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Falsifiability

Karl popper's basic scientific principle, karl popper's basic scientific principle.

Falsifiability, according to the philosopher Karl Popper, defines the inherent testability of any scientific hypothesis.

This article is a part of the guide:

• Inductive Reasoning
• Deductive Reasoning
• Hypothetico-Deductive Method
• Scientific Reasoning
• Testability

Browse Full Outline

• 1 Scientific Reasoning
• 2.1 Falsifiability
• 2.2 Verification Error
• 2.3 Testability
• 2.4 Post Hoc Reasoning
• 3 Deductive Reasoning
• 4.1 Raven Paradox
• 5 Causal Reasoning
• 6 Abductive Reasoning
• 7 Defeasible Reasoning

Science and philosophy have always worked together to try to uncover truths about the universe we live in. Indeed, ancient philosophy can be understood as the originator of many of the separate fields of study we have today, including psychology, medicine, law, astronomy, art and even theology.

Scientists design experiments and try to obtain results verifying or disproving a hypothesis, but philosophers are interested in understanding what factors determine the validity of scientific endeavors in the first place.

Whilst most scientists work within established paradigms, philosophers question the paradigms themselves and try to explore our underlying assumptions and definitions behind the logic of how we seek knowledge. Thus there is a feedback relationship between science and philosophy - and sometimes plenty of tension!

One of the tenets behind the scientific method is that any scientific hypothesis and resultant experimental design must be inherently falsifiable. Although falsifiability is not universally accepted, it is still the foundation of the majority of scientific experiments. Most scientists accept and work with this tenet, but it has its roots in philosophy and the deeper questions of truth and our access to it.

What is Falsifiability?

Falsifiability is the assertion that for any hypothesis to have credence, it must be inherently disprovable before it can become accepted as a scientific hypothesis or theory.

For example, someone might claim "the earth is younger than many scientists state, and in fact was created to appear as though it was older through deceptive fossils etc.” This is a claim that is unfalsifiable because it is a theory that can never be shown to be false. If you were to present such a person with fossils, geological data or arguments about the nature of compounds in the ozone, they could refute the argument by saying that your evidence was fabricated to appeared that way, and isn’t valid.

Importantly, falsifiability doesn’t mean that there are currently arguments against a theory, only that it is possible to imagine some kind of argument which would invalidate it. Falsifiability says nothing about an argument's inherent validity or correctness. It is only the minimum trait required of a claim that allows it to be engaged with in a scientific manner – a dividing line between what is considered science and what isn’t. Another important point is that falsifiability is not any claim that has yet to be proven true. After all, a conjecture that hasn’t been proven yet is just a hypothesis.

The idea is that no theory is completely correct , but if it can be shown both to be falsifiable  and supported with evidence that shows it's true, it can be accepted as truth.

For example, Newton's Theory of Gravity was accepted as truth for centuries, because objects do not randomly float away from the earth. It appeared to fit the data obtained by experimentation and research , but was always subject to testing.

However, Einstein's theory makes falsifiable predictions that are different from predictions made by Newton's theory, for example concerning the precession of the orbit of Mercury, and gravitational lensing of light. In non-extreme situations Einstein's and Newton's theories make the same predictions, so they are both correct. But Einstein's theory holds true in a superset of the conditions in which Newton's theory holds, so according to the principle of Occam's Razor , Einstein's theory is preferred. On the other hand, Newtonian calculations are simpler, so Newton's theory is useful for almost any engineering project, including some space projects. But for GPS we need Einstein's theory. Scientists would not have arrived at either of these theories, or a compromise between both of them, without the use of testable, falsifiable experiments. 

Popper saw falsifiability as a black and white definition; that if a theory is falsifiable, it is scientific , and if not, then it is unscientific. Whilst some "pure" sciences do adhere to this strict criterion, many fall somewhere between the two extremes, with  pseudo-sciences  falling at the extreme end of being unfalsifiable. 

Pseudoscience

According to Popper, many branches of applied science, especially social science, are not truly scientific because they have no potential for falsification.

Anthropology and sociology, for example, often use case studies to observe people in their natural environment without actually testing any specific hypotheses or theories.

While such studies and ideas are not falsifiable, most would agree that they are scientific because they significantly advance human knowledge.

