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Methodology

Inductive Reasoning | Types, Examples, Explanation

Published on January 12, 2022 by Pritha Bhandari . Revised on June 22, 2023.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning , where you go from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Note Inductive reasoning is often confused with deductive reasoning. However, in deductive reasoning, you make inferences by going from general premises to specific conclusions.

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What is inductive reasoning, inductive reasoning in research, types of inductive reasoning, inductive generalization, statistical generalization, causal reasoning, sign reasoning, analogical reasoning, inductive vs. deductive reasoning, other interesting articles, frequently asked questions about inductive reasoning.

Inductive reasoning is a logical approach to making inferences, or conclusions. People often use inductive reasoning informally in everyday situations.

You may have come across inductive logic examples that come in a set of three statements. These start with one specific observation, add a general pattern, and end with a conclusion.

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In inductive research, you start by making observations or gathering data. Then , you take a broad view of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

You distribute a survey to pet owners. You ask about the type of animal they have and any behavioral changes they’ve noticed in their pets since they started working from home. These data make up your observations.

To analyze your data, you create a procedure to categorize the survey responses so you can pick up on repeated themes. You notice a pattern : most pets became more needy and clingy or agitated and aggressive.

Inductive reasoning is commonly linked to qualitative research , but both quantitative and qualitative research use a mix of different types of reasoning.

There are many different types of inductive reasoning that people use formally or informally, so we’ll cover just a few in this article:

Inductive reasoning generalizations can vary from weak to strong, depending on the number and quality of observations and arguments used.

Inductive generalizations use observations about a sample to come to a conclusion about the population it came from.

Inductive generalizations are also called induction by enumeration.

• The flamingos here are all pink.
• All flamingos I’ve ever seen are pink.
• All flamingos must be pink.

Inductive generalizations are evaluated using several criteria:

• Large sample: Your sample should be large for a solid set of observations.
• Random sampling: Probability sampling methods let you generalize your findings.
• Variety: Your observations should be externally valid .
• Counterevidence: Any observations that refute yours falsify your generalization.

Statistical generalizations use specific numbers to make statements about populations, while non-statistical generalizations aren’t as specific.

These generalizations are a subtype of inductive generalizations, and they’re also called statistical syllogisms.

Here’s an example of a statistical generalization contrasted with a non-statistical generalization.

Causal reasoning means making cause-and-effect links between different things.

A causal reasoning statement often follows a standard setup:

• You start with a premise about a correlation (two events that co-occur).
• You put forward the specific direction of causality or refute any other direction.
• You conclude with a causal statement about the relationship between two things.
• All of my white clothes turn pink when I put a red cloth in the washing machine with them.
• My white clothes don’t turn pink when I wash them on their own.
• Putting colorful clothes with light colors causes the colors to run and stain the light-colored clothes.

Good causal inferences meet a couple of criteria:

• Direction: The direction of causality should be clear and unambiguous based on your observations.
• Strength: There’s ideally a strong relationship between the cause and the effect.

Sign reasoning involves making correlational connections between different things.

Using inductive reasoning, you infer a purely correlational relationship where nothing causes the other thing to occur. Instead, one event may act as a “sign” that another event will occur or is currently occurring.

• Every time Punxsutawney Phil casts a shadow on Groundhog Day, winter lasts six more weeks.
• Punxsutawney Phil doesn’t cause winter to be extended six more weeks.
• His shadow is a sign that we’ll have six more weeks of wintery weather.

It’s best to be careful when making correlational links between variables . Build your argument on strong evidence, and eliminate any confounding variables , or you may be on shaky ground.

Analogical reasoning means drawing conclusions about something based on its similarities to another thing. You first link two things together and then conclude that some attribute of one thing must also hold true for the other thing.

Analogical reasoning can be literal (closely similar) or figurative (abstract), but you’ll have a much stronger case when you use a literal comparison.

Analogical reasoning is also called comparison reasoning.

• Humans and laboratory rats are extremely similar biologically, sharing over 90% of their DNA.
• Lab rats show promising results when treated with a new drug for managing Parkinson’s disease.
• Therefore, humans will also show promising results when treated with the drug.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

In deductive reasoning, you make inferences by going from general premises to specific conclusions. You start with a theory, and you might develop a hypothesis that you test empirically. You collect data from many observations and use a statistical test to come to a conclusion about your hypothesis.

Inductive research is usually exploratory in nature, because your generalizations help you develop theories. In contrast, deductive research is generally confirmatory.

Sometimes, both inductive and deductive approaches are combined within a single research study.

Inductive reasoning approach

You begin by using qualitative methods to explore the research topic, taking an inductive reasoning approach. You collect observations by interviewing workers on the subject and analyze the data to spot any patterns. Then, you develop a theory to test in a follow-up study.

Deductive reasoning approach

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square goodness of fit test
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalization : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalization: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

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Guide To Inductive & Deductive Reasoning

Induction vs. Deduction

October 15, 2008, by The Critical Thinking Co. Staff

Induction and deduction are pervasive elements in critical thinking. They are also somewhat misunderstood terms. Arguments based on experience or observation are best expressed inductively , while arguments based on laws or rules are best expressed deductively . Most arguments are mainly inductive. In fact, inductive reasoning usually comes much more naturally to us than deductive reasoning.

Inductive reasoning moves from specific details and observations (typically of nature) to the more general underlying principles or process that explains them (e.g., Newton's Law of Gravity). It is open-ended and exploratory, especially at the beginning. The premises of an inductive argument are believed to support the conclusion, but do not ensure it. Thus, the conclusion of an induction is regarded as a hypothesis. In the Inductive method, also called the scientific method , observation of nature is the authority.

In contrast, deductive reasoning typically moves from general truths to specific conclusions. It opens with an expansive explanation (statements known or believed to be true) and continues with predictions for specific observations supporting it. Deductive reasoning is narrow in nature and is concerned with testing or confirming a hypothesis. It is dependent on its premises. For example, a false premise can lead to a false result, and inconclusive premises will also yield an inconclusive conclusion. Deductive reasoning leads to a confirmation (or not) of our original theories. It guarantees the correctness of a conclusion. Logic is the authority in the deductive method.

If you can strengthen your argument or hypothesis by adding another piece of information, you are using inductive reasoning. If you cannot improve your argument by adding more evidence, you are employing deductive reasoning.

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Inductive reasoning: conclusion merely likely Inductive reasoning begins with observations that are specific and limited in scope, and proceeds to a generalized conclusion that is likely, but not certain, in light of accumulated evidence. You could say that inductive reasoning moves from the specific to the general. Much scientific research is carried out by the inductive method: gathering evidence, seeking patterns, and forming a hypothesis or theory to explain what is seen.

Conclusions reached by the inductive method are not logical necessities; no amount of inductive evidence guarantees the conclusion. This is because there is no way to know that all the possible evidence has been gathered, and that there exists no further bit of unobserved evidence that might invalidate my hypothesis. Thus, while the newspapers might report the conclusions of scientific research as absolutes, scientific literature itself uses more cautious language, the language of inductively reached, probable conclusions:

What we have seen is the ability of these cells to feed the blood vessels of tumors and to heal the blood vessels surrounding wounds. The findings suggest that these adult stem cells may be an ideal source of cells for clinical therapy. For example, we can envision the use of these stem cells for therapies against cancer tumors [...].

Because inductive conclusions are not logical necessities, inductive arguments are not simply true. Rather, they are cogent: that is, the evidence seems complete, relevant, and generally convincing, and the conclusion is therefore probably true. Nor are inductive arguments simply false; rather, they are  not cogent .

