick, and also the members of the more public Ernst Mach Society (Verein Ernst Mach), (2) the smaller, but perhaps more influential Berlin Society for Empirical Philosophy (later called the Berlin Society for Scientific Philosophy), and (3) those influenced by or who interacted with members of the first two groups and shared an intellectual kinship with them. Besides Vienna and Berlin, there were important centers of the movement in England, France, Scandinavia, at several universities in the U.S., and even China. This characterization includes thinkers who disagreed with doctrines espoused by members of the original groups and even some who defined themselves in opposition to the movement. This results in a vague boundary, but it suffices to identify a movement in which a large number of able philosophers self-consciously participated and to distinguish logical empiricism from other movements.

It does not, however, distinguish logical empiricism from logical positivism, and it is doubtful that any principled such boundary can be drawn along doctrinal or sociological lines (Uebel 2013). Usually when distinctions are drawn, ‘logical empiricism’ is the wider term. Members of the Berlin group never used the term ‘positivism’ about themselves, but did use it concerning some unnamed Viennese in stressing their differences from the latter. In any case, these differences, even if real, were smaller than the differences within the Vienna Circle on one hand or within the Berlin group on the other. ‘Positivist’ is a term usually applied by opponents of various doctrines. It was used by some of the Viennese logical empiricists about themselves but generally with caution and in stressing the differences between their own views and those of the 19 th century positivists. The one philosopher who would have unhesitatingly described himself as (having been) a logical positivist was A.J. Ayer.

Another way of mapping the boundaries of logical empiricism is to list the specific philosophers who were centrally or peripherally part of it. This included many of the most important philosophers of the mid-twentieth century. Hans Hahn, Moritz Schlick, Rudolf Carnap, and Otto Neurath were leaders of the Vienna Circle, and Kurt Gödel regularly attended its meetings. The list of its members, visitors, and interlocutors is staggering, including A.J. Ayer, Herbert Feigl, Philipp Frank, Hans Hahn, Carl Hempel, Karl Menger, Richard von Mises, Ernest Nagel, Karl Popper, W.V. Quine, Frank Ramsay, Hans Reichenbach, Alfred Tarski, Friedrich Waismann, and Ludwig Wittgenstein, among many others. Not all of these would admit to being part of the logical empiricist movement, of course, but a case can be made that all contributed to it. The Berlin Society for Empirical (or Scientific) Philosophy was, as stated, smaller but perhaps more influential. Led by Hans Reichenbach, it included Kurt Grelling, Walter Dubislav, Kurt Lewin, Richard von Mises, Paul Oppenheim, and others. Hempel took his doctorate in Berlin, working with Reichenbach until the latter was forced to leave in 1933. Hempel also spent time in Vienna and Prague. Of course, among the foremost associates of the Berlin Society was Albert Einstein, who was also in Berlin also until 1933.

There was also an important group of logicians in Warsaw of which Alfred Tarski is the best known. Tarski interacted significantly with the logical empiricists in Vienna, Berlin, and the U.S., but it is more reasonable to classify the Polish logicians as an allied group rather than include them within the logical empiricist movement.

Because of the catastrophic dislocations of Europe in the 1930s, the main focus of the logical empiricism moved from central Europe to America by the close of that decade. Erkenntnis , the main journal of the movement, which had been edited by Reichenbach and Carnap, ceased publication by 1940. In 1930 Feigl moved to the U.S., and Carnap moved to Chicago in 1936. Hempel came to Chicago and Menger to Notre Dame in 1937. The ensuing years witnessed a massive exodus to America from central Europe. Reichenbach arrived in the U.S. in 1938 after five years in Turkey. Also in 1938 Gustav Bergmann and Philipp Frank emigrated. Edgar Zilsel came in 1939. Alfred Tarski was on a visit to the U.S. when Poland was invaded in 1939, and so he stayed. And by 1940 Richard von Mises was also in America.

In the U.S., these exiles were joined by the Americans Nelson Goodman, Charles Morris, W.V. Quine, Ernest Nagel, and, after the war, by Reichenbach’s UCLA students Hilary Putnam and Wesley Salmon. Adolf Grünbaum can also be considered as clearly in the Reichenbach lineage. And Wilfrid Sellars was, in his early years, a close associate of Feigl. The American incarnation of the logical empiricist movement enjoyed generally good relations with the American pragmatists, not only because many of the logical empiricists had a strong pragmatist component to their philosophy, but also because the pragmatists and logical empiricists shared a common concern for empirical methodology in the service of social reform. Institutionally, the movement was represented in most major American universities, and such journals as Philosophy of Science (with Carnap and Feigl on the Editorial Board and Reichenbach and Schlick on the Advisory Board) and Philosophical Studies (founded and edited for many years by Feigl and Sellars) provided ample outlet for their publications. In addition, the Inter-Scientific Discussion Group was founded by Philipp Frank at Harvard. That grew into the Institute for the Unity of Science, called by some the Vienna Circle in exile. Meanwhile in Chicago the Encyclopedia of Unified Science was established with Neurath, Carnap, and Morris as its editors.

But even from late 30s onward the movement was hardly limited to America. Ayer remained in England. Wittgenstein returned to Cambridge in 1929, but with regular visits to Vienna, including those on which he discussed issues surrounding a strong version of verificationism with Schlick and Waismann. Popper fled to New Zealand in 1937, and in 1946 moved to the London School of Economics. Neurath fled from Vienna to the Hague and then again in 1940 to England, where he remained till his death in 1945. Friedrich Waismann went to England in 1937. In 1939 Rose Rand, a less well-known member of the Vienna Circle, fled to England and then in 1954 emigrated once more to the U.S. There were like-minded thinkers in Scandinavia (such as Jørgen Jørgensen, Eino Kaila, and Arne Naess) and as far away as Argentina (H.A. Lindemann) and China (Tscha Hung).

It is impossible to say when logical empiricism ceased to be sufficiently cohesive to be identifiable as a continuing movement. Certainly by 1960 a great many philosophers, including many who had earlier clearly been part of the movement, were identifying themselves in opposition to what they took to be logical empiricism. And some members simply changed their minds or pursued different projects. Logical empiricism probably never commanded the assent of the majority of philosophers in either Europe or America, and by 1970 the movement was pretty clearly over—though with lasting influence whether recognized or not. In the 1980s there was a resurgence of historical interest in logical empiricism. That historical interest continues to clear away many of the caricatures and misconceptions about the logical empiricists. Among the major results of this work is the recognition of the tremendous variety and subtlety of views represented within the movement and the fact that many of the arguments later deployed by critics of logical empiricism had been pioneered by the logical empiricists themselves.

Given the emphasis on science and its technical apparatus, social renewal, clarity and rationality of belief, functionality, and above all the palpable sense of doing philosophy in an importantly new way, it is reasonable to associate logical empiricism with other forms of European modernism in the 1920s and 30s, such as Neue Sachlichkeit in art and the Bauhaus in architecture and design, and with mid-century modernism as well as with political liberalism, from the New Deal to the Great Society in the United States. There have been recognizably modernist developments in various fields including philosophy for centuries.

With a movement as large and complex as logical empiricism a great many factors went into raising the questions it would address, making them seem urgent, and making it seem as though the intellectual resources it would need to address these questions were either at hand or could be developed.

One long-term process with profound implications was the steady departure of the various sciences from philosophy to form autonomous disciplines. By early in the twentieth century mathematics, physics, chemistry, biology, and the social sciences were all pursued professionally and independently from philosophy. And psychology was just separating from philosophy. Yes, there were polymaths who could and did pursue a science and philosophy professionally. Those were increasingly rare, though single-discipline scientists did from time to time make philosophic-seeming pronouncements. But they did so from outside the field. This pattern of steady departures raised the pressing question: What sort of thing remained behind? Once mathematics and the empirical sciences all left, what was left for philosophy?

The nature of philosophy was always a vexed philosophic question, but now it was particularly insistent. Surely there was no domain of empirical facts that philosophy could call its own. All that real estate had been parceled out. One answer available at the time that logical empiricism flourished was that the genuinely philosophic remainder after the departure of the sciences is somehow deeper than the empirical sciences and gets at matters, perhaps cultural ones, that are more profound and important than anything that empirical science even can address. This is either because on this conception philosophy has a mode of access or “evidence” that the empirical sciences do not and cannot have, or because the very idea of fidelity to evidence and punctilious argument is somehow small-minded.

The logical empiricists found this answer unappealing. Indeed, this conception of philosophy is precisely what Carnap means by ‘metaphysics’. (As a consequence, what Carnap meant by that word is different from what late twentieth and early twenty-first century philosophers generally mean in describing their own work as analytic metaphysics.) The logical empiricists were eager to conceive of their enterprise as scientific and to engage in philosophy only insofar as it was also scientific. This science need not be empirical and need not include all that was traditional in philosophy that had not been incorporated into the independent sciences. The decision to be scientific can hardly be the end of the story. It requires rather better and more detailed answers to questions about what scientific methods are, how the mathematical (and other apparently non-empirical sciences) fit together with the empirical ones, and what, more precisely, philosophy’s role was.

A second series of developments that raised questions for logical empiricism to address were developments in the sciences themselves, especially the rise of non-Euclidean geometries in mathematics and the establishment of relativity theory in physics. These posed a serious challenge to what would otherwise be an attractive scientific philosophy, namely some version of Kantianism. Kant had recognized that the best of modern science was often mathematical in character and had labored to integrate both geometry and arithmetic into our empirical picture of the world. He had held that we could not represent the world except as a Euclidean structure and hence Euclidean geometry was, a priori, a permanent feature of any future physics. The demonstration that non-Euclidean pure geometrical structures were as consistent as Euclidean ones and that spaces can indeed be represented as a non-Euclidean manifolds was one half of the problem. The other half came when Einstein argued convincingly that physical space was best described as a non-Euclidean manifold of non-constant curvature. Plainly Euclidean geometry could not be guaranteed a future physics. Modern mathematical logic also posed a problem for other Kantian claims, but not in the same wrenching way.

Many logical empiricists started out as neo-Kantians: Reichenbach, Carnap, Schlick, and even Hempel (until he studied with Reichenbach, who by that time had revised his view). The difficulties with geometry and relativity certainly do not refute all forms of neo-Kantianism, but the difficulties are quite real nonetheless. The need is to understand how mathematics can be integrated into what is otherwise an empirical enterprise, i.e., physics, chemistry, biology, etc. Addressing this need was to be a major part of the logical empiricist program.

The background of logical empiricism described so far has been confined to the academic world, but events outside that domain shaped the movement as well. World War I was an unmitigated disaster for central Europe, followed by economic turmoil in the 20s and political upheavals of the 30s. It is hard to exaggerate these changes. Monarchies that had stood for centuries disappeared overnight and their empires disintegrated. This level of political convulsion had not been seen since the French Revolution, and that earlier upheaval was comparatively confined. Cultural changes were equally profound, and these were reflected by radical departures in the arts such as painting, music, and architecture, and even more importantly in new modes of living.

The logical empiricists were no mere bystanders. They, or at least the main leaders of the movement, were politically and culturally engaged. Even more important, this engagement was accompanied by the conviction that their cultures were incapable of the necessary reform and renewal because people were in effect enslaved by unscientific, metaphysical ways of thinking. Such ways of thinking might be exemplified in theology, in the racial hatreds of the day, in conceptions of property, and in traditional ideas about the “proper” roles of men and women in society. So to articulate a “scientific world conception” and to defend it against metaphysics was not just to express an academic position in the narrow sense. It was a political act as well; it was to strike a blow for the liberation of the mind. To articulate scientific methods and a scientific conception of philosophy was the essential first step in the reform of society and in the emancipation of humankind (Carnap 1958/2017, Creath 2009, Uebel 2012.

If all of this sounds like something out of the 18 th century Enlightenment, the analogy was not lost on the logical empiricists themselves. André Carus has argued that this is exactly what Carnap had in mind by “explication” (Carus 2007). Neurath frequently drew parallels between the logical empiricists’ anti-metaphysical program and the earlier Enlightenment ambitions. Certainly Kant had inveighed against the metaphysics of his time, and the anti-metaphysical tradition remained strong within the scientific community through the 19 th century.

The point so far was not to ask whether the logical empiricists were right in any of this. That question will come up later. So far the issue has been only to see the motivations that the logical empiricists had—and from their point of view—for addressing certain questions and for thinking that answers to those questions were urgently needed. None of this, however, says why the logical empiricists thought they had or could have the means to answer these questions. To that we now turn.

Since Newton the most paradigmatic examples of empirical science were those claims, usually quantitative ones, that were properly inferred from or appropriately confirmed by experience. Speaking very informally, these are the ones that we have good reason to believe or at least better reason to believe than the available alternatives. The problem, of course, is to specify the form of proper inferences, the form of an appropriate confirmation relation, and/or the structure of good reasons. The task is daunting, but logic in a suitably broad sense seems to be the right tool. Still speaking informally, logic seems to give us the structure of (good) reasoning. There are other conceptions of logic, of course, but this is a standard one and pretty well describes what the movement needed.