Popper had and still has his fair share of critics, and the question of how to demarcate legitimate scientific enquiry can get very convoluted. Some statements are logically falsifiable but not practically falsifiable – consider the famous example of “it will rain at this location in a million years' time.” You could absolutely conceive of a way to test this claim, but carrying it out is a different story.

Thus, falsifiability is not a simple black and white matter. The Raven Paradox shows the inherent danger of relying on falsifiability, because very few scientific experiments can measure all of the data, and necessarily rely upon generalization . Technologies change along with our aims and comprehension of the phenomena we study, and so the falsifiability criterion for good science is subject to shifting.

For many sciences, the idea of falsifiability is a useful tool for generating theories that are testable and realistic. Testability is a crucial starting point around which to design solid experiments that have a chance of telling us something useful about the phenomena in question. If a falsifiable theory is tested and the results are significant , then it can become accepted as a scientific truth.

The advantage of Popper's idea is that such truths can be falsified when more knowledge and resources are available. Even long accepted theories such as Gravity, Relativity and Evolution are increasingly challenged and adapted.

The major disadvantage of falsifiability is that it is very strict in its definitions and does not take into account the contributions of sciences that are observational and descriptive .

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Martyn Shuttleworth , Lyndsay T Wilson (Sep 21, 2008). Falsifiability. Retrieved May 22, 2024 from Explorable.com: https://explorable.com/falsifiability

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Being Scientific: Falsifiability, Verifiability, Empirical Tests, and Reproducibility

If you ask a scientist what makes a good experiment, you’ll get very specific answers about reproducibility and controls and methods of teasing out causal relationships between variables and observables. If human observations are involved, you may get detailed descriptions of blind and double-blind experimental designs. In contrast, if you ask the very same scientists what makes a theory or explanation scientific, you’ll often get a vague statement about falsifiability . Scientists are usually very good at designing experiments to test theories. We invent theoretical entities and explanations all the time, but very rarely are they stated in ways that are falsifiable. It is also quite rare for anything in science to be stated in the form of a deductive argument. Experiments often aren’t done to falsify theories, but to provide the weight of repeated and varied observations in support of those same theories. Sometimes we’ll even use the words verify or confirm when talking about the results of an experiment. What’s going on? Is falsifiability the standard? Or something else?

The difference between falsifiability and verifiability in science deserves a bit of elaboration. It is not always obvious (even to scientists) what principles they are using to evaluate scientific theories, 1 so we’ll start a discussion of this difference by thinking about Popper’s asymmetry. 2 Consider a scientific theory ( T ) that predicts an observation ( O ). There are two ways we could approach adding the weight of experiment to a particular theory. We could attempt to falsify or verify the observation. Only one of these approaches (falsification) is deductively valid:

Popper concluded that it is impossible to know that a theory is true based on observations ( O ); science can tell us only that the theory is false (or that it has yet to be refuted). He concluded that meaningful scientific statements are falsifiable.

Scientific theories may not be this simple. We often base our theories on a set of auxiliary assumptions which we take as postulates for our theories. For example, a theory for liquid dynamics might depend on the whole of classical mechanics being taken as a postulate, or a theory of viral genetics might depend on the Hardy-Weinberg equilibrium. In these cases, classical mechanics (or the Hardy-Wienberg equilibrium) are the auxiliary assumptions for our specific theories.

These auxiliary assumptions can help show that science is often not a deductively valid exercise. The Quine-Duhem thesis 3 recovers the symmetry between falsification and verification when we take into account the role of the auxiliary assumptions ( AA ) of the theory ( T ):

That is, if the predicted observation ( O ) turns out to be false, we can deduce only that something is wrong with the conjunction, ( T and AA ); we cannot determine from the premises that it is T rather than AA that is false. In order to recover the asymmetry, we would need our assumptions ( AA ) to be independently verifiable:

Falsifying a theory requires that auxiliary assumption ( AA ) be demonstrably true. Auxiliary assumptions are often highly theoretical — remember, auxiliary assumptions might be statements like the entirety of classical mechanics is correct or the Hardy-Weinberg equilibrium is valid ! It is important to note, that if we can’t verify AA , we will not be able to falsify T by using the valid argument above. Contrary to Popper, there really is no asymmetry between falsification and verification. If we cannot verify theoretical statements, then we cannot falsify them either.