It is an important difference from deductive reasoning that, while inductive reasoning cannot yield an absolutely certain conclusion, it can actually increase human knowledge (it is  ampliative ). It can make predictions about future events or as-yet unobserved phenomena.

For example, Albert Einstein observed the movement of a pocket compass when he was five years old and became fascinated with the idea that something invisible in the space around the compass needle was causing it to move. This observation, combined with additional observations (of moving trains, for example) and the results of logical and mathematical tools (deduction), resulted in a rule that fit his observations and could predict events that were as yet unobserved.

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• Deductive and Inductive Arguments | Internet Encyclopedia of Philosophy

" An  inductive argument  can be affected by acquiring new premises (evidence), but a deductive  argument  cannot be. For  example , this is a reasonably strong  inductive argument : ... If the arguer believes that the truth of the premises definitely establishes the truth of the conclusion, then the  argument  is deductive."

• Examples of Inductive Reasoning (Click link and scroll down for examples)

" The term " inductive reasoning " refers to reasoning that takes specific information and makes a broader generalization that is considered probable, allowing for the fact that the conclusion may not be accurate."

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Unit 1: What Is Philosophy?

LOGOS: Critical Thinking, Arguments, and Fallacies

Heather Wilburn, Ph.D

Critical Thinking:

With respect to critical thinking, it seems that everyone uses this phrase. Yet, there is a fear that this is becoming a buzz-word (i.e. a word or phrase you use because it’s popular or enticing in some way). Ultimately, this means that we may be using the phrase without a clear sense of what we even mean by it. So, here we are going to think about what this phrase might mean and look at some examples. As a former colleague of mine, Henry Imler, explains:

By critical thinking, we refer to thinking that is recursive in nature. Any time we encounter new information or new ideas, we double back and rethink our prior conclusions on the subject to see if any other conclusions are better suited. Critical thinking can be contrasted with Authoritarian thinking. This type of thinking seeks to preserve the original conclusion. Here, thinking and conclusions are policed, as to question the system is to threaten the system. And threats to the system demand a defensive response. Critical thinking is short-circuited in authoritarian systems so that the conclusions are conserved instead of being open for revision. [1]

A condition for being recursive is to be open and not arrogant. If we come to a point where we think we have a handle on what is True, we are no longer open to consider, discuss, or accept information that might challenge our Truth. One becomes closed off and rejects everything that is different or strange–out of sync with one’s own Truth. To be open and recursive entails a sense of thinking about your beliefs in a critical and reflective way, so that you have a chance to either strengthen your belief system or revise it if needed. I have been teaching philosophy and humanities classes for nearly 20 years; critical thinking is the single most important skill you can develop. In close but second place is communication, In my view, communication skills follow as a natural result of critical thinking because you are attempting to think through and articulate stronger and rationally justified views. At the risk of sounding cliche, education isn’t about instilling content; it is about learning how to think.

In your philosophy classes your own ideas and beliefs will very likely be challenged. This does not mean that you will be asked to abandon your beliefs, but it does mean that you might be asked to defend them. Additionally, your mind will probably be twisted and turned about, which can be an uncomfortable experience. Yet, if at all possible, you should cherish these experiences and allow them to help you grow as a thinker. To be challenged and perplexed is difficult; however, it is worthwhile because it compels deeper thinking and more significant levels of understanding. In turn, thinking itself can transform us not only in thought, but in our beliefs, and our actions. Hannah Arendt, a social and political philosopher that came to the United States in exile during WWII, relates the transformative elements of philosophical thinking to Socrates. She writes:

Socrates…who is commonly said to have believed in the teachability of virtue, seems to have held that talking and thinking about piety, justice, courage, and the rest were liable to make men more pious, more just, more courageous, even though they were not given definitions or “values” to direct their further conduct. [2]

Thinking and communication are transformative insofar as these activities have the potential to alter our perspectives and, thus, change our behavior. In fact, Arendt connects the ability to think critically and reflectively to morality. As she notes above, morality does not have to give a predetermined set of rules to affect our behavior. Instead, morality can also be related to the open and sometimes perplexing conversations we have with others (and ourselves) about moral issues and moral character traits. Theodor W. Adorno, another philosopher that came to the United States in exile during WWII, argues that autonomous thinking (i.e. thinking for oneself) is crucial if we want to prevent the occurrence of another event like Auschwitz, a concentration camp where over 1 million individuals died during the Holocaust. [3] To think autonomously entails reflective and critical thinking—a type of thinking rooted in philosophical activity and a type of thinking that questions and challenges social norms and the status quo. In this sense thinking is critical of what is, allowing us to think beyond what is and to think about what ought to be, or what ought not be. This is one of the transformative elements of philosophical activity and one that is useful in promoting justice and ethical living.

With respect to the meaning of education, the German philosopher Hegel uses the term bildung, which means education or upbringing, to indicate the differences between the traditional type of education that focuses on facts and memorization, and education as transformative. Allen Wood explains how Hegel uses the term bildung: it is “a process of self-transformation and an acquisition of the power to grasp and articulate the reasons for what one believes or knows.” [4] If we think back through all of our years of schooling, particularly those subject matters that involve the teacher passing on information that is to be memorized and repeated, most of us would be hard pressed to recall anything substantial. However, if the focus of education is on how to think and the development of skills include analyzing, synthesizing, and communicating ideas and problems, most of us will use those skills whether we are in the field of philosophy, politics, business, nursing, computer programming, or education. In this sense, philosophy can help you develop a strong foundational skill set that will be marketable for your individual paths. While philosophy is not the only subject that will foster these skills, its method is one that heavily focuses on the types of activities that will help you develop such skills.

Let’s turn to discuss arguments. Arguments consist of a set of statements, which are claims that something is or is not the case, or is either true or false. The conclusion of your argument is a statement that is being argued for, or the point of view being argued for. The other statements serve as evidence or support for your conclusion; we refer to these statements as premises. It’s important to keep in mind that a statement is either true or false, so questions, commands, or exclamations are not statements. If we are thinking critically we will not accept a statement as true or false without good reason(s), so our premises are important here. Keep in mind the idea that supporting statements are called premises and the statement that is being supported is called the conclusion. Here are a couple of examples:

Example 1: Capital punishment is morally justifiable since it restores some sense of

balance to victims or victims’ families.

Let’s break it down so it’s easier to see in what we might call a typical argument form:

Premise: Capital punishment restores some sense of balance to victims or victims’ families.

Conclusion: Capital punishment is morally justifiable.

Example 2 : Because innocent people are sometimes found guilty and potentially

executed, capital punishment is not morally justifiable.

Premise: Innocent people are sometimes found guilty and potentially executed.

Conclusion: Capital punishment is not morally justifiable.

It is worth noting the use of the terms “since” and “because” in these arguments. Terms or phrases like these often serve as signifiers that we are looking at evidence, or a premise.

Check out another example:

Example 3 : All human beings are mortal. Heather is a human being. Therefore,

Heather is mortal.

Premise 1: All human beings are mortal.

Premise 2: Heather is a human being.

Conclusion: Heather is mortal.

In this example, there are a couple of things worth noting: First, there can be more than one premise. In fact, you could have a rather complex argument with several premises. If you’ve written an argumentative paper you may have encountered arguments that are rather complex. Second, just as the arguments prior had signifiers to show that we are looking at evidence, this argument has a signifier (i.e. therefore) to demonstrate the argument’s conclusion.

So many arguments!!! Are they all equally good?