If logic was the tool that was wanted, it was newly ready for service. The progress of modern mathematical logic from Bolzano through Russell and beyond was truly impressive. Arguably, it could now express all parts of classical mathematics. Besides the first order predicate calculus one would need either set theory or higher order logic, but these were recent developments as well. Logic, like the empirical sciences, was progressive and could be approached cooperatively by more than one investigator. In Our Knowledge of the External World (1914) Russell had even positioned logic as the locus of scientific method in philosophy. It is small wonder then that those who were looking for something scientific in what was left of philosophy turned to logic. Wittgenstein’s no-content theory of logic in the Tractatus (1921/1922) was tantalizingly suggestive about how mathematics could be integrated into an overall empirical theory of the world. Wittgenstein also expressed a radical verificationism in the early 1930s in his conversations with Schlick, Waismann, and other members of the Vienna Circle. Many of the logical empiricists in turn could see in some version of that verificationism the ideal tool with which to carry out their anti-metaphysical program. There was, naturally, much left to accomplish, but even with Gödel’s results one could expect that further impressive strides in logic could be made. Indeed, much was accomplished even if the perfect account of scientific reasoning proved elusive. Perfection is elusive in all the sciences, but that is no reason for despair.

The logical empiricist movement is the sum of the interwoven trajectories of its members, so one way of describing that movement is to trace those various trajectories. To do so in detail for all those involved would take rather longer than the movement lasted. That would be inappropriate for one entry in an encyclopedia, especially one in which entries for many of the members will appear independently. The thumbnail sketches of the work of some representative figures below show the breadth and international character of the movement. While the list is long, it covers only a small fraction of those involved and leaves out many important thinkers.

It is not possible in an essay of this scope to trace all the issues that the logical empiricists addressed or even to treat any one of them with completeness. What is possible is to highlight some salient issues, clear away some misconceptions about them, and sketch a bit how those issues were developed over time. The first is a related set of concerns: empiricism, verificationism, and anti-metaphysics. The second is the logical empiricists’ treatment of logic and mathematics as analytic. Third is the related issues of the unity of science and reduction. And finally, comes the issue of probability. Given what has already been said, the reader should be aware that none of the doctrines discussed below was shared by all members of the logical empiricist movement.

Since antiquity the idea that natural science rests importantly on experience has been non-controversial. The only real questions about the sources of scientific knowledge are: Are there parts of science that do not rest on experience or rest also on something other than experience? If so what account can we give of those parts? And to the extent that science does rest on experience how can we know that it does? There is another question about science related to these, though not strictly about the sources of science, and that is: Why, in making claims about the world, should we be scientific as opposed to, say, mystical? The difficulty is that any scientific answer to this last question would reasonably be thought to beg the very question it purports to address.

Long before the twentieth century the prevailing opinion was that Euclidean geometry, standard mathematics, and logic did not rest on experience in any obvious way. They were largely presupposed in our empirical work, and it was difficult to see what if anything might disconfirm them. Geometry was a special case and might be handled in different ways that we shall not discuss here. That leaves logic and mathematics.

If Frege and Russell were right, then mathematics could be thought of as expressing no more than logical truths and handled in whatever way logic was to be treated. For Frege both mathematics and logic were analytic, but that, even if true, does not provide the needed answers. Wittgenstein’s no-content theory of logic suggested that all of the real claims, the ones that had genuine content, could be appropriately supported by experience, and the logical and hence mathematical claims had no content to support. This seemed to open the way for a thoroughgoing empiricism in which the logical and mathematical fit in with the ordinary claims of physics and biology in a harmonious way. The next subsection about analyticity discusses the question of whether the needed distinctions can be drawn.

In developing his theory of types Russell said in effect that some expressions that seem to be sentences in fact say nothing at all. This is because, despite appearances, they are not grammatically well formed. Wittgenstein found this suggestive. In the Tractatus he suggested that much else was nonsense as well including traditional metaphysics and supposed claims about the “higher”. When in late 1929 Wittgenstein proposed (Waismann 1967/1979), in conversations with Schlick and Waismann, a strict verificationism as a basis for identifying the legitimate parts of discourse, this seemed to the logical empiricists to be a very attractive tool for setting aside the unscientific parts of philosophy.

This does not mean, however, that all logical empiricists or even all members of the Vienna Circle accepted the strict verificationist view that in order to be meaningful a claim must be implied by a finite number of observation sentences. Even though those observation sentences need not be true, this view had the drawback that so-called laws of nature would not be meaningful on this criterion. Schlick was prepared to bite the bullet and hold that laws were not statements at all but principles of inference. Others were not prepared to go so far and sought more liberal formulations. This more liberal or “left” wing of the Vienna Circle included Carnap, Philipp Frank, Hahn, and Neurath. Carnap does not seem to have been a strict verificationist even in the Aufbau (1928/1967).

Over the years a great many different formulations of verificationist principles ensued. Most of them came to a bad end rather quickly, and this is sometimes taken as a convincing argument that any form of verificationism is utterly misguided. Perhaps, but we should be cautious. There are undoubtedly many different features joined in any one of the proposals, and even a sequence of failures may not show where to place the blame. The central idea behind verificationism is linking some sort of meaningfulness with (in principle) confirmation, at least for synthetic sentences. The actual formulations embodied not only such a link but various particular accounts of confirmation as well. Now confirmation is a complex matter, and it is unlikely that we shall have the final satisfactory account any time soon. This should not persuade us, however, that there are no satisfactory accounts of confirmation any more than our current lack of the final physics should convince us that there are no physical facts of the matter. So even a string of failures in formulating verificationist principles may mean no more than that the embedded accounts of confirmation are too simple but the link between meaningfulness and confirmation is nevertheless sound.

Even if we set this caution aside, there may be parts of a persistently employed strategy that lead to persistent failure. These parts and failures might be avoidable. To see how this may be so we will compare what is perhaps the most famous formulation of the verificationist principle, in Ayer 1936, with a later one, in Carnap 1956. A.J. Ayer had visited the Vienna Circle from late 1932 on into 1933, returning home for the summer term. While in Vienna he attended meetings of the Circle and overlapped for five weeks with Quine. Neither Carnap nor Neurath were there at the time, so the left wing of the Circle was not fully represented. When Ayer returned to England he published Language, Truth, and Logic in 1936. Even immediately it was widely discussed, and after the war sales were spectacular. For many in England this book was the epitome of logical positivism and remains so.

Ayer was careful to restrict his criterion of meaningfulness to synthetic sentences and to demand only in principle confirmation. And the formulation seems very natural: Confirmation is a feature that applies to sentences (or groups of them) and not to sub-sentential parts, and for an empiricist the content that a synthetic sentence has would be empirical content. So it would seem that to have empirical content a sentence, A , should either directly imply some observational sentence or add to the observational content of some other sentence, B . That is, the conjunction of A and B should imply some observational sentence not implied by B alone. This formulation may be natural, but it is also fatally flawed. It would declare any sentence whatsoever as meaningful: For any sentence A and any observation sentence O , A would be meaningful because it could be conjoined to A ⊃ O . The latter would not in general imply O , but the conjunction would.

Other more elaborate formulations followed along the same lines, and other more elaborate counterexamples appeared just as fast. Hempel reviewed the situation twice within about a year (Hempel 1950 and 1951). First he concluded that it was a lively and promising line of research and later concluded that it was not promising at all. In retrospect it may be that the problems arise because we were led by the fact that confirmation is a feature that applies to whole sentences into thinking that the level at which to apply the criterion was the level of whole sentences. Now a sentence with meaningless parts might well pass some test especially if the test involves its being combined with other sentences that can have meaningless parts. So one way to avoid this difficulty is to try to find a formulation that applies the test at the level of basic expressions, those that can be thought of as “not having parts” so to speak.

This is the strategy that Carnap employed in “The Methodological Character of Theoretical Concepts” (1956). Observational terms are assumed to have empirical content. Logical terms are assumed to have none. And all defined terms are assumed to be replaced by their definitions. If for some basic, non-logical term there is a sentence that contains that term as its only non-logical element and if that sentence implies some observation sentence, then that sentence has empirical content and so does its only non-logical term. If we have established that each term from some set, K , is empirically significant we might test still further terms by seeing whether those further terms can add to what is sayable with terms from K . Carnap’s actual definition is quite complicated, but it does seem to avoid the difficulties of its predecessors. It also allows an account of why those predecessors ran into trouble, viz., that they applied at the level of whole sentences (naturally enough) rather than to elementary terms.

Not long after Carnap’s definition was published David Kaplan devised what seemed to be counterexamples. They became fairly well known, but they were not published until 1975. Shortly thereafter it was shown (Creath 1976) that either Carnap’s definition is not open to the counterexamples as presented or it can be patched in a very natural way so that it avoids them. This does not show that there are no counterexamples or that there are no other features of the definition to which one might object. But it does show that the situation is not as dire as Hempel supposed in 1951.

We need to address another issue in considering verificationism, the persistent criticism that it is self-undercutting. The argument for this claim goes like this: The principle claims that every meaningful sentence is either analytic or verifiable. Well, the principle itself is surely not analytic; we understand the meanings of the words in it perfectly well because we understand our own language. And we still do not think it true, so it cannot be true in virtue of meaning. And it is not verifiable either (whatever we choose ‘verifiable’ to mean).

This sounds more compelling than it is. Ayer understood the principle to be a definition, defining a technical term, ‘meaning’. If so, then the sentence expressing the principle would indeed be analytic. So the self-undercutting charge strictly fails. But so construed and with nothing else said about it, the principle would not have the same punch as before. Why should a metaphysician care whether his or her utterances lack some technical feature?

Carnap explicitly takes up the “self-undercutting” charge against verifiability in Philosophy and Logical Syntax (1935), and he is not interested in introducing a new technical term, ‘meaning’, or in denying this new technical property to unverifiable sentences. Carnap is careful to distinguish the language for which the verifiability principle is given from the meta-language in which we talk about that language. This meta-language would be the language in which the principle would be expressed. This may seem to offer another strategy against the “self-undercutting” charge because the principle applies to a different language than that in which it is expressed. This is not Carnap’s strategy. Carnap fully understands that if the general verificationist strategy is followed, there will also be a verificationist principle expressed in the meta-meta-language governing the meta-language.

Carnap’s real defense of the principle was achieved by changing the nature of the discussion. By 1934 Carnap had introduced an important new element into his philosophy called the Principle of Tolerance. Tolerance is a radical idea. There is no uniquely correct logic (1934/1937 xiv–xv). Empiricism is a convention (Carnap, 1936/1937 33). Perhaps more precisely each of the various versions of empiricism (including some sort of verificationism) is best understood as a proposal for structuring the language of science. Before tolerance, both empiricism and verificationism are announced as if they are simply correct. Correspondingly, what Carnap called metaphysics was then treated as though it were, as a matter of brute fact, unintelligible. But what is announced thus dogmatically can be rejected equally dogmatically. Once tolerance is in place, alternative philosophic positions, including metaphysical ones, are construed as alternative proposals for structuring the language of science. No theoretical argument or evidence can show that one of the proposed languages is the uniquely correct one. Nor can theoretical arguments or evidence show that it is false. Neither proposals nor languages are the sort of thing to be true or false. Instead, proposals call for practical decisions and practical arguments rather than for theoretical reasons or evidence. Carnap believes that there are indeed very good practical reasons for adopting the proposal of verificationism, for choosing a language of science in which all substantive (synthetic) claims can, at least in principle, be brought before the court of public experience. The reason is that if we do not require this, the result is “wearisome controversies” that there is no hope of resolving. That, he thinks, is the sad history of attempts to get beyond science, and it is just too painful.

If the proposals constituting some version of verificationism are adopted, then in the language thus constituted it will be analytically true that there are no synthetic sentences that are both unverifiable and meaningful. The notion of meaning here is not some new technical invention. Rather, ‘meaning’ is used in something like the ordinary sense. No grammatically well-formed sentence of this new language violates the verifiability principle. And the principle itself is completely safe. Thought of in this way the verifiability principle does not describe natural language; it is not intended to. It is intended to reform language to make it a more useful tool for the purposes of science. Carnap is under no illusion that natural languages are free from what seem to be metaphysical commitments. Nor is he under the illusion that defenders of the sort of metaphysics he targets will readily step up to the challenge of presenting precise rules of grammar and inference. There is no weakening of his defense of empiricism, but it is put on a somewhat different footing.