Since verifying a theoretical statement is nearly impossible, and falsification often requires verification of assumptions, where does that leave scientific theories? What is required of a statement to make it scientific?

Carl Hempel came up with one of the more useful statements about the properties of scientific theories: 4 “The statements constituting a scientific explanation must be capable of empirical test.” And this statement about what exactly it means to be scientific brings us right back to things that scientists are very good at: experimentation and experimental design. If I propose a scientific explanation for a phenomenon, it should be possible to subject that theory to an empirical test or experiment. We should also have a reasonable expectation of universality of empirical tests. That is multiple independent (skeptical) scientists should be able to subject these theories to similar tests in different locations, on different equipment, and at different times and get similar answers. Reproducibility of scientific experiments is therefore going to be required for universality.

So to answer some of the questions we might have about reproducibility:

• Reproducible by whom ? By independent (skeptical) scientists, working elsewhere, and on different equipment, not just by the original researcher.
• Reproducible to what degree ? This would depend on how closely that independent scientist can reproduce the controllable variables, but we should have a reasonable expectation of similar results under similar conditions.
• Wouldn’t the expense of a particular apparatus make reproducibility very difficult? Good scientific experiments must be reproducible in both a conceptual and an operational sense. 5 If a scientist publishes the results of an experiment, there should be enough of the methodology published with the results that a similarly-equipped, independent, and skeptical scientist could reproduce the results of the experiment in their own lab.

Computational science and reproducibility

If theory and experiment are the two traditional legs of science, simulation is fast becoming the “third leg”. Modern science has come to rely on computer simulations, computational models, and computational analysis of very large data sets. These methods for doing science are all reproducible in principle . For very simple systems, and small data sets this is nearly the same as reproducible in practice . As systems become more complex and the data sets become large, calculations that are reproducible in principle are no longer reproducible in practice without public access to the code (or data). If a scientist makes a claim that a skeptic can only reproduce by spending three decades writing and debugging a complex computer program that exactly replicates the workings of a commercial code, the original claim is really only reproducible in principle. If we really want to allow skeptics to test our claims, we must allow them to see the workings of the computer code that was used. It is therefore imperative for skeptical scientific inquiry that software for simulating complex systems be available in source-code form and that real access to raw data be made available to skeptics.

Our position on open source and open data in science was arrived at when an increasing number of papers began crossing our desks for review that could not be subjected to reproducibility tests in any meaningful way. Paper A might have used a commercial package that comes with a license that forbids people at university X from viewing the code ! 6

Paper 2 might use a code which requires parameter sets that are “trade secrets” and have never been published in the scientific literature . Our view is that it is not healthy for scientific papers to be supported by computations that cannot be reproduced except by a few employees at a commercial software developer. Should this kind of work even be considered Science? It may be research , and it may be important , but unless enough details of the experimental methodology are made available so that it can be subjected to true reproducibility tests by skeptics, it isn’t Science.

• This discussion closely follows a treatment of Popper’s asymmetry in: Sober, Elliot Philosophy of Biology (Boulder: Westview Press, 2000), pp. 50-51.
• Popper, Karl R. “The Logic of Scientific Discovery” 5th ed. (London: Hutchinson, 1959), pp. 40-41, 46.
• Gillies, Donald. “The Duhem Thesis and the Quine Thesis”, in Martin Curd and J.A. Cover ed. Philosophy of Science: The Central Issues, (New York: Norton, 1998), pp. 302-319.
• C. Hempel. Philosophy of Natural Science 49 (1966).
• Lett, James, Science, Reason and Anthropology, The Principles of Rational Inquiry (Oxford: Rowman & Littlefield, 1997), p. 47
• See, for example www.bannedbygaussian.org

5 Responses to Being Scientific: Falsifiability, Verifiability, Empirical Tests, and Reproducibility

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“If we cannot verify theoretical statements, then we cannot falsify them either.

Since verifying a theoretical statement is nearly impossible, and falsification often requires verification of assumptions…”

An invalid argument is invalid regardless of the truth of the premises. I would suggest that an hypothesis based on unverifiable assumptions could be ‘falsified’ the same way an argument with unverifiable premises could be shown to be invalid. Would you not agree?