No, arguments are not equally good; there are many ways to make a faulty argument. In fact, there are a lot of different types of arguments and, to some extent, the type of argument can help us figure out if the argument is a good one. For a full elaboration of arguments, take a logic class! Here’s a brief version:

Deductive Arguments: in a deductive argument the conclusion necessarily follows the premises. Take argument Example 3 above. It is absolutely necessary that Heather is a mortal, if she is a human being and if mortality is a specific condition for being human. We know that all humans die, so that’s tight evidence. This argument would be a very good argument; it is valid (i.e the conclusion necessarily follows the premises) and it is sound (i.e. all the premises are true).

Inductive Arguments : in an inductive argument the conclusion likely (at best) follows the premises. Let’s have an example:

Example 4 : 98.9% of all TCC students like pizza. You are a TCC student. Thus, you like pizza.

Premise 1: 98.9% of all TCC students like pizza

Premise 2: You are a TCC student.

Conclusion: You like pizza. (*Thus is a conclusion indicator)

In this example, the conclusion doesn’t necessarily follow; it likely follows. But you might be part of that 1.1% for whatever reason. Inductive arguments are good arguments if they are strong. So, instead of saying an inductive argument is valid, we say it is strong. You can also use the term sound to describe the truth of the premises, if they are true. Let’s suppose they are true and you absolutely love Hideaway pizza. Let’s also assume you are a TCC student. So, the argument is really strong and it is sound.

There are many types of inductive argument, including: causal arguments, arguments based on probabilities or statistics, arguments that are supported by analogies, and arguments that are based on some type of authority figure. So, when you encounter an argument based on one of these types, think about how strong the argument is. If you want to see examples of the different types, a web search (or a logic class!) will get you where you need to go.

Some arguments are faulty, not necessarily because of the truth or falsity of the premises, but because they rely on psychological and emotional ploys. These are bad arguments because people shouldn’t accept your conclusion if you are using scare tactics or distracting and manipulating reasoning. Arguments that have this issue are called fallacies. There are a lot of fallacies, so, again, if you want to know more a web search will be useful. We are going to look at several that seem to be the most relevant for our day-to-day experiences.

• Inappropriate Appeal to Authority : We are definitely going to use authority figures in our lives (e.g. doctors, lawyers, mechanics, financial advisors, etc.), but we need to make sure that the authority figure is a reliable one.

Things to look for here might include: reputation in the field, not holding widely controversial views, experience, education, and the like. So, if we take an authority figure’s word and they’re not legit, we’ve committed the fallacy of appeal to authority.

Example 5 : I think I am going to take my investments to Voya. After all, Steven Adams advocates for Voya in an advertisement I recently saw.

If we look at the criteria for evaluating arguments that appeal to authority figures, it is pretty easy to see that Adams is not an expert in the finance field. Thus, this is an inappropropriate appeal to authority.

• Slippery Slope Arguments : Slippery slope arguments are found everywhere it seems. The essential characteristic of a slippery slope argument is that it uses problematic premises to argue that doing ‘x’ will ultimately lead to other actions that are extreme, unlikely, and disastrous. You can think of this type of argument as a faulty chain of events or domino effect type of argument.

Example 6 : If you don’t study for your philosophy exam you will not do well on the exam. This will lead to you failing the class. The next thing you know you will have lost your scholarship, dropped out of school, and will be living on the streets without any chance of getting a job.

While you should certainly study for your philosophy exam, if you don’t it is unlikely that this will lead to your full economic demise.

One challenge to evaluating slippery slope arguments is that they are predictions, so we cannot be certain about what will or will not actually happen. But this chain of events type of argument should be assessed in terms of whether the outcome will likely follow if action ‘x” is pursued.

• Faulty Analogy : We often make arguments based on analogy and these can be good arguments. But we often use faulty reasoning with analogies and this is what we want to learn how to avoid.

When evaluating an argument that is based on an analogy here are a few things to keep in mind: you want to look at the relevant similarities and the relevant differences between the things that are being compared. As a general rule, if there are more differences than similarities the argument is likely weak.

Example 7 : Alcohol is legal. Therefore, we should legalize marijuana too.

So, the first step here is to identify the two things being compared, which are alcohol and marijuana. Next, note relevant similarities and differences. These might include effects on health, community safety, economic factors, criminal justice factors, and the like.

This is probably not the best argument in support for marijuana legalization. It would seem that one could just as easily conclude that since marijuana is illegal, alcohol should be too. In fact, one might find that alcohol is an often abused and highly problematic drug for many people, so it is too risky to legalize marijuana if it is similar to alcohol.

• Appeal to Emotion : Arguments should be based on reason and evidence, not emotional tactics. When we use an emotional tactic, we are essentially trying to manipulate someone into accepting our position by evoking pity or fear, when our positions should actually be backed by reasonable and justifiable evidence.

Example 8 : Officer please don’t give me a speeding ticket. My girlfriend broke up with me last night, my alarm didn’t go off this morning, and I’m late for class.

While this is a really horrible start to one’s day, being broken up with and an alarm malfunctioning is not a justifiable reason for speeding.

Example 9 : Professor, I’d like you to remember that my mother is a dean here at TCC. I’m sure that she will be very disappointed if I don’t receive an A in your class.

This is a scare tactic and is not a good way to make an argument. Scare tactics can come in the form of psychological or physical threats; both forms are to be avoided.

• Appeal to Ignorance : This fallacy occurs when our argument relies on lack of evidence when evidence is actually needed to support a position.

Example 10 : No one has proven that sasquatch doesn’t exist; therefore it does exist.

Example 11 : No one has proven God exists; therefore God doesn’t exist.

The key here is that lack of evidence against something cannot be an argument for something. Lack of evidence can only show that we are ignorant of the facts.

• Straw Man : A straw man argument is a specific type of argument that is intended to weaken an opponent’s position so that it is easier to refute. So, we create a weaker version of the original argument (i.e. a straw man argument), so when we present it everyone will agree with us and denounce the original position.

Example 12 : Women are crazy arguing for equal treatment. No one wants women hanging around men’s locker rooms or saunas.

This is a misrepresentation of arguments for equal treatment. Women (and others arguing for equal treatment) are not trying to obtain equal access to men’s locker rooms or saunas.

The best way to avoid this fallacy is to make sure that you are not oversimplifying or misrepresenting others’ positions. Even if we don’t agree with a position, we want to make the strongest case against it and this can only be accomplished if we can refute the actual argument, not a weakened version of it. So, let’s all bring the strongest arguments we have to the table!

• Red Herring : A red herring is a distraction or a change in subject matter. Sometimes this is subtle, but if you find yourself feeling lost in the argument, take a close look and make sure there is not an attempt to distract you.

Example 13 : Can you believe that so many people are concerned with global warming? The real threat to our country is terrorism.

It could be the case that both global warming and terrorism are concerns for us. But the red herring fallacy is committed when someone tries to distract you from the argument at hand by bringing up another issue or side-stepping a question. Politicians are masters at this, by the way.

• Appeal to the Person : This fallacy is also referred to as the ad hominem fallacy. We commit this fallacy when we dismiss someone’s argument or position by attacking them instead of refuting the premises or support for their argument.

Example 14 : I am not going to listen to what Professor ‘X’ has to say about the history of religion. He told one of his previous classes he wasn’t religious.

The problem here is that the student is dismissing course material based on the professor’s religious views and not evaluating the course content on its own ground.

To avoid this fallacy, make sure that you target the argument or their claims and not the person making the argument in your rebuttal.