It is important to emphasize that Carnap’s Principle of Tolerance introduces a new conception of philosophy with far-ranging implications beyond those just discussed concerning verification. The idea that philosophy is concerned with language and its analysis was not new. What is novel is the idea that what had been seen as philosophical claims were better understood as proposals for structuring the language of science. Since these languages and the concepts they contained were to be thought of as tools, none of which was uniquely correct, the choice among the alternatives was a practical decision about usefulness for certain purposes rather than a theoretical question. Philosophy still has important work to do: It can analyze existing concepts. And since many existing concepts are vague, it can also make them more precise in a variety of ways through explication. Philosophy can also investigate wholly new concepts. In all this, philosophy explores the consequences of structuring the language of science in this way or that. It becomes, thus, a kind of conceptual engineering. Conceptual analysis, explication, construction, and engineering continue to be fruitful ideas in philosophy, though it is not always understood how much of this was initiated or shaped by Carnap and other logical empiricists.

Logic, mathematics, and mathematical geometry had traditionally seemed to be confirmationally “different”. Indeed it is hard to indicate any conditions under which any parts of them would be disconfirmed. Leibniz had called them truths of reason. Hume said that they represented relations of ideas. Kant had held that the truths in these areas were a priori. Mathematics and geometry were not analytic for Kant, but logic was. Kant had two criteria of analyticity, apparently thinking them equivalent. First, in subject-predicate sentences, an analytic sentence is one in which the concept of the predicate is contained in that of the subject. Second, an analytic sentence is one whose denial is self-contradictory. This seems to include not only the sentences whose surface logical form would be of the required sort but also those that can be got from such logical truths by making substitutions that were conceptually equivalent. The more modern rough analog of this is to say that the analytic sentences are those that are true in virtue of logic and definition.

Frege certainly developed logic beyond that which was available to Kant, but he did not think of himself as changing the analytic status of it. Logic is after all the only avenue we have for giving meaning to the notion of (logical) contradiction. Of course Frege also attempted to reduce mathematics to logic (including both first and second order logic), and insofar as that reduction was successful it would have implied that mathematics was analytic as well. Frege said little of geometry, but for him it was synthetic a priori.

Carnap had not only studied with Frege, but like many of the logical empiricists he had started out as a neo-Kantian as well. So especially in view of Russell’s relatively more successful attempt at reducing mathematics to logic, it was perhaps natural that Carnap would consider both mathematics and logic as analytic. Geometry could be handled in several different ways that we will not discuss here. But from fairly early on there was widespread agreement among the logical empiricists that there was no synthetic a priori, and that logic and mathematics and perhaps much else that seemed impervious to empirical disconfirmation should be thought of as analytic. The point of drawing the analytic-synthetic distinction, then, is not to divide the body of scientific truths or to divide philosophy from science, but to show how to integrate them into a natural scientific whole. Along the way the distinction clarifies which inferences are to be taken as legitimate and which are not. If, as Carnap and Neurath were, you are impressed by Duhemian arguments to the effect that generally claims must be combined in order to test them, the analytic-synthetic distinction allows you to clarify which combinations of claims are testable.

If analytic, a sentence is true in virtue of the conventions of language. In saying that, however, we must pause to confront two widespread confusions. First, Quine alleges (1963, 385f) that the notion of analyticity was developed and purports to explain for both Kant and Carnap how certainty is possible. In fact certainty has little or nothing to do with analyticity for the leading logical empiricists. In saying that such claims are based on convention they were explicitly calling attention to the revisability of conventions and the sentences that owed their meanings to those conventions. Second, nowadays any talk of convention is likely to prompt the response: “But that cannot be! No proposition can be made true by our conventions or decisions.” Unless it is a proposition about conventions, this second sentence of the response is true. But it is also completely irrelevant. Analyticity applies to sentences rather than propositions. Our conventions and decisions can and do affect what expressions mean and thus what sentences mean. Once the meaning is specified, it may well be that any sentence that has this meaning would be true even if, for example, the point masses of the universe were arranged quite otherwise than they in fact are. These are the analytic sentences. No claim is being made that meaning causes anything or that convention makes anything true. The “making” image here is out of place. It is just that in these cases the truth value of the sentence may well be functionally dependent on meaning alone. If it is, then in this special sense, truth value depends on meaning, and that depends on convention. Other sentences whose meanings are specified might well be true or false depending on how things in the external world, so to speak, are arranged. In this other category of sentence the truth value is not functionally dependent on meaning alone. They are the synthetic sentences. Now this puts matters extremely informally. But at least the nature of the confusions over certainty and convention should be clear.

In the Logical Syntax of Language (1934/1937) Carnap defined ‘analytic’ in a new way in order to circumvent Gödel’s incompleteness results. The method used was to distinguish between a derivation relation (the relation that holds between some premises and what can be got from them in a finite number of steps) and a consequence relation. The latter is an essentially semantic relation that holds between some premises and some other claim such that on all valuations under which the premises are all true, so is that other claim. This definition bears a stronger resemblance to Tarski’s account in (Tarski 1936b/1956). In any case, Carnap is able to show that for any sentence of pure mathematics either it or its negation is a consequence of the null set of premises. This leaves Gödel’s results completely intact as they concerned what is provable, that is, derivable from the null set of premises or from any one consistent axiomatization of mathematical truths.

As noted above, another innovation of Logical Syntax is the Principle of Tolerance. While it reflects a long-standing attitude on Carnap’s part, the principle itself is new. Later Carnap was to say that the Principle of Tolerance was “perhaps better called the principle of conventionality” (Carnap 1942, 247), that is, the conventionality of linguistic forms. Tolerance stabilizes the verification principle as well as Carnap’s empiricism, and it reinforces the idea that the analytic-synthetic distinction is always relative to a particular language (Creath 2009).

In the late 1950s Carnap began exploring (1963a and 1966) how a notion of analyticity might be developed for novel theoretical terms where the theories in which those terms are embedded are presented by means of a system of postulates. It is not clear that the account he developed was intended to supersede his earlier account. In any case Carnap’s suggestion is as follows (where for convenience terms are used autonomously): Let T be the totality of theoretical postulates, and C be the totality of mixed sentences (the sentences of the theory containing both antecedent and novel terms). Also let R ( TC ) be the Ramsey sentence for TC , that is, the result of replacing each of the non-observational terms in TC with predicate variables and closing that open sentence with corresponding existential quantifiers. R ( TC ) ⊃ TC can, Carnap says, be thought of as the analytic sentence for the theory, that is, a sentence that gives to the theoretical terms of TC their meaning. Over the last decade, this idea of Carnap’s has provoked considerable discussion that has not yet been resolved. Whatever worries there may be concerning this part of Carnap’s view, they are distinct from the more famous concerns raised by Quine.

Quine began having doubts about analyticity about 1940, though he seems not to have been firmly committed against it until later. In any case his doubts were not published until 1951 in his famous paper “Two Dogmas of Empiricism”. Quine’s readers have understood his arguments in many different ways. The most general form of his complaint is that ‘analytic’ so far lacks the appropriate tie to observational criteria that Carnap’s own account of theoretical terms in empirical science would demand. More specifically, where there has been an attempt at such a general criterion it has resulted in either a “drastic failure as tended to admit all or no sentences as analytic, or there has been a circularity” (Quine 1963, 404) of a kind that defines ‘analytic’ in terms that themselves lack the appropriate empirical criteria and so can be accounted for only by appeal to analyticity itself.

This complaint falls far short, as Quine well understood, of a proof that Carnap’s appeal to analyticity was doomed. First, it relies on the demand that theoretical terms must satisfy some empirical significance criterion. Many people at the time, including some who followed Quine in rejecting analyticity, also rejected any general empirical significance demand for theoretical terms. Second, one could accept the demand for theoretical terms in physics or chemistry and deny, as Carnap did, that the demand applied to his own work. This is because Carnap saw himself as working in an area within metamathematics rather than in empirical linguistics. Third, Quine did not pretend to have considered all of the possibilities for the explication of analyticity. And so it may be possible to meet Quine’s demands to the extent that they are legitimate. Fourth and finally, Quine seems in Roots of Reference (1974) to have provided an explication for ‘analytic’ that meets his demand for empirical/behavioral criteria without inducing either the drastic failure or the circularity envisioned above.

There is another somewhat independent thrust to Quine’s campaign against analyticity. In the last section of “Two Dogmas” (1951) Quine gives an extremely attractive sketch for an alternative epistemology that apparently makes no appeal to analyticity. Insofar as that sketch can be filled out successfully it would constitute a dispensability argument against analyticity. Whether it can be thus filled out, however, remains to be seen.

Quine’s other provocative theses, including especially his claims about the indeterminacy of translation, while relevant to his assessment of analyticity, would carry us too far afield to consider their ramifications here. As with most topics in philosophy there is no uniform agreement in the literature as to whether the notion of analyticity is or can be made sufficiently clear for use in scientific philosophy. Nor is there such agreement that Quine’s epistemological sketch can be satisfactorily filled out. Both approaches have their defenders and their detractors. But between them they seem to be the most promising avenues for integrating the logic-mathematical part of science with the more straightforwardly empirical parts. Since Carnap is and Quine can be argued to be within the logical empiricist tradition, this progress toward such unification can be counted as part of the legacy of the movement.

The commitment of some of the logical empiricists to the unity of science has been in recent years often discussed but less often understood. One hears in conversation that it was a sort of rearguard action designed to preserve as much as possible of a phenomenalist version of ontological reduction. One reads in print that it can be refuted by the obvious fact that the various sciences have quite distinct theoretical vocabularies (Suppes 1978). Both reactions are misplaced.

It was the left wing of the Vienna Circle, and above all Otto Neurath, that championed the unity of science. They also promoted physicalism, anti-foundationalism, and a generally naturalistic viewpoint. A main focus of their activities from the late 30s was The Encyclopedia of Unified Science edited by Neurath in Europe and Carnap and Charles Morris in Chicago. A great many philosophers of many different persuasions participated in that project. The project may have been unified science, but they did not have a completely unified view of what that project was. Here we will discuss the Neurath and Carnap versions of it to see what their central concerns were.

Neurath seems to have had two primary motivations to advance under the banner of the unity of science. First, he was concerned that there be no a priori methodological cleavage between the natural and the social sciences. On the social scientific side he was concerned that these sciences not condone some private, mysterious mode of insight (empathy) whose results could not be checked against more ordinary public observation. Such a methodology would be a harbor for metaphysics. On the natural scientific side, he was concerned to point out that, for Duhemian and other reasons, the situation is much messier than is sometimes supposed, and so invidious comparisons by natural scientists at the expense of social science were unwarranted.

Second, because Neurath was socially and politically engaged he was concerned that the various sciences be connected in such a way that they could be used together to solve complex human and social problems. For this, considerable overlap of vocabulary was needed, and this he called a “universal jargon”.

In recent years it is sometimes claimed that Neurath meant by the unity of science what some contemporary philosophers have defended as the disunity of science. One cannot rule this claim out a priori. But the often substantial differences among the current defenses of disunity make evaluating this claim difficult. It is fair to say, however, that Neurath was suspicious of grand hypotheses, familiar since the 19 th century to derive all of chemistry, biology, psychology, and the social sciences (in that order) from a few basic principles of physics. It is unclear whether this stems from a general opposition to system building, since he was eager to develop inferential connections among the various sciences. Perhaps this is better expressed as an opposition to speculative system building and to the idea that there is only one way of systematizing our science than to systematicity as such.

Carnap’s position on unity is different from Neurath’s, but they overlap. Carnap distinguished the unity of the language of science from the unity of the laws of science. He wanted to defend the former and to say what would be required for the latter. As far as the unity of the language of science, Carnap did in the Aufbau try to initiate a program for defining all of scientific concepts on the basis of a very small number of basic concepts, perhaps only one basic concept. That does afford a certain conceptual economy, but it is now generally held by Carnap scholars (see especially Friedman 1987 and Richardson 1998) that ontological reduction and reduction to a phenomenalist basis was far from his motive. Carnap explicitly acknowledged that another system of definitions, one with a physicalist basis, might also be possible. Instead of ontological economy and a phenomenal basis, Carnap’s project seems to have been the more Kantian one of indicating how semantic intersubjectivity is possible: How can it be that, even though I have only my own experiences and you have only yours, we can nevertheless share a common body of concepts? The answer is given in terms of shared inferential structure and identifying any given concept with a unique place within that shared overall structure. This is a highly holistic conception of concepts and it depends on thinking of the body of scientific commitments as a whole, as a unity.

The Aufbau was largely drafted before Carnap joined the Vienna Circle. Once there and under some influence from Neurath, Carnap campaigned more insistently for physicalism and for the unity of science. They seemed often to be two sides of the same coin. From 1933 onward there was a succession of monograph series with ‘Unified Science’ in the title. Until his death in 1945, Neurath was in each case the main editor and Carnap either the associate editor or one of the associate editors. The International Encyclopedia of Unified Science , begun in 1938 is undoubtedly the most famous of these. Carnap’s own essay on this topic “Logical Foundations of the Unity of Science” (1938) was printed as part of the very first number in the encyclopedia.