“Falsifying a theory requires that auxiliary assumption (AA) be demonstrably true.”

No, it only requires them to be true.

In the falisificationist method, you can change the AA so long as that increases the theories testability. (the theory includes AA and the universal statement, btw) . In your second box you misrepresent the first derivation. in the conclusion it would be ¬(t and AA). after that you can either modify the AA (as long as it increase the theories falsifiability) or abandon the theory. Therefore you do not need the third box, it explains something that does not need explaining, or that could be explained more concisely and without error by reconstructing the process better. This process is always tentative and open to re-evaluation (that is the risky and critical nature of conjectures and refutations). Falsificationism does not pretend conclusiveness, it abandoned that to the scrap heap along with the hopelessly defective interpretation of science called inductivism.

“Contrary to Popper, there really is no asymmetry between falsification and verification. If we cannot verify theoretical statements, then we cannot falsify them either.” There is an asymmetry. You cannot refute the asymmetry by showing that falsification is not conclusive. Because the asymmetry is a logical relationship between statements. What you would have shown, if your argument was valid or accurate, would be that falsification is not possible in practice. Not that the asymmetry is false.

Popper wanted to replace induction and verification with deduction and falsification.

He held that a theory that was once accepted but which, thanks to a novel experiment or observation, turns out to be false, confronts us with a new problem, to which new solutions are needed. In his view, this process is the hallmark of scientific progress.

Surprisingly, Popper failed to note that, despite his efforts to present it as deductive, this process is at bottom inductive, since it assumes that a theory falsified today will remain falsified tomorrow.

Accepting that swans are either white or black because a black one has been spotted rests on the assumption that there are other black swans around and that the newly discovered black one will not become white at a later stage. It is obvious but also inductive thinking in the sense that they project the past into the future, that is, extrapolate particulars into a universal.

In other words, induction, the process that Popper was determined to avoid, lies at the heart of his philosophy of science as he defined it.

Despite positivism’s limitations, science is positive or it is not science : positive science’s theories are maybe incapable of demonstration (as Hume wrote of causation), but there are not others available.

If it is impossible to demonstrate that fire burns, putting one’s hand in it is just too painful.

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What does it mean for science to be falsifiable?

Posted on July 31, 2021 by Evan Arnet

Science is falsifiable. Or at least, this is what I (like many Americans) learned in many of my high school and college science classes. Clearly, the idea has appeal among scientists and non-scientists alike:

But what exactly does “falsifiable” mean? And why is it valued by some scientists, but dismissed or even considered actively harmful by others?

Imagine you are an infectious disease expert investigating COVID-19. You want to determine whether, absent vaccination, COVID-19 always causes at least some lung damage. To prove this claim is true, you would have to check every case and see if every time a patient has COVID, there is also lung damage. And for every case you check, there are more new cases to check.

However, to prove this claim is false, you merely need to document a single case in which someone who previously had COVID has no lung damage. This is an extension of the logical point that to prove a general claim, you need to confirm every instance, but to disprove a general claim, you only need a single counterexample. 

The legendary philosopher of science Karl Popper argued that good science is falsifiable, in that it makes precise claims which can be tested and then discarded (falsified) if they don’t hold up under testing. For example, if you find a case of COVID-19 without lung damage, then you falsify the hypothesis that it always causes lung damage. According to Popper, science progresses by making conjectures, subjecting them to rigorous tests, and then discarding those that fail.

He contrasted this with ostensibly unscientific systems, like astrology. Let’s say your horoscope says “something of consequence will happen in your life tomorrow.” Popper argued that a claim like this is so vague, so devoid of clear content, that it can’t be meaningfully falsified and, therefore, isn’t scientific. 

Contemporary scholars who study scientific methodology are often frustrated by the implication that science is logically falsifiable. The problem is that scientists can always make excuses to avoid falsifying a claim. The discovery of Neptune is a famous case. Astronomers had noticed irregularities in the orbit of Uranus. One possibility would be that these irregularities violated the theory currently used to explain planetary motion, called Newtonian mechanics, and that this theory should be rejected. At face value, these observations seemed to falsify Newtonian mechanics. But, no one actually argued for this. Instead, they searched for explanations for the irregularities — including the possibility of another planet. Two astronomers, Urban Leverrier in France and John Couch Adams in England, independently used mathematics to predict the location of this previously unknown planet. Astronomical observations by Johann Gottfried Galle confirmed the existence of a planet and, thus, Neptune was discovered.