• Hasty Generalization : We make and use generalizations on a regular basis and in all types of decisions. We rely on generalizations when trying to decide which schools to apply to, which phone is the best for us, which neighborhood we want to live in, what type of job we want, and so on. Generalizations can be strong and reliable, but they can also be fallacious. There are three main ways in which a generalization can commit a fallacy: your sample size is too small, your sample size is not representative of the group you are making a generalization about, or your data could be outdated.

Example 15 : I had horrible customer service at the last Starbucks I was at. It is clear that Starbucks employees do not care about their customers. I will never visit another Starbucks again.

The problem with this generalization is that the claim made about all Starbucks is based on one experience. While it is tempting to not spend your money where people are rude to their customers, this is only one employee and presumably doesn’t reflect all employees or the company as a whole. So, to make this a stronger generalization we would want to have a larger sample size (multiple horrible experiences) to support the claim. Let’s look at a second hasty generalization:

Example 16 : I had horrible customer service at the Starbucks on 81st street. It is clear that Starbucks employees do not care about their customers. I will never visit another Starbucks again.

The problem with this generalization mirrors the previous problem in that the claim is based on only one experience. But there’s an additional issue here as well, which is that the claim is based off of an experience at one location. To make a claim about the whole company, our sample group needs to be larger than one and it needs to come from a variety of locations.

• Begging the Question : An argument begs the question when the argument’s premises assume the conclusion, instead of providing support for the conclusion. One common form of begging the question is referred to as circular reasoning.

Example 17 : Of course, everyone wants to see the new Marvel movie is because it is the most popular movie right now!

The conclusion here is that everyone wants to see the new Marvel movie, but the premise simply assumes that is the case by claiming it is the most popular movie. Remember the premise should give reasons for the conclusion, not merely assume it to be true.

• Equivocation : In the English language there are many words that have different meanings (e.g. bank, good, right, steal, etc.). When we use the same word but shift the meaning without explaining this move to your audience, we equivocate the word and this is a fallacy. So, if you must use the same word more than once and with more than one meaning you need to explain that you’re shifting the meaning you intend. Although, most of the time it is just easier to use a different word.

Example 18 : Yes, philosophy helps people argue better, but should we really encourage people to argue? There is enough hostility in the world.

Here, argue is used in two different senses. The meaning of the first refers to the philosophical meaning of argument (i.e. premises and a conclusion), whereas the second sense is in line with the common use of argument (i.e. yelling between two or more people, etc.).

• Henry Imler, ed., Phronesis An Ethics Primer with Readings, (2018). 7-8. ↵
• Arendt, Hannah, “Thinking and Moral Considerations,” Social Research, 38:3 (1971: Autumn): 431. ↵
• Theodor W. Adorno, “Education After Auschwitz,” in Can One Live After Auschwitz, ed. by Rolf Tiedemann, trans. by Rodney Livingstone (Stanford: Stanford University Press, 2003): 23. ↵
• Allen W. Wood, “Hegel on Education,” in Philosophers on Education: New Historical Perspectives, ed. Amelie O. Rorty (London: Routledge 1998): 302. ↵

LOGOS: Critical Thinking, Arguments, and Fallacies Copyright © 2020 by Heather Wilburn, Ph.D is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Inductive Reasoning

LESSON SUMMARY

This lesson shows how to recognize and construct an inductive argument. These arguments move from specific facts to general conclusions by using common sense and/or past experience.

Induction is the process of reasoning from the specific (particular facts or instances) to the general (principles, theories, rules). It uses two premises that support the probable truth of the conclusion. Thus, an inductive argument looks like this: If A is true and B is true, then C is probably true.

How can you determine or measure what is probable or improbable? By using two things:

1. past experience

2. common sense

Past experience tells you what you might be able to expect. For instance, "for the past three weeks, my colleague has showed up a half hour late for work. Today, she will probably be late, too." Common sense allows you to draw an inference, or a "smart guess," based on the premises, such as, "They need five people on the team. I'm one of the strongest of the seven players at the tryouts. It's likely that I will be picked for the team."

Because you must make a leap from the premises to the truth of the conclusion, inductive reasoning is more likely to fail and produce fallacies, such as a hasty conclusion fallacy (see Lesson 15 to learn about these fallacies). Even so, most reasoning is inductive. One of the basic theories of modern biology, cell theory, is a product of inductive reasoning. It states that because every organism that has been observed is made up of cells, it is most likely that all living things are made up of cells.

There are two forms of inductive arguments. Those that compare one thing, event, or idea to another to see if they are similar are called comparative arguments. Those that try to determine cause from effect are causal arguments.

Continue reading here: Chicken and Egg Confusing Cause and Effect

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Readers' Questions

What is the goal of inductive thinking?

Is radiant thinking inductive?

Pursuing Truth: A Guide to Critical Thinking

Chapter 2 arguments.

The fundamental tool of the critical thinker is the argument. For a good example of what we are not talking about, consider a bit from a famous sketch by Monty Python’s Flying Circus : 3

2.1 Identifying Arguments

People often use “argument” to refer to a dispute or quarrel between people. In critical thinking, an argument is defined as

A set of statements, one of which is the conclusion and the others are the premises.

There are three important things to remember here:

• Arguments contain statements.
• They have a conclusion.
• They have at least one premise

Arguments contain statements, or declarative sentences. Statements, unlike questions or commands, have a truth value. Statements assert that the world is a particular way; questions do not. For example, if someone asked you what you did after dinner yesterday evening, you wouldn’t accuse them of lying. When the world is the way that the statement says that it is, we say that the statement is true. If the statement is not true, it is false.

One of the statements in the argument is called the conclusion. The conclusion is the statement that is intended to be proved. Consider the following argument:

Calculus II will be no harder than Calculus I. Susan did well in Calculus I. So, Susan should do well in Calculus II.

Here the conclusion is that Susan should do well in Calculus II. The other two sentences are premises. Premises are the reasons offered for believing that the conclusion is true.

2.1.1 Standard Form

Now, to make the argument easier to evaluate, we will put it into what is called “standard form.” To put an argument in standard form, write each premise on a separate, numbered line. Draw a line underneath the last premise, the write the conclusion underneath the line.

• Calculus II will be no harder than Calculus I.
• Susan did well in Calculus I.
• Susan should do well in Calculus II.

Now that we have the argument in standard form, we can talk about premise 1, premise 2, and all clearly be referring to the same thing.

2.1.2 Indicator Words

Unfortunately, when people present arguments, they rarely put them in standard form. So, we have to decide which statement is intended to be the conclusion, and which are the premises. Don’t make the mistake of assuming that the conclusion comes at the end. The conclusion is often at the beginning of the passage, but could even be in the middle. A better way to identify premises and conclusions is to look for indicator words. Indicator words are words that signal that statement following the indicator is a premise or conclusion. The example above used a common indicator word for a conclusion, ‘so.’ The other common conclusion indicator, as you can probably guess, is ‘therefore.’ This table lists the indicator words you might encounter.

Each argument will likely use only one indicator word or phrase. When the conlusion is at the end, it will generally be preceded by a conclusion indicator. Everything else, then, is a premise. When the conclusion comes at the beginning, the next sentence will usually be introduced by a premise indicator. All of the following sentences will also be premises.

For example, here’s our previous argument rewritten to use a premise indicator:

Susan should do well in Calculus II, because Calculus II will be no harder than Calculus I, and Susan did well in Calculus I.