The dates here are relevant because by the time of this essay Carnap had already decided (Carnap 1936–37) that theoretical terms could not in general be given explicit definitions in the observation language even though the observation reports were already in a physicalist vocabulary. The partially defined theoretical terms could not be eliminated. This seems to have caused Carnap no consternation at all, and it never seems to have occurred to him that there was any conflict whatever between this result and the unity of science. This is because by this point the elimination of concepts was not the point of the exercise; their inferential and evidential integration was.

In the 1936–37 article, “Testability and Meaning” Carnap called the partial definitions themselves “reduction sentences” and the system of definitions of theoretical terms, both partial and complete, as a reduction of the theoretical terms to the observational basis. Plainly he means by the word ‘reduction’ something other than what we currently mean, not that there is anything univocal about current uses of the word. By ‘reduction’ of vocabulary A to vocabulary B Carnap means the specification of the inferential relations that would allow us to say what sentences or combinations of sentences in A would count as evidence for sentences in B .

This is also the key to what Carnap means by the unity of the language of science. The language of science is unified, no matter how different and exotic its various technical vocabularies may be, when each of its terms is reduced to (can be tested in) a common public observation vocabulary. The call for the unity of the language of science, then, amounts to no more than the demand that the various claims of the separate sciences should be publicly testable in a common observation language. Controversies will of course arise as to what the observational vocabulary should be and what are the acceptable forms of linkage. Carnap’s demand for unity in the language of science abstracts from those controversies to concentrate on the goal of public testability. That does not seem to be an unreasonable demand.

The unity of the language of science so far discussed is quite a different issue from the unity of the laws of science. And Carnap’s attitudes toward them are quite different. The latter issue concerns the extent to which the laws of one special science can be inferred from those of another. Carnap tries to articulate what would be involved in such a unification, but he nowhere says that such a unity is either possible or mandatory. Finding any sort of inferential connections among sets of laws would be welcome of course. But the question of how much unity there is, if any, among the various sciences is an empirical question that philosophers are ill equipped to answer. Philosophers should not make pronouncements, especially in advance of having putative laws in hand, either that scientific laws are unified or that they are not. A certain modest deference to the empirical facts that philosophers generally do not have, again, does not seem unreasonable.

Taking unity as a working hypothesis, as some philosophers have done, amounts to looking for inferential and nomological connections among various sets of laws, but not to the assertion that such connection will be found. Even if we accept the idea that such connections would be welcome if found, the question of whether one should spend significant effort in looking for them is not thereby answered. That would be a difficult and delicate practical question of how to apportion one’s research effort that for the purposes of this essay we must set aside.

There are two broad approaches to probability represented in logical empiricism. One of these, the so-called frequentist approach, has an extensive 19 th century history and was further developed from about 1920 onward by Richard von Mises and Hans Reichenbach. The other is the epistemic approach to probability. This goes back at least to Laplace at the end of the 18 th century. In the 20 th century Rudolf Carnap, who explored what he called logical probability, and Frank Ramsey and Richard Jeffrey whose accounts can be distinguished from Carnap’s and are often called subjective probability, all defended the epistemic approach. While Ramsey visited the Vienna Circle he was not much influenced by its members on these matters. By contrast, Jeffrey studied and later collaborated with Carnap but also made significant contributions of his own.

It is natural to begin thinking about probabilities with a simple mathematical account that takes as its point of departure various games of chance involving cards, dice, or coins. Bettors have long noted that some outcomes are much more likely than others. In this context it is convenient to take the probability of a kind of outcome to be the ratio of such outcomes to all possible outcomes. Usually for reasons of symmetry in the physical set up, the possible outcomes are assumed to be equally likely. Where that assumption happens to be true or nearly so the empirical results of, say, a great many throws of a pair of dice tends to be close to what the simple mathematical account would suggest. Conversely, where the outcomes deviate from the expected ratios, bettors begin to suspect that the dice, coins, and cards (or the manipulations of them) are not all that they seem. The suspicion is that the outcomes are not equally likely and that the simple mathematical account does not apply.

These facts suggest both two limitations of the simple account and the beginnings of a way around them. The first limitation is that the account applies only where the outcomes can be partitioned into alternatives that are equally likely. This is not the case when dice are loaded or in such real world cases as radioactive decay or weather forecasting. A second limitation is that the account, in describing the possible outcomes as equally likely, implicitly appeals to the very probability notion for which clarification was sought. The realization that we can sometimes discover the falsehood of the assumption of equal likelihood and make a much more reasonable estimate of probability by making a large number of trials is very suggestive. And from his dissertation onward Reichenbach worked out a variety of imagined physical models that could guide ones thinking about probability in useful ways. The result is what is often called the frequency theory of probability (or sometimes the statistical frequency theory or the limit frequency theory).

Even a perfectly fair coin in an odd number of flips will never result in exactly the same number of heads and of tails. When the coin is fair and the number of flips is even, an outcome perfectly balanced between heads and tails is not guaranteed either. So, even on the assumption that the probability of the coin’s coming up heads does not change over the course of the trials, we need to be cautious. A larger number of flips might make us more confident that the ratio we have seen is close to the “actual” value, but there is no finite number of flips after which we can say that the observed ratio is exactly right. We will never make an infinite number of flips either, and in actual cases a large finite number of flips might so erode the coin as to bias the coin and discredit the result. Notwithstanding these limitations on an actual series of trials one can imagine an infinite series of trials and define a notion of probability with respect to it. This raises its own difficulty, namely that ratios are not defined for infinite collections. They would be defined, however, for any finite initial segment of such an infinite series, thus giving a sequence of ratios. If this sequence of ratios settles down on a limit, the probability of the coin showing a head given that it has been flipped can be defined as the limit of the ratio of heads to total flips as the number of flips goes to infinity.

While probability thus defined has a somewhat counterfactual character, that is not an obvious defect. Moreover, this notion of probability applies perfectly well to biased coins and loaded dice, as well as to radioactive decay. On the surface at least it also seem to avoid using the notion of probability in its own definition, and in these respects it seems to be an important improvement over the simple mathematical model with which we began. The definition locates the probability objectively “out in nature” so to speak, and this comports well with Reichenbach’s scientific realism.

A problem that remained troublesome concerns the fact that one often wants to assign probabilities to particular events, events that in the nature of things cannot be repeated in all their particularity. Thus it is unclear how a frequency theory of probability is to be applied to such individual cases. This is often called the problem of the single case. It is a little difficult to assess how serious this is, because in actual practice we often have no difficulty in making probability assignments to single cases. Suppose we are interested in the probability of rain tomorrow. Tomorrow will never be repeated, and we want to estimate the probability now. What we do is to look back through the records to find days relevantly like today and determine in what fraction of those cases those days were followed by rainy days and use that as our estimate. Even if we are comfortable with this practice, however, it is another matter to say why this should give us a reasonable estimate of the value of the limit involved in a logically impossible infinite sequence. This problem of the single case was much discussed, and Wesley Salmon made progress in dealing with it. Indeed, Salmon’s account of statistical explanation can be viewed as a substantial mitigation of the problem of the single case (W. Salmon 1970).

There are residual difficulties in making estimates of the probabilities on the basis of finite evidence. The problem is that even when we are assured that the sequence of ratios has a limit, we have no a priori grounds for saying how close the current ratio is to that limit. We can boldly estimate the limit by means of the so-called “straight rule”. This just takes the most recent ratio as the desired estimate. This is a good practical solution where the number of trials is already high, but this does not really say why the estimate should be good, how good it is supposed to be, or how many trials would be high enough. In addition, the straight rule can yield counterintuitive results where the number of trials is small.

Though there are these issues outstanding, frequency theories define a concept of probability indispensable for quantum theories and for a wide variety of other applications in the natural and social sciences. It was not the only concept of probability to be developed by the logical empiricist tradition. The primary other such concept was the epistemic conception of probability. We will begin with Carnap and then move to those who developed a subjectivist account.

Carnap is addressing a different issue than was addressed by von Mises and Reichenbach. Instead of focusing on physical phenomena and ratios within them, Carnap focuses on arguments and takes as his point of departure the widespread conviction that some arguments are stronger, in varying degrees, than others, even for the same conclusion. Similarly some bodies of evidence can give us more reason to believe a given conclusion than would another body of evidence. Carnap sets as his task the development of a quantitative concept of probability that will clarify and explicate these widespread convictions. Such a quantitative concept would be an extraordinarily useful tool, and it would be a useful successor to our ordinary, somewhat scattered notions of confirmation and induction.

Carnap approaches the problem by first considering extremely limited artificial languages and trying to find a confirmation function that will work for that. If he succeeds he would then try to develop an account that would work for a broader and richer range of languages. In this his approach is like that of a physicist developing a physical theory for the highly artificial situation of a billiard table or air track and then broadening the theory to deal with a wider range of cases. In Carnap’s case, however, it is somewhat unclear what success would be in an artificial language very much unlike our own. In any case, Carnap is not trying to describe our linguistic habits but to clarify or even to replace them with something more useful.

As early as Logical Syntax (Carnap 1934/1937, 244/316–17) Carnap had suggested that Wittgenstein’s remarks in the Tractatus about ranges ( Tractatus , 4.463) might be a starting point for thinking about probability. By 1945 Carnap also distinguished the two approaches described here, insisting that they were not competitors but were attempting to explicate two different concepts of probability. One need not choose one as the only concept; both concepts were useful. Reichenbach, by contrast, never conceded that both concepts were needed and insisted that his frequency notion could serve all epistemic purposes for which any notion of probability is needed.

Carnap’s general strategy was first to identify a broad class of confirmation functions, as subjectivists Ramsay and de Finetti were also to do, and then find a natural way of limiting this class still further. The confirmation functions have to meet some basic mathematical conditions. The axioms that state these conditions partially define a function, and this function can be interpreted in a number of ways. Carnap himself lists three in Carnap 1950. In (1955), John Kemeny (one of Carnap’s collaborators and later a co-inventor of BASIC programming language and still later president of Dartmouth College) gave an argument that persuaded Carnap that it was more fruitful to think of the function as indicating fair betting quotients rather than evidential support. This took Carnap even closer in conception to the work of such subjectivists as Ramsey and de Finetti. Indeed, the discussion of fair betting quotients, and related issues of Dutch book arguments had been initiated by de Finetti.

In Logical Foundations of Probability (1950) Carnap had discussed Bayes’ theorem and promised to expand the discussion in a second volume. Carnap’s interest in Bayesianism grew, but that second volume never materialized, quite possibly because rapid development of the field was still under way at the time of Carnap’s death. As his work proceeded Carnap tended to explain probabilities by reference to events and propositions rather than speak overtly about sentences. A similar change appears in the rest of Carnap’s work as well. It is not clear, however, whether this amounts to a major change of view or a change in what he sees as the most felicitous mode of expression. As the years progressed Carnap tended to see the remaining differences between himself and his subjectivist co-workers as chiefly differences in emphasis. In any case the subjectivist tradition is now dominant in philosophical discussions of probability (Zabell 2007, 293). Richard Jeffrey, whose own work arose out of logical empiricism, carried on that tradition for 35 years after Carnap’s death. Jeffrey himself made major contributions including a principle for updating ones beliefs when the evidence one learns is not certain. The world knows this principle as “Jeffrey conditionalization”; he called it simply “probability kinematics”.

Popper’s view of probability, his propensity theory, differs from either of the two approaches discussed above. Unlike the epistemic approach of Carnap and others, Popper was not trying to clarify inductive relations because he did not believe that there are inductive inferences. Theories can be corroborated by their passing severe tests, but they are not thereby inductively confirmed or made more probable. For a discussion of whether there are any significant similarities between Popper’s idea of corroboration and the ideas of inductive confirmation that he rejects, see (Salmon 1967, 1968).

Propensities are thought of as tendencies of a physical event or state to produce another event or state. Because propensities are to be features of external events and not, to use Hume’s phrase, relations of ideas, the propensity theory and the statistical-frequency theory are sometimes grouped together as accounts of chance. Popper has specifically applied propensities to single non-repeatable events (1957), and that suggests that the concept of propensity does not involve any essential reference to long sequences of events. Popper has also taken propensities as producing outcomes with a certain limit frequency (1959). This does suggest a rather closer tie to the statistical frequency approach. Later philosophers developed both sorts of propensity theories, single-case theories and long-run theories. (Gillies 2000) And like other approaches to probability and induction all these views remain controversial. While we will not discuss the relative merits of the various approaches further, those who are interested in Popper’s views in this area should look at the many papers on probability, induction, confirmation, and corroboration, and Popper’s replies, in The Philosophy of Karl Popper (Schilpp 1974).