Put simply, to test a hypothesis, you have to make a bunch of other assumptions, or auxiliary hypotheses. You have to assume that your instruments are working, that you did the math correctly, that you didn’t miss any relevant causes (like Neptune), etc. When something goes awry, you can then choose whether the real error lies in your main hypothesis or in an auxiliary hypothesis. 

For an illustration of this problem, imagine you are baking lasagna. You Google lasagna recipes, find a recipe that looks good, and get cooking. You take your lasagna out of the oven, take a bite, and…it tastes terrible. Does this mean you can falsify the hypothesis that the lasagna recipe is good? Not necessarily. Maybe you didn’t follow the recipe correctly, or the olive oil was rancid, or any number of problems other than the recipe itself.

Similar to the COVID example above, we can imagine a scientist arguing that because of poor resolution in a CT scan, lung damage was not detected when it did in fact occur. In other words, the presumed false hypothesis is not that COVID always causes lung damage. Instead, what is allegedly false is the assumption, or auxiliary hypothesis, that the CT scan was detailed enough to detect the lung damage.

This general argument against falsification is sometimes attributed to the philosopher W. V. O. Quine in a famous 1951 article, but it was actually a widely-expressed concern, including by Karl Popper himself. However, Popper thought that features necessary for the testing of scientific claims would be accepted as background conditions by the scientific community and, therefore, falsification could proceed. For example, after it is accepted that the oven temperature is correct and the ingredients are in good condition and measured properly, then one can test whether the lasagna recipe is any good.

Regardless, when a scientist touts the falsifiability of science, it is rare that they are a strict devotee of Popper. (He held some unorthodox views, e.g., we can never actually gain confidence in a theory, we can only eliminate alternatives.) Usually they mean that, unlike some other systems, science makes deliberately clear predictions and actively attempts to disprove claims.

One of the amazing things about science is not so much its tight logical structure — the scientific process can actually be quite messy — but rather, that science aims to test claims and consider countermanding evidence. The sociologist of science Robert Merton referred to this as “organized skepticism.” (Incidentally, despite his reputation for prioritizing logical falsification, Karl Popper was attentive to this social aspect of science.)

Falsification as a matter of scientific practice, rather than logic, is especially significant because humans like to be right. We are inclined to seek out evidence which supports rather than challenges our existing opinions, a well-known phenomenon that is often referred to as confirmation bias . Science fights against this cognitive tendency by encouraging individual scientists to think critically about their own work and for the broader community to be skeptical of each other. 

Falsification does not stand alone as the mark of the scientific, and a lot of scientific research aims to confirm claims or to evaluate claims on metrics other than strict truth or falsity. Nonetheless, the willingness and intent to vigorously confront claims with evidence remains a key aspect of the scientific community. This requires attention to the formulation of claims to ensure they are testable. But, even more important is the careful coordination across the scientific community that allows scientific skepticism to lead to productive research.

Edited by Jennifer Sieben and Joe Vuletich

This was a fantastic explanation of a concept that I’ve always had difficulty understanding.

Great article, you really explain it well! I was looking for the line, “science tries to disprove itself by falsification,” and this article was on the list.

At the health sciences center where I worked for 8 years, the idea was widespread that anybody could come up with an explanation or hypothesis for some physiology or biochemical facts, so much so that you couldn’t be bothered if all it did was explain the data. A lecture with a mathematical model involving modeling biochemistry with 100 different equation in a seminar led to the reaction (from me) , how would you know if one or more equation was wrong? Feynman, the skeptical physicist from the Bronx would make a characteristic short reply to a non-falsifiable claim “how would you know?”. The writers above in this thread point out that a community that uses publication of scientific results in the newly public publications of the new scientific societies of the 16nth century that made replication of studies possible and publication is a key factor. I have heard chemists reply disdainfully of the guy whose published synthesis can never be repeated. You may have heard about the humor magazine “journal of irreproducible results”. Doubting your own assumptions maybe 1 per day, is a potentially painful exercise that is at the heart of being a scientist. A person who tends to rote memorization, or good boy behavior may not be a scientists if they do not think in terms of falsification but simply truthiness. It is disturbing that some people propose that string theory does not need to generate testable results and can get by on beauty alone.