Sometimes, an argument will contain no indicator words at all. In that case, the best thing to do is to determine which of the premises would logically follow from the others. If there is one, then it is the conclusion. Here is an example:

Spot is a mammal. All dogs are mammals, and Spot is a dog.

The first sentence logically follows from the others, so it is the conclusion. When using this method, we are forced to assume that the person giving the argument is rational and logical, which might not be true.

2.1.3 Non-Arguments

One thing that complicates our task of identifying arguments is that there are many passages that, although they look like arguments, are not arguments. The most common types are:

• Explanations
• Mere asssertions
• Conditional statements
• Loosely connected statements

Explanations can be tricky, because they often use one of our indicator words. Consider this passage:

Abraham Lincoln died because he was shot.

If this were an argument, then the conclusion would be that Abraham Lincoln died, since the other statement is introduced by a premise indicator. If this is an argument, though, it’s a strange one. Do you really think that someone would be trying to prove that Abraham Lincoln died? Surely everyone knows that he is dead. On the other hand, there might be people who don’t know how he died. This passage does not attempt to prove that something is true, but instead attempts to explain why it is true. To determine if a passage is an explanation or an argument, first find the statement that looks like the conclusion. Next, ask yourself if everyone likely already believes that statement to be true. If the answer to that question is yes, then the passage is an explanation.

Mere assertions are obviously not arguments. If a professor tells you simply that you will not get an A in her course this semester, she has not given you an argument. This is because she hasn’t given you any reasons to believe that the statement is true. If there are no premises, then there is no argument.

Conditional statements are sentences that have the form “If…, then….” A conditional statement asserts that if something is true, then something else would be true also. For example, imagine you are told, “If you have the winning lottery ticket, then you will win ten million dollars.” What is being claimed to be true, that you have the winning lottery ticket, or that you will win ten million dollars? Neither. The only thing claimed is the entire conditional. Conditionals can be premises, and they can be conclusions. They can be parts of arguments, but that cannot, on their own, be arguments themselves.

Finally, consider this passage:

I woke up this morning, then took a shower and got dressed. After breakfast, I worked on chapter 2 of the critical thinking text. I then took a break and drank some more coffee….

This might be a description of my day, but it’s not an argument. There’s nothing in the passage that plays the role of a premise or a conclusion. The passage doesn’t attempt to prove anything. Remember that arguments need a conclusion, there must be something that is the statement to be proved. Lacking that, it simply isn’t an argument, no matter how much it looks like one.

2.2 Evaluating Arguments

The first step in evaluating an argument is to determine what kind of argument it is. We initially categorize arguments as either deductive or inductive, defined roughly in terms of their goals. In deductive arguments, the truth of the premises is intended to absolutely establish the truth of the conclusion. For inductive arguments, the truth of the premises is only intended to establish the probable truth of the conclusion. We’ll focus on deductive arguments first, then examine inductive arguments in later chapters.

Once we have established that an argument is deductive, we then ask if it is valid. To say that an argument is valid is to claim that there is a very special logical relationship between the premises and the conclusion, such that if the premises are true, then the conclusion must also be true. Another way to state this is

An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.

An argument is invalid if and only if it is not valid.

Note that claiming that an argument is valid is not the same as claiming that it has a true conclusion, nor is it to claim that the argument has true premises. Claiming that an argument is valid is claiming nothing more that the premises, if they were true , would be enough to make the conclusion true. For example, is the following argument valid or not?

• If pigs fly, then an increase in the minimum wage will be approved next term.
• An increase in the minimum wage will be approved next term.

The argument is indeed valid. If the two premises were true, then the conclusion would have to be true also. What about this argument?

• All dogs are mammals
• Spot is a mammal.
• Spot is a dog.

In this case, both of the premises are true and the conclusion is true. The question to ask, though, is whether the premises absolutely guarantee that the conclusion is true. The answer here is no. The two premises could be true and the conclusion false if Spot were a cat, whale, etc.

Neither of these arguments are good. The second fails because it is invalid. The two premises don’t prove that the conclusion is true. The first argument is valid, however. So, the premises would prove that the conclusion is true, if those premises were themselves true. Unfortunately, (or fortunately, I guess, considering what would be dropping from the sky) pigs don’t fly.

These examples give us two important ways that deductive arguments can fail. The can fail because they are invalid, or because they have at least one false premise. Of course, these are not mutually exclusive, an argument can be both invalid and have a false premise.

If the argument is valid, and has all true premises, then it is a sound argument. Sound arguments always have true conclusions.

A deductively valid argument with all true premises.

Inductive arguments are never valid, since the premises only establish the probable truth of the conclusion. So, we evaluate inductive arguments according to their strength. A strong inductive argument is one in which the truth of the premises really do make the conclusion probably true. An argument is weak if the truth of the premises fail to establish the probable truth of the conclusion.

There is a significant difference between valid/invalid and strong/weak. If an argument is not valid, then it is invalid. The two categories are mutually exclusive and exhaustive. There can be no such thing as an argument being more valid than another valid argument. Validity is all or nothing. Inductive strength, however, is on a continuum. A strong inductive argument can be made stronger with the addition of another premise. More evidence can raise the probability of the conclusion. A valid argument cannot be made more valid with an additional premise. Why not? If the argument is valid, then the premises were enough to absolutely guarantee the truth of the conclusion. Adding another premise won’t give any more guarantee of truth than was already there. If it could, then the guarantee wasn’t absolute before, and the original argument wasn’t valid in the first place.

2.3 Counterexamples

One way to prove an argument to be invalid is to use a counterexample. A counterexample is a consistent story in which the premises are true and the conclusion false. Consider the argument above:

By pointing out that Spot could have been a cat, I have told a story in which the premises are true, but the conclusion is false.

Here’s another one:

• If it is raining, then the sidewalks are wet.
• The sidewalks are wet.
• It is raining.

The sprinklers might have been on. If so, then the sidewalks would be wet, even if it weren’t raining.

Counterexamples can be very useful for demonstrating invalidity. Keep in mind, though, that validity can never be proved with the counterexample method. If the argument is valid, then it will be impossible to give a counterexample to it. If you can’t come up with a counterexample, however, that does not prove the argument to be valid. It may only mean that you’re not creative enough.

• An argument is a set of statements; one is the conclusion, the rest are premises.
• The conclusion is the statement that the argument is trying to prove.
• The premises are the reasons offered for believing the conclusion to be true.
• Explanations, conditional sentences, and mere assertions are not arguments.
• Deductive reasoning attempts to absolutely guarantee the truth of the conclusion.
• Inductive reasoning attempts to show that the conclusion is probably true.
• In a valid argument, it is impossible for the premises to be true and the conclusion false.
• In an invalid argument, it is possible for the premises to be true and the conclusion false.
• A sound argument is valid and has all true premises.
• An inductively strong argument is one in which the truth of the premises makes the the truth of the conclusion probable.
• An inductively weak argument is one in which the truth of the premises do not make the conclusion probably true.
• A counterexample is a consistent story in which the premises of an argument are true and the conclusion is false. Counterexamples can be used to prove that arguments are deductively invalid.

( Cleese and Chapman 1980 ) . ↩︎

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Kinds of Arguments

Contemporary Western philosophy treats arguments as coming in two main types, deductive and inductive. The basic distinction and difference will be mentioned here.

Deductive arguments are arguments in which the premises (if true) guarantee the truth of the conclusion. The conclusion of a successful deductive argument cannot possibly be false, assuming its premises are true. This is what it means to label an argument as “valid” in logic. The form or structure of a deductive argument is the essential aspect to consider. Somewhat counter-intuitively, the premises do not need to be true for the conclusion to be true.