In 1967 John Passmore reported that: “Logical positivism, then, is dead, or as dead as a philosophical movement ever becomes.” (1967, 57) Earlier in the same article he had equated logical positivism with logical empiricism, so presumably that was dead too. At that time few would have disagreed with Passmore, even though Carnap was still alive and active. But in speaking of this movement Passmore was referring not to a movement but to specific doctrines, and his interpretation of them was much influenced by Ayer. Even so, Passmore conceded that the movement had left a legacy and that “the spirit which inspired the Vienna circle” persisted. It still does.

Part of the movement’s legacy lies in contemporary philosophy of science. In the US nearly all philosophers of science can trace their academic lineages to Reichenbach. Most were either his students or students of his students and so on. His scientific realism inspired a generation of philosophers, even those clearly outside the movement. Even the reaction against various forms of realism that have appeared in recent decades have roots in the logical empiricist movement. Moreover, philosophers of science are expected to know a great deal of the science about which they philosophize and to be cautious in telling practicing scientists what concepts they may or may not use. In these respects and others contemporary philosophers promote a kind of naturalism, and by so doing they follow both the precept and the example of the logical empiricists.

There are other issues where the legacy of logical empiricism is still visible. Two different approaches to probability are still under discussion. One of them explores the objective chances of external events; this investigation follows in the tradition of the frequency theory of Reichenbach and von Mises. The second approach has an epistemic conception of probability as exemplified by Carnap. S.L. Zabell summarizes the current situation as follows:

But although the technical contributions of Carnap and his school remain of considerable interest today, Carnap’s most lasting influence was more subtle but also more important: he largely shaped the way current philosophy views the nature and role of probability, in particular its widespread acceptance of the Bayesian paradigm (as, for example, in Earman, 1992; Howson and Urbach, 1993; and Jeffrey, 2004). (Zabell 2007, 294)

There is also a continuing concern for how the various sciences fit together. Some have scouted theoretical unification and others a more pluralistic model, just as the logical empiricists did. There was for a while a vogue for the disunity of science. Some even said that their conception of the disunity of science is just what Neurath meant by the unity of science. Parts of the discussion were intended as challenges to logical empiricism, but often the arguments used were pioneered by the logical empiricists themselves.

For the 30 years after Passmore’s report metaphysics became ever more visible in philosophy. It was a diverse development, but in the self-conceptions of many of its most prominent practitioners there was no attempt to shun science or logic or to think that metaphysics had access to facts that were deeper than or beyond those that a proper science could reach. So the metaphysics that blossomed was not necessarily of the sort that Carnap, Neurath, Reichenbach, and others combated. Finally, in contemporary meta-philosophy variously logical empiricist ideas on ontology (Blatti and Lapointe 2016), explication (Kitcher 2008, and Carus 2007), and philosophy as conceptual engineering (Creath 1990, Chalmers 2020, and Haslanger 2000) continue to be of interest.

Even in its heyday many philosophers who on either doctrinal or sociological grounds can be grouped with the logical empiricists did not see themselves that way. We should not expect philosophers today to identify with the movement either. Each generation finds its place by emphasizing its differences from what has gone before. But the spirit of the movement still has its adherents. There are many who value clarity and who want to understand the methodology of science, its structure, and its prospects. There are many who want to find a natural home within a broad conception of science for conceptual innovation, for logic and mathematics, and for their own study of methodology. And importantly there are those who see in science a prospect for intellectual and social reform and who see in their own study of science some hope for freeing us all from the merely habitual ways of thinking “by which we are now possessed” (Kuhn 1962, 1). These are the motives that define the movement called logical empiricism. As Twain might have said, the reports of its death are greatly exaggerated.

Cited Literature

• Ayer, A.J., 1936, Language Truth, and Logic , London: Gollancz.
• Blatti, S. and S. Lapointe (eds.), 2016, Ontology After Carnap , Oxford: Oxford University Press.
• Carnap, R., 1928/1967, Der logische Aufbau der Welt , translated by R.A. George as The Logical Structure of the World , Berkeley: University of California Press.
• –––, 1934/1937, Logische Syntax der Sprache , translated by A. Smeaton as The Logical Syntax of Language , London: Kegan Paul, Trench, Trubner & Co.
• –––, 1935, Philosophy and Logical Syntax , London: Kegan Paul, Trench, Trubner, & Co.
• –––, 1936–37, “Testability and Meaning”, Philosophy of Science , 3: 419–71, 4: 1–40.
• –––, 1938, “Logical Foundations of the Unity of Science”, International Encyclopedia of Unified Science (Volume 1, Number 1), Chicago: University of Chicago Press, 42–62.
• –––, 1942, Introduction to Semantics , Cambridge, MA: Harvard University Press.
• –––, 1950, Logical Foundations of Probability , Chicago: University of Chicago Press.
• –––, 1958 [2017], “Value Concepts”, transcribed and translated by A. Carus, Synthese 194: 185–94. [Original manuscript available online ]
• –––, 1963a, “Carl G. Hempel on Scientific Theories”, in The Philosophy of Rudolf Carnap , P.A. Schilpp (ed.), LaSalle, IL: Open Court, 958–66.
• –––, 1963b, “K.R. Popper on Probability and Induction”, in The Philosophy of Rudolf Carnap , P.A. Schilpp (ed.), LaSalle, IL: Open Court, 995–998.
• –––, 1966, Philosophical Foundations of Physics , M. Gardner (ed.), New York: Basic Books.
• Carus, A.W., 2007, Carnap and Twentieth-Century Thought : Explication as Enlightenment , Cambridge: Cambridge University Press.
• Chalmers, D., 2020, “What is Conceptual Engineering and Should It to Be?”, Inquiry , published online 16 September 2020. doi:10.1080/0020174X.2020.1817141
• Creath, R., 1976, “On Kaplan on Carnap on Significance”, Philosophical Studies , 30: 393–400.
• –––, 1990, “Introduction”, in Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work , R. Creath (ed.), Los Angeles: University of California Press, 1–43.
• –––, 2009, “The Gentle Strength of Tolerance: The Logical Syntax of Language and Carnap’s Philosophical Programme”, in Carnap’s Logical Syntax of Language , P. Wagner (ed.), Houndsmills, Basingstoke, UK: Palgrave Macmillan, 203–214.
• Earman, J., 1992, Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory , Cambridge, MA: MIT Press.
• Friedman, M., 1987, “Carnap’s Aufbau Reconsidered”, Noûs , 21: 521–45.
• Gillies, D., 2000, “Varieties of Propensity”, British Journal for the Philosophy of Science , 51: 807–835.
• Gödel, K., 1995, “Is Mathematics Syntax of Language?” in K. Gödel, Collected Works (Volume 3), S. Fefferman, et al. (eds.), Oxford: Oxford University Press, 334–362.
• Haslanger, S. 2000, “Gender and Race (What Are They? What Do We Want Them to Be?”, Noûs , 34: 31–55.
• Hempel, C.G., 1950, “Problems and Changes in the Empiricist Criterion of Meaning”, Revue International de Philosophie , 11: 41–63.
• –––, 1951, “The Concept of Cognitive Significance: A Reconsideration”, Proceedings of the American Academy of Arts and Sciences , 80: 61–77.
• Howson, C. and Urbach, P., 1993, Scientific Reasoning: The Bayesian Approach , LaSalle, IL: Open Court.
• –––, 2004, Subjective Probability: The Real Thing , Cambridge: Cambridge University Press.
• Kaplan, D., 1975, “Significance and Analyticity: A Comment on Some Recent Proposals of Carnap”, in Rudolf Carnap, Logical Empiricist , J. Hintikka (ed.), Dordrecht, Boston: Reidel, 87–94.
• Kemeny, J., 1955, “Fair Bets and Inductive Probabilities”, Journal of Symbolic Logic , 20: 263–73.
• Kitcher, Philip. 2008, “Carnap and the Caterpillar”, Philosophical Topics , 36: 111–27.
• Kuhn, T., 1962, The Structure of Scientific Revolutions , International Encyclopedia of Unified Science (Volume II, Number 2), Chicago: University of Chicago Press.
• Passmore, J., 1967, “Logical Positivism”, The Encyclopedia of Philosophy (Volume 5), P. Edwards (ed.), New York: Macmillan, 52–57.
• Popper, K., 1935/1959, Logik der Forschung , translated by the author as The Logic of Scientific Discovery , New York: Basic Books.
• –––, 1957, “The Propensity Interpretation of the Calculus of Probability”, S. Körner (ed.), The Colston Papers , 9: 65–70.
• –––, 1959, “The Propensity Interpretation of Probability”, British Journal for the Philosophy of Science , 10: 25–42.
• Quine, W.V., 1951, “Two Dogmas of Empiricism”, Philosophical Review , 60: 20–43.
• –––, 1963, “Carnap and Logical Truth”, in The Philosophy of Rudolf Carnap , P. Schilpp (ed.), LaSalle, IL: Open Court, 385–406.
• –––, 1974, The Roots of Reference , LaSalle, IL: Open Court.
• Reichenbach, H., 1916/2008, Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit , edited and translated by F. Eberhardt and C. Glymour as The Concept of Probability in the Mathematical Representation of Reality , LaSalle, IL: Open Court.
• –––, 1938, Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge , Chicago: University of Chicago Press.
• Richardson, A., 1998, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism , Cambridge: Cambridge University Press.
• Russell, B., 1914, Our Knowledge of the External World as a Field for Scientific Method in Philosophy , LaSalle, IL: Open Court.
• Salmon, W., 1967, The Foundations of Scientific Inference , Pittsburgh: University of Pittsburgh Press.
• –––, 1968, “The Justification of Inductive Rules of Inference”, in The Problem of Inductive Logic , I. Lakatos (ed.), Amsterdam: North-Holland, 24–43.
• –––, 1970, “Statistical Explanation”, in Nature and Function of Scientific Theories , R. Colodny (ed.), Pittsburgh: University of Pittsburgh Press, 173–231.
• Schilpp, P. (ed.), 1974, The Philosophy of Karl Popper , LaSalle, IL: Open Court.
• Suppes, P., 1978, “The Plurality of Science”, in PSA 1978: Proceedings of the 1978 Biennial Meeting of the Philosophy of Science Association (Volume 2), P. Asquith and I. Hacking (eds.), East Lansing, MI: Philosophy of Science Association, 3–16.
• Tarski, A., 1936a/1956, “Der Wahrheitsbegriff in den formalisierten Sprachen”, translated by J.H. Woodger as “The Concept of Truth in Formalized Languages” in Logic, Semantics, Metamathematics , by A. Tarski, Oxford: Clarendon Press, 152–278.
• –––, 1936b/1956, “Über den Begriff den logischen Folgerung”, translated by J.H. Woodger as “On the Concept of Logical Consequence”, in Logic, Semantics, Metamathematics , by A. Tarski, Oxford: Clarendon Press, 409–20.
• Uebel, T., 2012, “Carnap, Philosophy, and ‘Politics in its Broadest Sense’”, in Carnap and the Legacy of Logical Empiricism , R. Creath (ed.), Vienna: Springer, 133–145.
• –––, 2013, “Logical Positivism – Logical Empiricism: What’s in a Name?”, Perspectives of Science , 21: 58–99.
• Waismann, F., 1967/1979, Wittgenstein und der Wiener Kreis , translated by J. Schulte and B. McGinnis as Wittgenstein and the Vienna Circle , Oxford: Basil Blackwell.
• Wittgenstein, L., 1921/1922, Logische-Philosophische Abhandlung , translated by C.K. Ogden as Tractatus Logico-Philosophicus , London: Routledge & Kegan Paul.
• Zabell, S. L., 2007, “Carnap on Probability and Induction”, in The Cambridge Companion to Carnap , M. Friedman and R. Creath (eds.), Cambridge: Cambridge University Press, 273–294.