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Falsifications and scientific progress: Popper as sceptical optimist

• Published: 30 January 2014
• Volume 1 , pages 179–184, ( 2014 )

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• Carlo Veronesi 1  

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A scientific theory must be falsifiable, and scientific knowledge is always tentative, or conjectural. These are the main ideas of Popper’s Logic of Scientific Discovery . Since 1960 his writings contain some essential developments of these views and make some steps towards epistemological optimism. Although we cannot justify any claim that a scientific theory is true, the aim of science is the search of truth and we have no reason to be sceptical about the notion of getting nearer to the truth. Our knowledge can grow, and science can progress. Nevertheless, Popper’s theory of approximation to the truth is problematic and is still the subject of studies and discussions.

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1 References to two fundamental problems of knowledge

Popper’s philosophy of science takes as a starting point two fundamental problems of knowledge theory: the problem of induction, which Popper calls ‘Hume’s problem’, and the problem of demarcation, which is called ‘Kant’s problem’.

The problem of demarcation consists in the search for a criterion that makes it possible to distinguish empirical science from metaphysical speculation, philosophical systems and other forms of human knowledge. One answer to this problem is widely agreed upon: science is based on facts and is distinguished by its inductive method, which derives universal laws by generalising the results of observations and experiments. Thus, to demarcate science recourse is made to a ‘principle of induction’, which can be expressed as follows: if an observable property is valid for a certain number of members of a class, then it is valid for all members of the class. Popper, like Hume, declares himself contrary to induction and, like Kant, maintains that science begins with hypotheses and not with the gathering of experimental data, but all the same he thinks that it is possible to provide a criterion of demarcation. Hume maintained that induction, as a method of formulating laws or habits, was an irrational procedure, and according to Popper as well, it is not legitimate to go from particular cases to a universal law, that is, one that is valid for a potentially infinite set of cases; it is only permissible to go, in the presence of contrasting observations, to the falsification of the law. Using an example that is by now well known, Popper argues that, no matter how many white swans are observed, no one can be certain that the law ‘All swans are white’ will always be valid in all regions of space and time: a single observation of a black swan can render it false. It is precisely the possibility of falsification that characterises the empirical sciences and which, according to Popper, draws the line of demarcation between the theories of science and the doctrines of metaphysics or pseudoscience.

Elsewhere [ 15 ] we remarked that a young Popper arrived to this idea under the impression of the great upheaval in physics wrought by Einstein’s theory of relativity. Newton’s theory of gravitation, based on action at a distance of masses, had carried the day for more than two centuries but was replaced, at the beginning of the twentieth century, by relativistic physics. In 1919 the English astronomer Arthur Eddington organised two scientific expeditions to measure, during an eclipse of the sun in the southern hemisphere, an effect of general relativity which, in a normal day of sunshine, would have been impossible to observe. It was during this expedition that confirmation arrived that the trajectory of the luminous rays of the stars, even though these are without mass in the classic sense of the term, are curved when they pass near the sun. This result, predicted by Einstein and unforeseeable according to Newton’s theory, led to the global triumph of the new relativistic physics, even appearing on the front page of the New York Times . In that same year––1919––young Popper was able to attend a lecture given by Einstein in Vienna, remaining impressed by the fact that the physics of Newton, which appeared indisputable, could be replaced by a better theory, especially because Einstein himself had explained that in its turn the theory of relativity could also be confuted. Popper became convinced that we can never be sure in science that the truth has been reached, nor could even the most thoroughly tested theories escape the risk of falsification.

The falsifiability of scientific theories, which for Popper was suggested by logic and by the history of science, could also appear to be a rule of common sense. No theory should be taken into account if it evades all checks and if it cannot be contradicted by any observable fact. The predictions of soothsayers and astrologers, often so vague and imprecise as to be suitable for any kind of situation, are neither reliable nor scientific. Thus, science cannot reasonably include theories that render the search for counter-examples impractical, even though this means excluding theories that enjoy greater consideration than astrology.