Arguments are a linguistic representation of an inference. So, using slightly different terminology, we can define deductive inferences . In a successful deductive inference, the premises and the denial of the conclusion constitute an inconsistent set of statements. An alternative way to describe the same relation: in a successful deductive inference, the truth of the premises makes the falsity of the conclusion logically impossible. A successful deductive inference is valid .

Deductive Example

1) All dogs are mammals.

2) All mammals breathe air.

_______________________________________________

SO: All dogs breathe air.

Inductive arguments are arguments with premises which make it likely that the conclusion is true but don’t absolutely guarantee its truth . Inductive arguments are by far the most common type of argument we see in our daily lives. We can assess inductive arguments along a spectrum of successful (stronger) to unsuccessful (weaker). The more successful (stronger) argument suggests that the premises mean the conclusion is probably true, with a high degree of likelihood. It is important to remember that inductive arguments can never fully guarantee the truth of the conclusion.

Using slightly different terminology, we can consider inductive inferences, referring to the actual thinking process in someone’s mind. In a successful inductive inference, the truth of the premises makes the falsity of the conclusion possible, but unlikely. Inductive inferences can be evaluated as “stronger” or “weaker” depending on the probability.

Inductive Example

1) The Interstate Bridge is regularly inspected by qualified engineers.

2) Vehicles have been driving over it for years.

SO: It will be safe to drive over it tomorrow.

One thing that makes applying the distinction between deductive and inductive arguments a bit tricky is this: we can’t look only at the premises OR only at the conclusion. Instead, we need to focus on the relationship between the premise(s) and the conclusion to tell what kind of argument we have.

A further contributor to trickiness: we can’t be distracted by the question of whether the statements are true or false. To classify an argument as deductive or inductive, we need to grant that the premises are true in a hypothetical way. We have to ask the question, “If those premises were true, would it be IMPOSSIBLE for the conclusion to be false?” If so, it is a deductive argument. Or “If those premises were true, would it be UNLIKELY, but still possible, that the conclusion is false? If so, it is an inductive argument.

As an example, consider this valid deductive argument:

1) All clouds are made out of spun sugar.

2) Anything made out of spun sugar is high in calories.

SO: All clouds are high in calories.

This argument is deductively successful because the truth of the premises would make the falsity of the conclusion impossible. Odd, isn’t it?

Some arguments are presented with premises missing. In those cases, the determination of deductive or inductive will depend on how that premise is filled in.

For example: I had an apple for lunch, so I had something healthy!

Exercise: Deductive or Inductive?

Determine if the following arguments are deductive or inductive. It is a good idea to put the arguments in standard form first, so you are clear about the relation between premises and conclusion.

Critical Thinking in Academic Research Copyright © 2022 by Cindy Gruwell and Robin Ewing is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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20 Arguments V: Introduction to Deductive and Inductive Arguments

An argument, as we are using the term, is a series of claims (the premises) which attempt to establish the truth or probable truth of another claim (the conclusion). The premises thus give reasons someone is supposed to believe that the conclusion is true. Or, put differently, the conclusion is inferred from the premises.

We’ve focused on identifying what is left out or unstated in arguments (hidden or implicit premises). And we’ve talked about the need to tease out different strands of reasoning for a given conclusion, by identifying overlapping arguments that are each made up of sets of inter-connected premises.

But we’ve otherwise been lumping all arguments together. Since our goal is to be able to  assess arguments, i.e., to see when they provide good  reasons for a conclusion, we now need to make a distinction between two different kinds of arguments . This will let us see that there are different standards for judging the success of an argument, and common kinds of errors, or “fallacies” that go with each. (While we’ll cover a couple of these fallacies in this Module, it’s really only in the next that we will focus on them in detail.)

Two Kinds of Arguments

The distinction between kinds of arguments is rooted in the different intent they have: some arguments aim for a conclusion that follows necessarily from the premises. That is, if the premises are true, then the conclusion must be true as well. Other arguments, however — and, indeed, most of the arguments we actually make in ordinary life and even in science — only aim for a conclusion that is probably true, given the truth of the premises. That’s because most of our reasoning occurs in situations where there is some degree of uncertainty or ignorance.

Arguments with these different aims have different names.

• A deductive argument is an argument whose conclusion is intended to follow with logical   necessity  from the given premises.
• An inductive argument is an argument whose conclusion is intended to follow with some degree of  probability  from the given premises.

Here’s a quick example of each, just to illustrate the difference. Note that the conclusion is the same in each; what differs is how it is being supported by its premises.

Example Deductive and Inductive Arguments

Example Deductive Argument :

• If it rained yesterday, then it will rain today.
• It rained yesterday.

    Therefore, it will rain today.

Example Inductive Argument :

• It rained the day before yesterday.

Therefore, it will rain today.

In the first, deductive argument, the two premises necessarily imply or logically entail the conclusion. That is, you couldn’t assert them as true without also logically committing yourself to the truth of the conclusion, on pain of logical contradiction. (And remember back to our reading of Plato: a basic requirement for good reasoning is that it be coherent, i.e., non-self-contradictory.)

Note that whether the conclusion is logically implied by the premises has nothing to do with the truth of any of the claims involved. Even if the premises are false, a conclusion can still logically follow from them .

In the second, inductive argument, the two premises taken together give you some reason for thinking the conclusion will be true. A pattern of weather over a couple of days is a good, if imperfect, basis for predicting what the next day’s weather will be. But obviously, weather changes, so even if the prediction is likely to be true, it’s not necessarily true. E ven if the premises are true, and even if they provide good reasons for thinking the conclusion will be true, it might still turn out that the conclusion is false .

This is characteristic of inductive arguments. The premises explain why you think a conclusion is likely  to be true, but it builds in an acknowledgement that the conclusion  might turn out to be false. Thus, it’s never an objection  to an inductive argument that the conclusion  might  not be true. The question to ask is whether the premises give you reasons for thinking that the conclusion is  more  likely to be true than not to be.

Now, when reasons are given for a conclusion that is to some degree uncertain, as happens in inductive arguments, that often means the person giving the reasons is, in some way, making a judgment call about what’s likely. So, there is some individual  assessment built into much inductive reasoning. However, that doesn’t mean that you’re dealing with  mere opinion . An argument gives  reasons  that others are supposed to be able to accept. It can do this well or not. So, it’s irrelevant whether there is opinion involved. The question is whether the reasons given are compelling or not.

And relatedly:

Crucial Point:  The fact that claims about what is probable or likely involve an element of individual judgment on the part of the person making them does not mean that the person’s values  are involved.

For example, a meteorologist who says it is likely to rain tomorrow may disagree with another who says that it is not likely to rain. Even though this dispute involves a difference in individual opinion — professional opinion in this case — there is no issue about what’s good/bad/right/wrong/should/shouldn’t be done. This is a dispute purely about facts, not values.

The next two chapters will go into depth and detail about inductive and deductive arguments. Each will have some exercises associated with it for you to do to practice identifying and analyzing them.

Phil-P102 Critical Thinking and Applied Ethics Copyright © 2020 by R. Matthew Shockey is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License , except where otherwise noted.

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5.2: Cogency and Strong Arguments

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Strength and Weakness

Inductive arguments are said to be either strong or weak. There’s no absolute cut-off between strength and weakness, but some arguments will be very strong and others very weak, so the distinction is still useful even if it is not precise. A strong argument is one where, if the premises were true, the conclusion would be very likely to be true. A weak argument is one where the conclusion does not follow from the premises (i.e. even if the premises were true, there would still be a good chance that the conclusion could be false.)