Other Selected Literature

• Awodey, S. and A. W. Carus, 2004, “How Carnap Could Have Replied to Gödel”, in S. Awodey and C. Klein (eds.), Carnap Brought Home: The View From Jena , LaSalle, IL: Open Court, 203–223.
• Cartwright, N. , J. Cat, L. Fleck, and T. Übel, 1996, Otto Neurath: Philosophy Between Science and Politics , Cambridge: Cambridge University Press.
• Carnap, R. 2019, The Collected Works of Rudolf Carnap, Vol. 1, Early Writings , A. Carus et al. (eds.), Oxford: Oxford University Press.
• Creath, R. 1990, Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work , R. Creath (ed.), Los Angeles: University of California Press.
• –––, 1999, Reconsidering Logical Positivism , Cambridge: Cambridge University Press.
• –––, 2000, A Parting of the Ways: Carnap, Cassirer, and Heidegger , LaSalle, IL: Open Court.
• Friedman, M. and R. Creath (eds.), 2007, The Cambridge Companion to Carnap , Cambridge: Cambridge University Press.
• Frost-Arnold, G., 2013, Carnap, Tarski, and Quine at Harvard: Conversations of Logic, Mathematics, and Science , Chicago: Open Court.
• Hintikka, J. (ed.), 1962, Logic and Language: Studies Dedicated to Professor Rudolf Carnap on the Occasion of His Seventieth Birthday , Dordrecht: Reidel.
• ––– (ed.), 1975, Rudolf Carnap, Logical Empiricist: Materials and Perspectives , Dordrecht: Reidel.
• Howson, C., 1973, “Must the Logical Probability of Laws be Zero?” British Journal for Philosophy of Science , 24: 153–163.
• Jeffrey, R., 1975, “Probability and Falsification: Critique of the Popper Program”, Synthese , 30: 95–117.
• Mancosu, P., “Harvard 1940–41: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science”, History and Philosophy of Logic , 26: 327–57.
• Miller, D., 1997, “Sir Karl Raimund Popper, CH, FBA”, Biographical Memoirs of Fellows of the Royal Society of London , 43: 367–409.
• Parrini, P., W. Salmon, and M. Salmon (eds.), 2003, Logical Empiricism: Historical and Contemporary Perspectives , Pittsburgh: University of Pittsburgh Press.
• Rescher, N. (ed.), 1985, The Heritage of Logical Positivism , Lanham, MD: University Presses of America.
• Rescher, N., 2006, “The Berlin School of Logical Empiricism and Its Legacy”, Erkenntnis , 64: 281–304.
• Richardson, A. and Übel, T. (eds.), 2007, The Cambridge Companion to Logical Empiricism , New York: Cambridge University Press.
• Salmon, W. and G. Wolters (eds.), 1994, Language, Logic, and the Structure of Scientific Theories: The Carnap-Reichenbach Centennial , Pittsburgh: University of Pittsburgh Press, and Konstanz, Germany: University of Konstanz Press.
• Sarkar, S., (ed.), 1992, Synthese: Carnap: A Centenary Reappraisal , 93(1–2).
• Schilpp, P. (ed.), 1963, The Philosophy of Rudolf Carnap , LaSalle, IL: Open Court.
• Spohn, W. (ed.), 1991, Erkenntnis: Special Volume in Honor of Rudolf Carnap and Hans Reichenbach , 35(1–3).
• Stadler, F., 1997/2001, Studien zum Wiener Kreis: Entwicklung und Wirkung des Logischen Empiricismus im Kontext , translated by C. Nielsen, et al. as The Vienna Circle: Studies in the Origins, Development and Influence of Logical Empiricism , Vienna: Springer.
• Übel, T., 2007, Empiricism at the Crossroads: The Vienna Circle’s Protocol-Sentence Debate Revisited , LaSalle, IL: Open Court.
• Zabell, S. L., 1996, “Confirming Universal Generalizations”, Erkenntnis , 45: 267–283.

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Rudolf Carnap , maintained by Douglas Marshall (University of Minnesota).
• Institute Vienna Circle , Society for the Advancement of the Scientific World Conception, Vienna.
• Willard Van Orman Quine , maintained by Douglas Boynton Quine.
• Archives of Scientific Philosophy , Special Collections Department, University Library System, University of Pittsburgh.
• Vienna Circle Foundation , to promote studies of the work of members of the Vienna Circle and to protect the Vienna Circle Archive, Amsterdam (this webpage is archived at the Internet Archive).

Ayer, Alfred Jules | Carnap, Rudolf | Gödel, Kurt | Hempel, Carl | Neurath, Otto | Popper, Karl | Quine, Willard Van Orman | Reichenbach, Hans | Sellars, Wilfrid | Tarski, Alfred | Vienna Circle

Copyright © 2022 by Richard Creath < creath @ asu . edu >

• Accessibility

Support SEP

Mirror sites.

View this site from another server:

• Info about mirror sites

The Stanford Encyclopedia of Philosophy is copyright © 2023 by The Metaphysics Research Lab , Department of Philosophy, Stanford University

Library of Congress Catalog Data: ISSN 1095-5054

What Is Logical Reasoning?

Imagine doing a task in the workplace, or outside, without thinking it through. It may be because you are pressed…

Imagine doing a task in the workplace, or outside, without thinking it through. It may be because you are pressed for time, have certain pre-existing beliefs or the situation is emotionally charged.

Does being in such situations lead to you take impulsive decisions that you regret later? Do you think these impulsive decisions could probably have been avoided with a little bit of deliberate thought?

In order to avoid impulsive decisions, it’s important to think things through. In other words, use logical reasoning.

Derived from the Greek word ‘logikos’, logic is defined as the study of correct reasoning, especially regarding making inferences.

With a lot of complex definitions of what is logical reasoning, it might come across as something difficult to grasp. The easiest way to figure it out is by asking a simple question: ‘Does it make sense?’  Essentially, whenever we talk about logic, we are simply investigating whether the idea, statement, or conclusion makes sense.

Logical reasoning is a process that takes place in the left hemisphere of the human brain. Taking all the relevant data into account, the ‘logical’ or the left brain employs strategies based on collective knowledge and the individual’s past experiences to problem-solve and make rational decisions.

What Is Logical Thinking?

Fundamentally, logical thinking is the act of analyzing a problem or a scenario and then coming up with a rational and satisfactory answer or conclusion. Typically, we use our logical reasoning skills to analyze and consider a problem objectively and distantly. This allows us to make an informed decision about the mode and manner in which we must act.

The importance of logical thinking is unparalleled because it can help you reach crucial decisions, assist in problem-solving, stimulate creative thinking, and set achievable goals. All of these things come in handy from the point of view of career development.

Whether one has just begun working in a new environment or wants to fast-track their career, we all find ourselves in situations that require the deployment of logical thinking skills.

Importance Of Logical Thinking At The Workplace

Problem-solving, multitasking, and decision-making skills are appreciated at the workplace. The importance of logical thinking is reinforced by celebrated business tycoons, world leaders, and a large section of the industrial workforce.

It is sometimes imperative to distance yourself from the situation at hand so that you can see the bigger picture. As the renowned writer Salman Rushdie said, “The only people who see the entire picture are the ones who step out of the frame.” Distancing yourself from the problem allows the brain to focus on the data in its entirety and allows the individual to take the emotion out of it.

A lot of times, our emotions cloud our logical thinking skills. We lose objectivity if the matter is too close to the heart or if we are extremely involved, both physically (ability and productivity) and mentally (emotionally and strategically).

Maintaining complex social and professional relationships requires a strong logical thinking mindset. To navigate the modern workplace efficiently, one has to take a multitude of factors into consideration. ( www.genusinnovation.com ) After all, work is not just about the work but also about the people you work with!

With logical thinking, you can create effective strategies to get the job done. Thinking clearly and logically will allow you to divide, design, and delegate the relevant workload. Managing a batch of data, systems, or even employees requires a tremendous amount of planning for there to be no glitches in execution.

Incorporating these logical thinking skills into your mental make-up is essential since the modern workplace demands razor-sharp cognitive skills.  Most work nowadays does not require physical exertion, but mental precision. To keep pace with hours and hours of endless meetings, investor presentations, or client meetings, it is important to equip yourself with these tools.

Harappa Education offers a course called Reasoning Logically where leading behavior scientists, educators, and trainers will teach you about the workings of the brain and about unleashing the power of logical reasoning skills.  This course shares information about the Systems of Thinking framework which can help you boost your brainpower as well as improve your planning and execution skills.

Explore topics such as the  Meaning of Heuristic , the  Systems of Thinking  & How our Mind Works  from our Harappa Diaries blog section and hone strategically thinking skills in business.

• Skip to Content
• Skip to Main Navigation
• Skip to Search

Indiana University Indianapolis Indiana University Indianapolis IU Indianapolis

• Meet the AVC
• Campus Career and Advising Services
• IU Indianapolis Career EDGE
• Office of Student Employment
• Instructor Quick Guide
• Student Engagement Roster (SER)
• Student Commencement Speaker
• Honors College
• Institute for Engaged Learning
• University College

Analytical Reasoning

• Arts/Humanities
• Civics Literacy
• Core Communication
• Cultural Understanding
• Life and Physical Sciences
• Social Sciences
• General Education Course Proposals
• General Education Review
• IU Indianapolis Profiles
• Learning Communities
• Development of New Degrees, Minors, and Certificates
• Meeting Minutes
• Policies (General Education)
• Undergraduate Affairs Committee Roster

Division of Undergraduate Education

• Undergraduate Curricula
• General Education
• General Education Core

General education courses for Analytical Reasoning

Students must choose Option 1 or Option 2 for the Analytical Reasoning domain:

• Option 1: Take 6 credit hours of college math from List A.
• Option 2: Take 3 credit hours of college math from List A and 3 credit hours from List B.

Course learning outcomes

Instructors teaching courses in the Analytical Reasoning domain include at least half of the following learning goals so students can successfully complete this general education core requirement.

Upon completion of the course, students will be able to:

• Interpret information that has been presented in mathematical form (e.g., with functions, equations, graphs, diagrams, tables, words, geometric figures)
• Represent information/data in mathematical form as appropriate (e.g., ,with functions, equations, graphs, diagrams, tables, words, geometric figures)
• Demonstrate skill in carrying out mathematical (e.g., algebraic, geometric, logical, statistical) procedures flexibly, accurately, and efficiently to solve problems
• Analyze mathematical arguments, determining whether stated conclusions can be inferred
• Communicate which assumptions have been made in the solution process
• Analyze mathematical results in order to determine the reasonableness of the solution
• Cite the limitations of the process where applicable
• Clearly explain the representation, solution, and interpretation of the math problem

Additional courses for List A for IUPUC students only

Delisted courses for list b, full list of all transferable general education courses at iu indianapolis, division of undergraduate education social media channels.

• Faculty/Staff Tools

• Daily Crossword
• Word Puzzle
• Word Finder
• Word of the Day
• Synonym of the Day
• Word of the Year
• Language stories
• All featured
• Gender and sexuality
• All pop culture
• Writing hub
• Grammar essentials
• Commonly confused
• All writing tips
• Pop culture
• Writing tips

Advertisement

[ ej- oo - key -sh uh n ]

Synonyms: learning , schooling , instruction

• the act or process of imparting or acquiring particular knowledge or skills, as for a profession.

a university education.

to show one's education.

Synonyms: enlightenment , knowledge , learning

• the science or art of teaching; pedagogics.

/ ˌɛdjʊˈkeɪʃən /

• the act or process of acquiring knowledge, esp systematically during childhood and adolescence

his education has been invaluable to him

education is my profession

a course in education

a university education

consumer education

Discover More

Other words from.

• anti·edu·cation adjective
• noned·u·cation noun
• over·edu·cation noun
• preed·u·cation noun
• proed·u·cation adjective
• super·edu·cation noun

Word History and Origins

Origin of education 1

Synonym Study

Example sentences.

Simply listening to a lecture is not effective in the real world, and yet that largely remains the default mode of education online.

While Brunskill doesn’t believe there’s any silver bullet solution to fixing education or recruitment systems, he remains optimistic in Forage’s future.

A new study shows that academic medical researchers, who represent some of the most accomplished scientists with decades of education under their belts, are no exception to that trend.

Enormous investment in education going right the way back into the early 19th century.

In this bleak time for public education, I’ve been straining to decipher some silver linings.

Education controls the transmission of values and molds the spirit before dominating the soul.

What they believe impacts economic policy, foreign policy, education policy, environmental policy, you name it.

Congress is attempting to pass the buck on federal funding for education.

The Supreme Court eventually stepped in and ended legal segregation in the landmark 1954 decision, Brown v. Board of Education.

This is why arguments for little to no federal oversight of education are so disturbing.

It seems to be a true instinct which comes before education and makes education possible.

I am pleading for a clear white light of education that shall go like the sun round the whole world.

He became a doctor in two hours, and it only cost him twenty dollars to complete his education.

And now let me come to the second problem we opened up in connection with college education—the problem of its extension.

If we are to have a real education along lines of expression we must begin with the "content," or cause, of expression.

Related Words

• improvement
• information
• scholarship

More About Education

What is a basic definition of  education .

Education is both the act of teaching knowledge to others and the act of receiving knowledge from someone else. Education also refers to the knowledge received through schooling or instruction and to the institution of teaching as a whole. Education has a few other senses as a noun.

Education is a word that covers both the act of instructing and the act of learning. It usually refers specifically to the teaching of children or younger people and the learning done by them.

Real-life examples: Elementary schools, high schools, and colleges are institutions focused on education: People are taught important information and life skills at these places. Medical schools, law schools, and driving schools provide more specialized forms of education.

Used in a sentence: The proper education of children is considered important in every country. 