Most arguments in courts of law attempt to be strong arguments; they are generally not attempts at valid arguments.

So, the following example is a strong argument.

John was found with a gun in his hand, running from the apartment where Tom's body was found. Three witnesses heard a gunshot right before they saw John run out. The gun in John's possession matched the ballistics on the bullet pulled from Tom's head. John had written a series of threatening letters to Tom. In prison, John confessed to his cellmate that he had killed Tom. Therefore, John is the murder of Tom.

Given that all the premises were true, it would be very likely that the conclusion would be true.

Importantly, strength has nothing to do with the actual truth of the premises!

This is something people frequently forget, so it’s worth repeating: A STRONG ARGUMENT NEEDN’T HAVE ANY TRUE PREMISES! ALL THE PREMISES OF A STRONG ARGUMENT CAN BE FALSE!

The argument is strong because: if the premises WERE true, the conclusion would be likely to be true.

So the following arguments are strong:

98% of Dominicans have superpowers. Lucy is Dominican. I saw Lucy leap from the top of a tall building last week and walk away unscathed. Lucy has superpowers.

People from the lost continent of Atlantis have been manipulating the world’s governments for years by placing Atlantean wizards in positions of power. Whenever possible, they place an Atlantean wizard in the executive position of the most powerful government on earth. They did this in the Roman empire, the Mongol empire, and the British empire. Currently, the United States is the most powerful country on earth. Barack Obama was born in Hawai’i, where about 45% of the people are actually Atlanteans. While he was a Senator from Illinois, he received over 10 billion dollars in funds from a mysterious holding company called “Atlantis Incorporated.” Several journalists claim that they have seen Barack Obama perform feats of magic. For example, Shep Smith of Fox News said he saw Barack Obama walk on water. Barack Obama is clearly an Atlantean wizard.

Two leading researchers in genetics have found that, in every sample of DNA they looked at, there were traces of kryptonite. They examined 1600 samples, from 1600 separate individuals, including an equal distribution from all continents. The results were then replicated in another, larger study of 2700 samples, also taken from all continents. We conclude, then, that normal DNA contains kryptonite.

Cogency: If an argument is strong and all its premises are true, the argument is said to be cogent.

The following arguments are weak. The premises provide little, if any, evidence for the conclusions:

I saw your boyfriend last night and he was talking to another girl. So he’s cheating on you.

Senator Bonham served 8 years in military, whereas his opponent, Mr. Malham never served one day of military service. So you should vote for Senator Bonham.

More people buy Juff ™ brand peanut butter than any other brand, so you should by Juff ™!

It’s notable, again, that the truth of the premises is irrelevant. A weak argument can have true premises and a true conclusion. What makes it weak is that the premises do not provide good reason to believe the conclusion.

Induction 45

All of the argument forms we have looked at so far have been deductively valid. That meant, we said, that the conclusion follows from necessity if the premises are true. But to what extent can we ever be sure of the truth of those premises? Inductive argumentation is a less certain, more realistic, more familiar way of reasoning that we all do, all the time. Inductive argumentation recognizes, for instance, that a premise like “All horses have four legs” comes from our previous experience of horses. If one day we were to encounter a three-legged horse, deductive logic would tell us that “All horses have four legs” is false, at which point the premise becomes rather useless for a deducer. In fact, deductive logic tells us that if the premise “All horses have four legs” is false, even if we know there are many, many four-legged horses in the world, when we go to the track and see hordes of four-legged horses, all we can really be certain of is that “There is at least one four-legged horse.”

Inductive logic allows for the more realistic premise, “The vast majority of horses have four legs”. And inductive logic can use this premise to infer other useful information, like “If I’m going to get Chestnut booties for Christmas, I should probably get four of them.” The trick is to recognize a certain amount of uncertainty in the truth of the conclusion, something for which deductive logic does not allow. In real life, however, inductive logic is used much more frequently and (hopefully) with some success. Let’s take a look at some of the uses of inductive reasoning.

Predicting the Future

We constantly use inductive reasoning to predict the future. We do this by compiling evidence based on past observations, and by assuming that the future will resemble the past. For instance, I make the observation that every other time I have gone to sleep at night, I have woken up in the morning. There is actually no certainty that this will happen, but I make the inference because of the fact that this is what has happened every other time. In fact, it is not the case that “All people who go to sleep at night wake up in the morning”. But I’m not going to lose any sleep over that. And we do the same thing when our experience has been less consistent. For instance, I might make the assumption that, if there’s someone at the door, the dog will bark. But it’s not outside the realm of possibility that the dog is asleep, has gone out for a walk, or has been persuaded not to bark by a clever intruder with sedative-laced bacon. I make the assumption that if there’s someone at the door, the dog will bark, because that is what usually happens.

Explaining Common Occurrences

We also use inductive reasoning to explain things that commonly happen. For instance, if I’m about to start an exam and notice that Bill is not here, I might explain this to myself with the reason that Bill is stuck in traffic. I might base this on the reasoning that being stuck in traffic is a common excuse for being late, or because I know that Bill never accounts for traffic when he’s estimating how long it will take him to get somewhere. Again, that Bill is actually stuck in traffic is not certain, but I have some good reasons to think it’s probable. We use this kind of reasoning to explain past events as well. For instance, if I read somewhere that 1986 was a particularly good year for tomatoes, I assume that 1986 also had some ideal combination of rainfall, sun, and consistently warm temperatures. Although it’s possible that a scientific madman circled the globe planting tomatoes wherever he could in 1986, inductive reasoning would tell me that the former, environmental explanation is more likely. (But I could be wrong.)

Generalizing

Often we would like to make general claims, but in fact it would be very difficult to prove any general claim with any certainty. The only way to do so would be to observe every single case of something about which we wanted to make an observation. This would be, in fact, the only way to prove such assertions as, “All swans are white”. Without being able to observe every single swan in the universe, I can never make that claim with certainty. Inductive logic, on the other hand, allows us to make the claim, with a certain amount of modesty.

Inductive Generalization

Inductive generalization allows us to make general claims, despite being unable to actually observe every single member of a class in order to make a certainly true general statement. We see this in scientific studies, population surveys, and in our own everyday reasoning. Take for example a drug study. Some doctor or other wants to know how many people will go blind if they take a certain amount of some drug for so many years. If they determine that 5% of people in the study go blind, they then assume that 5% of all people who take the drug for that many years will go blind. Likewise, if I survey a random group of people and ask them what their favourite colour is, and 75% of them say “purple”, then I assume that purple is the favourite colour of 75% of people. But we have to be careful when we make an inductive generalization. When you tell me that 75% of people really like purple, I’m going to want to know whether you took that survey outside a Justin Bieber concert.

Let’s take an example. Let’s say I asked a class of 400 students whether or not they think logic is a valuable course, and 90% of them said yes. I can make an inductive argument like this:

(P1) 90% of 400 students believe that logic is a valuable course.

(C) Therefore 90% of students believe that logic is a valuable course.

There are certain things I need to take into account in judging the quality of this argument. For instance, did I ask this in a logic course? Did the respondents have to raise their hands so that the professor could see them, or was the survey taken anonymously? Are there enough students in the course to justify using them as a representative group for students in general?