Related to this sense, education refers to the specific level or type of instruction a person has received.

Used in a sentence: He has a high school education. 

Education also means the specific knowledge or scholarship a person has acquired from being taught.

Real-life examples: Doctors have an education in medicine. Chemists have an education in chemistry. Bankers have an education in finance or economics.

Used in a sentence: She has an education in languages and is fluent in French and Italian. 

Education is also used to refer to the process or institution of teaching in general.

Real-life examples: Most teachers have college degrees in education. Nations often devote a portion of their budget to education.

Used in a sentence: My brother decided to pursue a career in education.

Where does  education come from?

The first records of education come from around 1525. It comes from the Latin ēducātiōn-. Education combines the verb educate , meaning “to teach or to train,” and the suffix -ion , which turns a verb into a noun.

Did you know ... ?

What are some other forms related to education ?

• antieducation (adjective)
• noneducation (noun)
• overeducation (noun)
• preeducation (noun)
• proeducation (adjective)
• supereducation (noun)

What are some synonyms for education ?

• instruction

What are some words that share a root or word element with education ? 

• educational

What are some words that often get used in discussing education ?

• elementary school
• high school

How is  education used in real life?

Education is a common word used to refer to teaching and learning. Almost everyone agrees that a person should receive some form of education.

For 80% of foreign business executives, the education and training of France's workforce make France attractive for foreign investment. — Gérard Araud (@GerardAraud) May 11, 2017

Too many of our young people cannot afford a college education and those who are leaving college are faced with crushing debt. — Bernie Sanders (@BernieSanders) June 24, 2015

We need to continuously invest in education. That means early childhood education, AP classes, and investing in New York City’s teachers. — Bill de Blasio (@BilldeBlasio) November 15, 2017

Try using  education !

True or False?

If a person has a college education, that means they have gained knowledge and instruction at a college.

• Election 2024
• Entertainment
• Newsletters
• Photography
• Personal Finance
• AP Investigations
• AP Buyline Personal Finance
• AP Buyline Shopping
• Press Releases
• Israel-Hamas War
• Russia-Ukraine War
• Global elections
• Asia Pacific
• Latin America
• Middle East
• Election Results
• Delegate Tracker
• AP & Elections
• Auto Racing
• 2024 Paris Olympic Games
• Movie reviews
• Book reviews
• Personal finance
• Financial Markets
• Business Highlights
• Financial wellness
• Artificial Intelligence
• Social Media

House passes bill to expand definition of antisemitism amid growing campus protests over Gaza war

Pro-Palestinian protesters camp out in tents at Columbia University on Saturday, April 27, 2024 in New York. With the death toll mounting in the war in Gaza, protesters nationwide are demanding that schools cut financial ties to Israel and divest from companies they say are enabling the conflict. Some Jewish students say the protests have veered into antisemitism and made them afraid to set foot on campus. (AP Photo)

FILE -President of Columbia University Nemat Shafik testifies before the House Committee on Education and the Workforce hearing on “Columbia in Crisis: Columbia University’s Response to Antisemitism” on Capitol Hill in Washington, Wednesday, April 17, 2024. Columbia University president Nemat (Minouche) Shafik is no stranger to navigating complex international issues, having worked at some of the world’s most prominent global financial institutions.(AP Photo/Mariam Zuhaib, File)

• Copy Link copied

WASHINGTON (AP) — The House passed legislation Wednesday that would establish a broader definition of antisemitism for the Department of Education to enforce anti-discrimination laws, the latest response from lawmakers to a nationwide student protest movement over the Israel-Hamas war.

The proposal, which passed 320-91 with some bipartisan support, would codify the International Holocaust Remembrance Alliance’s definition of antisemitism in Title VI of the Civil Rights Act of 1964, a federal anti-discrimination law that bars discrimination based on shared ancestry, ethnic characteristics or national origin. It now goes to the Senate where its fate is uncertain.

Action on the bill was just the latest reverberation in Congress from the protest movement that has swept university campuses. Republicans in Congress have denounced the protests and demanded action to stop them, thrusting university officials into the center of the charged political debate over Israel’s conduct of the war in Gaza. More than 33,000 Palestinians have been killed since the war was launched in October, after Hamas staged a deadly terrorist attack against Israeli civilians.

If passed by the Senate and signed into law, the bill would broaden the legal definition of antisemitism to include the “targeting of the state of Israel, conceived as a Jewish collectivity.” Critics say the move would have a chilling effect on free speech throughout college campuses.

“Speech that is critical of Israel alone does not constitute unlawful discrimination,” Rep. Jerry Nadler, D-N.Y., said during a hearing Tuesday. “By encompassing purely political speech about Israel into Title VI’s ambit, the bill sweeps too broadly.”

Advocates of the proposal say it would provide a much-needed, consistent framework for the Department of Education to police and investigate the rising cases of discrimination and harassment targeted toward Jewish students.

“It is long past time that Congress act to protect Jewish Americans from the scourge of antisemitism on campuses around the country,” Rep. Russell Fry, R-S.C., said Tuesday.

The expanded definition of antisemitism was first adopted in 2016 by the International Holocaust Remembrance Alliance, an intergovernmental group that includes the United States and European Union states, and has been embraced by the State Department under the past three presidential administrations, including Joe Biden’s

Previous bipartisan efforts to codify it into law have failed. But the Oct. 7 terrorist attack by Hamas militants in Israel and the subsequent war in Gaza have reignited efforts to target incidents of antisemitism on college campuses.

Separately, Speaker Mike Johnson announced Tuesday that several House committees will be tasked with a wide probe that ultimately threatens to withhold federal research grants and other government support for universities, placing another pressure point on campus administrators who are struggling to manage pro-Palestinian encampments, allegations of discrimination against Jewish students and questions of how they are integrating free speech and campus safety.

The House investigation follows several high-profile hearings that helped precipitate the resignations of presidents at Harvard and the University of Pennsylvania. And House Republicans promised more scrutiny, saying they were calling on the administrators of Yale, UCLA and the University of Michigan to testify next month.

The House Oversight Committee took it one step further Wednesday, sending a small delegation of Republican members to an encampment at nearby George Washington University in the District of Columbia. GOP lawmakers spent the short visit criticizing the protests and Mayor Muriel Bowser’s refusal to send in the Metropolitan Police Department to disperse the demonstrators.

Bowser on Monday confirmed that the city and the district’s police department had declined the university’s request to intervene. “We did not have any violence to interrupt on the GW campus,” Bowser said, adding that police chief Pamela Smith made the ultimate decision. “This is Washington, D.C., and we are, by design, a place where people come to address the government and their grievances with the government.”

It all comes at a time when college campuses and the federal government are struggling to define exactly where political speech crosses into antisemitism. Dozens of U.S. universities and schools face civil rights investigations by the Education Department over allegations of antisemitism and Islamophobia.

Among the questions campus leaders have struggled to answer is whether phrases like “from the river to the sea, Palestine will be free” should be considered under the definition of antisemitism.

The proposed definition faced strong opposition from several Democratic lawmakers, Jewish organizations as well as free speech advocates.

In a letter sent to lawmakers Friday, the American Civil Liberties Union urged members to vote against the legislation, saying federal law already prohibits antisemitic discrimination and harassment.

“H.R. 6090 is therefore not needed to protect against antisemitic discrimination; instead, it would likely chill free speech of students on college campuses by incorrectly equating criticism of the Israeli government with antisemitism,” the letter stated.

Jeremy Ben-Ami, president of the centrist pro-Israel group J Street, said his organization opposes the bipartisan proposal because he sees it as an “unserious” effort led by Republicans “to continually force votes that divide the Democratic caucus on an issue that shouldn’t be turned into a political football.”

Associated Press writers Ashraf Khalil, Collin Binkley and Stephen Groves contributed to this report.

• Skip to main content
• Keyboard shortcuts for audio player

Campus protests over the Gaza war

House passes bill aimed to combat antisemitism amid college unrest.

Barbara Sprunt

Speaker of the House Mike Johnson visited Columbia University on April 24 to meet with Jewish students and make remarks about concerns that the ongoing demonstrations have become antisemitic. Alex Kent/Getty Images hide caption

Speaker of the House Mike Johnson visited Columbia University on April 24 to meet with Jewish students and make remarks about concerns that the ongoing demonstrations have become antisemitic.

The House of Representatives passed a bill on Wednesday aimed at addressing reports of rising antisemitism on college campuses, where activists angered by Israel's war against Hamas have been protesting for months and more recently set up encampments on campus grounds .

The Antisemitism Awareness Act would see the adoption of the International Holocaust Remembrance Alliance's definition of antisemitism for the enforcement of federal anti-discrimination laws regarding education programs.

The bill passed with a 320-91 vote. Seventy Democrats and 21 Republicans voted against the measure.

The international group defines antisemitism as "a certain perception of Jews, which may be expressed as hatred toward Jews" and gives examples of the definition's application, which includes "accusing Jews as a people of being responsible for real or imagine wrongdoing committed by a single Jewish person or group" and making " dehumanizing, demonizing, or stereotypical allegations about Jews as such or the power of Jews as collective."

Rep. Mike Lawler, R-N.Y., introduced the legislation.

"Right now, without a clear definition of antisemitism, the Department of Education and college administrators are having trouble discerning whether conduct is antisemitic or not, whether the activity we're seeing crosses the line into antisemitic harassment," he said on the House floor before passage.

The bill goes further than an executive order former President Donald Trump signed in 2019 . Opponents argue the measure could restrict free speech.

"This definition adopted by the International Holocaust Remembrance Alliance includes 'contemporary examples of antisemitism'," said Rep. Jerry Nadler in a speech on the House floor ahead of the vote. "The problem is that these examples may include protected speech in some context, particularly with respect to criticism of the state of Israel."

Fellow New York Democrat Rep. Ritchie Torres , one of the 15 Democratic cosponsors of the bill, told NPR he finds that argument unconvincing.

"There's a false narrative that the definition censors criticism of the Israeli government. I consider it complete nonsense," Torres said in an interview with NPR.

"If you can figure out how to critique the policies and practices of the Israeli government without calling for the destruction of Israel itself, then no reasonable person would ever accuse you of antisemitism," he added.

Issue should 'transcend partisan politics'

While members of both parties have criticized reports of antisemitism at the protests, Republicans have made the issue a central political focus.

House Speaker Mike Johnson made a rare visit last week to Columbia University, where demonstrators were demanding the school divest from companies that operate in Israel. Johnson and a handful of GOP lawmakers met with a group of Jewish students.

"They are really concerned that their voices are not being heard when they may complain about being assaulted, being spit on, being told that all Jews should die — and they are not getting any response from the individuals who are literally being paid to protect them," Rep. Anthony D'Esposito, R-N.Y., told NPR of the meeting.

On Tuesday, Johnson held a press conference focused on antisemitism with a group of House Republicans at the U.S. Capitol.

"Antisemitism is a virus and it will spread if it's not stamped out," Johnson said. "We have to act, and House Republicans will speak to this fateful moment with moral clarity."

Rep. Pramila Jayapal, D-Wash., who chairs the House progressive caucus, says Republicans are playing politics.

"Many of these Republicans didn't say a word when Trump and others in Charlottesville and other places were saying truly antisemitic things. But all of a sudden now they want to bring forward bills that divide Democrats and weaponize this," she said.

Torres said he wished Johnson had done a bipartisan event with House Democrats to "present a united front."

"You know, it's impossible to take the politics out of politics, but the fight against all forms of hate, including antisemitism, should transcend partisan politics," he said.

Student protestors chant near an entrance to Columbia University on April 30. Columbia University has restricted access to the school's campus to students residing in residential buildings on campus and employees who provide essential services to campus buildings after protestors took over Hamilton Hall overnight. Michael M. Santiago/Getty Images hide caption

Student protestors chant near an entrance to Columbia University on April 30. Columbia University has restricted access to the school's campus to students residing in residential buildings on campus and employees who provide essential services to campus buildings after protestors took over Hamilton Hall overnight.

Jewish students speak about feeling harassed

Hear from students who met with speaker johnson.

There was increased urgency to move legislation to the floor after lawmakers started hearing stories of Jewish students feeling unwelcome on campuses.

Eliana Goldin, a junior at Columbia and the Jewish Theological Seminary, said the escalation of protests on and around her campus have made her feel unsafe.

"I know many, many people who have been harassed because they wear a Jewish star necklace," Goldin told NPR. Goldin was one student who received a message from Rabbi Elie Buechler of Columbia a week ago.

"The events of the last few days...have made it clear that Columbia University's Public Safety and the NYPD cannot guarantee Jewish students' safety in the face of extreme antisemitism and anarchy," the message read. "It deeply pains me to say that I would strongly recommend you return home as soon as possible and remain home until the reality in and around campus has dramatically improved."