If I did, in fact, make a class of 400 logic students raise their hands in response to the question of whether logic is valuable course, then we can identify a couple of problems with this argument. The first is bias. We can assume that anyone enrolled in a logic course is more likely to see it as valuable than any random student. I have therefore skewed the argument in favour of logic courses. I can also question whether the students were answering the question honestly. Perhaps if they are trying to save the professor’s feelings, they are more likely to raise their hands and assure her that the logic course is a valuable one.

Now let’s say I’ve avoided those problems. I have assured that the 400 students I have asked are randomly selected, say, by soliciting email responses from randomly selected students from the university’s entire student population. Then the argument looks stronger.

Another problem we might have with the argument is whether I have asked enough students so that the whole population is well-represented. If the student body as a whole consists of 400 students, my argument is very strong. If the student body numbers in the tens of thousands, I might want to ask a few more before assuming that the opinions of a few mirror those of the many. This would be a problem with my sample size.

Let’s take another example. Now I’m going to run a scientific study, in which I will pay someone $50 to take a drug with unknown effects and see if it makes them blind. In order to control for other variables, I open the study only to white males between the ages of 18 and 25.

A bad inductive argument would say:

(P1) 40% of 1000 people who took the drug went blind.

(C) Therefore 40% of people who take the drug will go blind.

A better inductive argument would make a more modest claim:

(P1) 40% of the 1000 people who took the drug went blind.

(C) Therefore 40% of white males between the ages of 18 and 25 who take the drug will go blind.

The point behind this example is to show how inductive reasoning imposes an important limitation on the possible conclusions a study or a survey can make. In order to make good generalizations, we need to ensure that our sample is representative, non-biased, and sufficiently sized.

Statistical Syllogism

Where in an inductive generalization we saw statement expressing a statistic applied to a more general group, we can also use statistics to go from the general to the particular. For instance, if I know that most computer science majors are male, and that some random individual with the androgynous name “Cameron” is an computer science major, then we can be reasonably certain that Cameron is a male. We tend to represent the uncertainty by qualifying the conclusion with the word “probably”. If, on the other hand, we wanted to say that something is unlikely, like that Cameron were a female, we could use “probably not”. It is also possible to temper our conclusion with other similar qualifying words.

Let’s take an example.

(P1) Of the 133 people found guilty of homicide last year in Canada, 79% were jailed.

(P2) Socrates was found guilty of homicide last year in Canada.

(C) Therefore, Socrates was probably jailed.

In this case we can be reasonably sure that Socrates is currently rotting in prison. Now the certainty of our conclusion seems to be dependent on the statistics we’re dealing with. There are definitely more certain and more uncertain cases.

(P1) In the last election, 50% of voting Americans voted for Obama, while 48% voted for Romney.

(P2) Jim is a voting American.

(C) Therefore, Jim probably voted for Obama.

Clearly, this argument is not as strong as the first. It is only slightly more likely than not that Jim voted for Obama. In this case we might want to revise our conclusion to say:

(C) Therefore, it is slightly more likely than not that Jim voted for Obama.

In other cases, the likelihood that something is or is not the case approaches certainty. For example:

(P1) There is a 0.00000059% chance you will die on any single flight, assuming you use one of the most poorly rated airlines.

(P2) I’m flying to Paris next week.

(C) There’s more than a million to one chance that I will die on my flight.

Note that in all of these examples, nothing is ever stated with absolute certainty. It is possible to improve the chances that our conclusions will be accurate by being more specific, or finding out more information. We would know more about Jim’s voting strategy, for instance, if we knew where he lived, his previous voting habits, or if we simply asked him for whom he voted (in which case, we might also want to know how often Jim lies).

Induction by Shared Properties

Induction by shared properties involves noting the similarity between two things with respect to their properties, and inferring from this that they may share other properties.

A familiar example of this is how a company might recommend products to you based on other customers’ purchases. Amazon.com tells me, for instance, that customers who bought the complete Sex and the City DVD series also bought Lipstick Jungle and Twilight.

Assuming that people buy things because they like them, we can rephrase this as:

(P1) There are a large number of people who, if they like Sex and the City and Twilight, will also like Lipstick Jungle.

I could also make the following observation:

(P2) I like Sex and the City and Twilight.

And then infer from there two premises that:

(C) I would also like Lipstick Jungle.

And I did. In general, induction by shared properties assumes that if something has properties w, x, y, and z, and if something else has properties w, x, and y, then it’s reasonable to assume that that something else also has property z. Note that in the above example all of the properties were actually preferences with regard to entertainment. The kinds of properties involved in the comparison can and will make an argument better or worse. Let’s consider a worse induction.

(P1) Lisa is tall, has blonde hair, has blue eyes, and rocks out to Nirvana on weekends.

(P2) Gina is tall, has blonde hair, and has blue eyes.

(C) Therefore Gina probably rocks out to Nirvana on weekends.

In this case the properties don’t seem to be related in the same way as in the first example. While the first three are physical characteristics, the last property instead indicates to us that Lisa is stuck in a 90’s grunge phase. Gina, though she shares several properties with Lisa, might not share the same undying love for Kurt Cobain. Let’s try a stronger argument.

(P1) Bob and Dick both wear plaid shirts all the time, wear large plastic-rimmed glasses, and listen to bands you’ve never heard of.

(P2) Bob drinks PBR.

(C) Dick probably also drinks PBR.

Here we can identify the qualities that Bob and Dick have in common as symptoms of hipsterism. The fact that Bob drinks PBR is another symptom of this affectation. Given that Dick is exhibiting most of the same symptoms, the idea that Dick would also drink PBR is a reasonable assumption to make.

Practical Uses

A procedure very much like Induction by Shared Properties is performed by nurses and doctors when they diagnose a patient’s condition. Their thinking goes like this:

(P1) Patients who have elephantitus display an increased heart rate, elevated blood pressure, a rash on their skin, and a strong desire to visit the elephant pen at the zoo.

(P2) The patient here in front of me has an increased heart rate, elevated blood pressure, and a strong desire to visit the elephant pen at the zoo.

(C) It is probable, therefore, that the patient here in front of me has elephantitus.

The more that a patient’s symptoms match the ‘textbook definition’ of a given disease, then the more likely it is that the patient has that disease. Caregivers then treat the patient for the

disease that they think the patient probably has. If the disease doesn’t respond to the treatment, or the patient starts to present different symptoms, then they consider other conditions with similar symptoms that the patient is likely to have.

Induction by Shared Relations

Induction by shared relations is much like induction by shared properties, except insofar that what is shared are not properties, but relations. A simple example is the causal relation, from which we might make an inductive argument like this:

(P1) Percocet, Oxycontin and Morphine reduce pain, cause drowsiness, and may be habit forming.

(P2) Heroin also reduces pain and causes drowsiness.

(C) Heroin is probably also habit forming.

In this case the effects of reducing pain, drowsiness, and addiction are all assumed to be caused by the drugs listed. We can use an induction by shared relation to make the probable conclusion that if heroin, like the other drugs, reduces pain and causes drowsiness, it is probably also habit forming.

Another interesting example are the relations we have with other people. For instance, Facebook knows everything about you. But let’s focus on the “friends with” relation. They compare who your friends are with the friends of your friends in order to determine who else you might actually know. The induction goes a little like this:

(P1) Donna is friends with Brandon, Kelly, Steve, and Brenda.

(P2) David is friends with Brandon, Kelly, and Steve.

(C) David probably also knows Brenda.

We could strengthen that argument if we knew that Brandon, Kelly, Steve, and Brenda were all friends with each other as well. We could also make an alternate conclusion based on the same argument above:

(C) David probably also knows Donna.

They do, after all, know at least three of the same people. They’ve probably run into each other at some point.