Demonstrators say their protest is peaceful and that some of the antisemitic events that have garnered national attention have come from people outside of the university.

Goldin said she was part of an interaction that got a lot of online attention of someone yelling at her and others to "go back to Poland." She said she was disappointed in the reaction from the broader Columbia community, even though the person was likely not a student.

"I do think if someone were to say, 'go back to Africa' to a Black student, it would one, be abhorrent," Goldin said. "And correctly, the entire Columbia student body would feel outraged at that, and we would all be able to rally around it. But of course, when someone says 'go back to Poland' to a Jew, we don't feel the same outrage and the same unity against that."

Torres said lawmakers should listen to students like Goldin.

"If there are Black students, who claim to experience racism, we rightly respect their experiences. The same would be true of Latino students, the same would be true of Asian students," he said. "If there are Jewish students who are telling us that they do not feel safe, why are we questioning the validity of their experiences? Why are we not affording them the sensitivity that we would have for every other group?"

Columbia University did not respond to NPR about questions about their handling of the protests.

A demonstrator breaks the windows of the front door of the building in order to secure a chain around it to prevent authorities from entering as demonstrators from the pro-Palestine encampment barricade themselves inside Hamilton Hall, an academic building at Columbia University, on April 30. Alex Kent/Getty Images hide caption

A demonstrator breaks the windows of the front door of the building in order to secure a chain around it to prevent authorities from entering as demonstrators from the pro-Palestine encampment barricade themselves inside Hamilton Hall, an academic building at Columbia University, on April 30.

'It just really kind of erodes the soul'

Xavier Westergaard, a Ph.D. student at Columbia, attended the meeting between the House GOP delegation and Jewish students.

"The mood in the room was relief that someone so high up in the government made this a priority," he said, referring to Johnson.

"Jewish students, including myself, have been the victims of physical violence and intimidation. This goes from shoving, spitting, being told to go back to Europe," he said. "It just really kind of erodes the soul if you hear it too many times."

He added: "And this is not just happening outside the gates, on the sidewalk where anyone from anywhere can come and demonstrate. We do have the First Amendment in this country. This was actually on campus. The university has responsibilities to protect their students from harassment on the basis of religion or creed or national origin."

A consistent refrain among protesters is that criticizing the policies of the Israeli government doesn't equate to antisemitism.

Westergaard agrees, but says that's not what he's experiencing.

"I've heard, 'We want all Zionists off campus.' I've heard 'death to the Zionist state, death to Zionists.' And as a Jew, I feel that Zionism and Judaism can be teased apart with a tremendous amount of care and compassion and knowledge," he said. "But it's also just a dog whistle that people use when they're talking about the Jews."

Juliana Castillo, an undergraduate, was also at the meeting with Johnson. She said calls for the safety of students doesn't just include physical well-being.

"There are things like intimidation, like feeling uncomfortable being openly Jewish or taking a direct route across campus," she said. "It doesn't always manifest as a lack of physical safety. Sometimes it manifests as being unwelcome in a class or feeling like people's viewpoints or perspectives are not respected."

She said even isolated incidents of antisemitism that get circulated widely online have a "creeping impact on people."

"Just knowing that something has happened to your friends, or to people you know in a place you're familiar with, makes it difficult to have a sense that this is your campus," she said. "These things do build up."

Bipartisan push on more bills to counter antisemitism

Lawmakers say this bill is just one step — and that there's more action the chamber should take to combat antisemitism.

Torres and Lawler have introduced another bill that would place a monitor on a campus to report back to the federal government on whether the university is complying with Title VI , which prohibits discrimination based on race, color or national origin in places like colleges that receive federal funding.

"A law is only as effective as its enforcement, and the purpose here is to provide an enforcement mechanism where none exist," Torres said. "And I want to be clear: the legislation would empower the federal Department of Education not to impose a monitor on every college or university, only when there's reason to suspect a violation of Title VI."

Meanwhile, House Minority Leader Hakeem Jeffries is urging Johnson to bring the bipartisan Countering Antisemitism Act to the floor.

"The effort to crush antisemitism and hatred in any form is not a Democratic or Republican issue" said Jeffries in a statement.

Letter to Speaker Mike Johnson on the Bipartisan Countering Antisemitism Act. pic.twitter.com/z3weUD54zm — Hakeem Jeffries (@RepJeffries) April 29, 2024

The bill would establish a senior official in the Department of Education to monitor for antisemitism on college campuses and create a national coordinator in the White House to oversee a new interagency task force to counter antisemitism.

"We have negotiated that bill for nine months. It is bipartisan. It's bicameral," said North Carolina Democrat Kathy Manning, who co-chairs the House Bipartisan Task Force for Combating Antisemitism.

Manning was part of a trio of House Democrats who visited Columbia University last week to hear from Jewish students.

Manning points to a study from the American Jewish Committee that found that 46% of American Jews since October 7 say they have altered their behavior out of fear of antisemitism .

"I find that deeply disturbing, that in the United States of America, people are now afraid to be recognized in public as being Jewish," Manning said.

US House passes controversial bill that expands definition of anti-Semitism

Rights groups warn that the definition could further chill freedom of speech as protests continue on college campuses.

The United States House of Representatives has overwhelmingly passed a bill that would expand the federal definition of anti-Semitism, despite opposition from civil liberties groups.

The bill passed the House on Wednesday by a margin of 320 to 91, and it is largely seen as a reaction to the ongoing antiwar protests unfolding on US university campuses. It now goes to the Senate for consideration.

Keep reading

The take: university protests spread across the us, at least 200 arrested at may day clashes in turkey, university gaza protests rage on with columbia arrests and violence at ucla.

If the bill were to become law, it would codify a definition of anti-Semitism created by the International Holocaust Remembrance Alliance (IHRA) in Title VI of the Civil Rights Act of 1964.

That is a federal anti-discrimination law that bars discrimination based on shared ancestry, ethnic characteristics or national origin. Adding IHRA’s definition to the law would allow the federal Department of Education to restrict funding and other resources to campuses perceived as tolerating anti-Semitism.

But critics warn IHRA’s definition could be used to stifle campus protests against Israel’s war in Gaza, which has claimed the lives of 34,568 Palestinians so far.

What is the definition?

IHRA’s working definition of anti-Semitism is “a certain perception of Jews, which may be expressed as hatred toward Jews. Rhetorical and physical manifestations of anti-Semitism are directed toward Jewish or non-Jewish individuals and/or their property, toward Jewish community institutions and religious facilities”.

According to the IHRA, that definition also encompasses the “targeting of the state of Israel, conceived as a Jewish collectivity”.

The group also includes certain examples in its definition to illustrate anti-Semitism. Saying, for instance, that “the existence of a State of Israel is a racist endeavor” would be deemed anti-Semitic under its terms. The definition also bars any comparison between “contemporary Israeli policy” and “that of the Nazis”.

However, IHRA does specify that “criticism of Israel similar to that leveled against any other country cannot be regarded as anti-Semitic”.

Bipartisan criticism

Rights groups, however, have raised concerns the definition nevertheless conflates criticism of the state of Israel and Zionism with anti-Semitism.

In a letter sent to lawmakers on Friday, the American Civil Liberties Union (ACLU) urged House members to vote against the legislation, saying federal law already prohibits anti-Semitic discrimination and harassment.

The bill is “therefore not needed to protect against anti-Semitic discrimination”, the letter said.

“Instead, it would likely chill free speech of students on college campuses by incorrectly equating criticism of the Israeli government with anti-Semitism.”

Those fears were echoed within the House of Representatives itself. During a hearing on Tuesday, Representative Jerry Nadler, a Democrat, said the scope of the definition was too broad.

“By encompassing purely political speech about Israel into Title VI’s ambit, the bill sweeps too broadly,” he said.

Representative Thomas Massie, a Republican, also criticised the bill in a post on the social media platform X, noting that it only referred to the IHRA definition, without providing the exact language or stating clearly which parts would be enshrined into law.

“To find the legally adopted definition of anti-Semitism, one must go to [the IHRA website],” he wrote.

“Not only is the definition listed there, but one also finds specific examples of anti-Semitic speech. Are those examples made part of the law as well?”

Concerns on campus

The IHRA adopted its current definition of anti-Semitism in 2016, and its framing has been embraced by the US State Department under President Joe Biden and his two predecessors.

The vote on Wednesday comes as renewed protests have swept across college campuses in opposition to Israel’s war in Gaza. April has seen the spread of encampments on university lawns, as students call for university leaders to divest from Israel and for government officials to call for a ceasefire.

The Biden administration and other top Washington officials have pledged steadfast support for Israel, despite mounting humanitarian concerns over its military campaign.

US lawmakers also have upped the pressure on university administrators to quash the protests, which they have portrayed as inherently anti-Semitic.

Protest leaders across the country, however, have rejected that characterisation. Instead, they accuse administrators and local officials of conflating support for Palestinians with anti-Semitism.

They also have said their rights are being trampled by administrators who seek to appease lawmakers, prompting at times violent police crackdowns on the encampments.

On Tuesday, House Speaker Mike Johnson announced that several House committees would be tasked with a probe into alleged campus anti-Semitism. But critics fear the investigation could ultimately threaten to withhold federal research grants and other government support from the universities where the protests are occurring.

• India Today
• Business Today
• Reader’s Digest
• Harper's Bazaar
• Brides Today
• Cosmopolitan
• Aaj Tak Campus
• India Today Hindi

IPM aptitude test: How to attempt the logical reasoning section

Here are some tips for effectively tackling the logical reasoning section of the ipm aptitude test..

Listen to Story

IPM (Integrated Programme in Management) offered by IIMs is aimed at students who have passed class 12/Higher Secondary or equivalent from schools across India. Its mission is to produce contextually relevant, socially-conscious managers and leaders with a foundation of world-class education in social sciences followed by management education.

Pradeep Pandey, Academic Head at T.I.M.E., has provided insights into comprehending the logical reasoning section of the IPM aptitude test.

Management is becoming one of the highly sought-after career options owing to the lucrative salaries and great career prospects.

There are three entrance tests for IPM, IPMAT, JIPMAT and IPMAT Rohtak. The IPMAT (Integrated Programme in Management Aptitude Test) is a national-level exam conducted by IIM Indore for admission to its five-year integrated programme, JIPMAT is for admission to the 5-Year Integrated Programme in Management in IIM Bodh Gaya and IIM Jammu, whereas IPMAT Rohtak is for a similar programme in IIM Rohtak.

The logical reasoning is one of the marks fetching sections in JIPMAT and IPMAT Rohtak, whereas IPM Indore does not have a logical reasoning (LR) section.

Last year the candidates found the difficulty level of the LR section in the range of easy-moderate in JIPMAT. Since candidates recently had the experience of the relatively easy IPMAT Rohtak 2023, they were expecting a similar paper in JIPMAT too. But JIPMAT had a few surprises and was not as easy a nut to crack. It was tougher than JIPMAT 2022.

However, the overall difficulty level can not be said to have exceeded the moderate level.

IPMAT Indore: IPMAT Indore 2023 stuck to its pattern from previous years. The paper had 30 MCQs, 15 short answer questions from Quantitative ability and 45 questions from Verbal ability. The duration of the exam is 120 minutes. Also, there was a negative marking of one mark for MCQ and none for short answer questions. Some of the Data Interpretation questions might be asked in the Quantitative Aptitude section.

JIPMAT: There are 3 sections in this exam. Last year, Quantitative ability had 33 questions, Logical Reasoning had 33 Questions and Verbal ability had 34 questions. So, the paper had a total of 100 questions with 4 marks for the right answer and -1 for the wrong answer. The Logical Reasoning section was a doable section with moderate-level questions.

In JIPMAT 2023, there were 3 sets of DI - one set on Pie charts and two on data given in the form of tables.

One element of surprise was the presence of a pure arithmetic-type question in the LR section - there was a question about time and distance. Other questions included Coding-Decoding and missing numbers. There were 2–3 questions from Clocks and Calendars, 3 questions from number series and one question from Critical Reasoning. A good attempt in this section can be considered to be in the range of 28–30 questions.

IPMAT Rohtak: There were no surprises in IPMAT Rohtak 2023 in terms of pattern. The exam had 3 sections with 40 questions each. There were 4 marks for the correct answer and -1 for the wrong answer. There was no sectional time limit. The LR section was the easiest of the three sections and good attempts could again be considered to be around 35.

There were almost 5 questions about blood relations, and a few questions from Coding-decoding, Directions, Quantitative comparison, and Syllogism. There were three sets of 4–5 questions each, from a Linear arrangement, a Circular arrangement and a Matrix arrangement, which were quite straightforward. There were no questions about data interpretation.

There were also 5–6 questions about data sufficiency which were quite tricky. Statement-Conclusion, Assumptions, Strengthen-weaken arguments and cause and effect questions were also present.