Even the psychoanalysis of Freud, according to Popper, is closer to metaphysics than to science, because no kind of human behaviour can be either predicted or excluded on the basis of this theory. Instead, Popper’s position on Marxism is rather more detailed: in his opinion Marx’s doctrine was born as a falsifiable theory, with historically verifiable predictions, but then the followers of Marxism fitted it out with a battery of auxiliary hypotheses to prevent its being clearly contradicted by the facts. In this way they often managed to reinterpret theories and facts so as to make them agree, but in saving the theory, they sacrificed its scientificity.

2 The optimistic turn of Popper’s thinking

In his important 1935 Logik der Forschung [translated into English as The Logic of Scientific Discovery (1959)], Popper, in order to give credence to the thesis that verifications of theories (no matter how numerous) are in any case insufficient, took care to clear the field from another idea of an inductivist or verificationist nature, that is, that evidence in favour, even if unable to lead to the truth, can in any case increase the probability of theories (obviously in the absence of counter-examples). According to him, the probability of a universal law turns out to be equal to zero because the number of favourable cases, necessarily finite, must be seen in reference to the infinity totality of possible cases. Hence the results in favour can in no way increase the probability of a theory; they can only increase the degree of ‘corroboration’. Popper uses the term ‘corroboration’ to provide an indication of how well a theory has stood up to the attempts to confute it, as well as its provisional acceptability. To this end, the number of examples in favour does not count. Banal evidence, such as that which might derive from the repetition of the same experiment, does not increase the corroboration. A theory can be said to be corroborated only if it passes rigorous tests of risky predictions, that is, those at high risk of falsification. More precisely, Popper connects the degree of corroboration of a theory to the success in the prediction of events that are unexpected, surprising and considered improbably in light of previous knowledge. The prediction that the distance between two fixed stars, measured during the day, would be different from that measured at night, would have been unthinkable without Einstein’s theory of gravitation (which predicts that light must be attracted to the sun in exactly the same way that heavy bodies are). Thus, confirmation of this prediction by the British expeditions during the 1919 eclipse provided extraordinary corroboration of Einstein’s theory. However, the corroboration of a theory is a temporal account of its past successes, which provides no guarantee of its ability to pass future tests. Newton’s physics, over the course of two centuries, had registered a series of confirmations as well as of corroborating successes, culminating in the discovery of Neptune. This planet, whose existence has been postulated to explain the anomaly of the orbit of Uranus, was discovered in 1846 by the German astronomer Johann Gottfried Galle in exactly the region of space in which the earlier calculations (based on Newton’s celestial mechanics) by John Couch Adams and Urbain Le Verrier had situated it. The sensational success of this prediction provided a huge amount of support for the Newtonian theory, but did not prevents its later refutation.

For the reasons we have just given, in the final pages of The Logic of Scientific Discovery (which is still a youthful work, published when the author was just over 30), Popper observes that corroboration is not a value of truth, and that in his logic of science it was possible to avoid the use of concepts of ‘true’ and ‘false’ [ 7 : pp. 273–274]. In this order of ideas, he spoke of progress only as the elimination of erroneous theories in favour of others that were more comprehensive, or as the discovery of new problems that were deeper and more general [ 7 : p. 281], almost as if, as Imre Lakatos noted, scientific progress consisted in ‘an increased awareness of ignorance rather than a growth of knowledge’ [ 2 : p. 155]. However, after the publication of Logic , Popper came into contact with Alfred Tarski’s theory of truth, which led him to change the tone of his own philosophy and integrate the logic of discovery, in which it only seemed possible to reveal the error, with the theory of verisimilitude and the approximation to truth.

The Polish logician Tarski––explains Popper––had rehabilitated a theory of truth as a ‘correspondence to the facts’, which is another common sense idea of the truth. Following Tarski it is possible to write that ‘the sentence “snow is white” is true if and only if snow is white’ [ 13 : p. 64].

The discussion seems rather trivial, but what Tarski made evident––and this is the decisive element of his discovery––was that to speak about the correspondence of a sentence with the facts we need an ‘object language’ and a ‘metalanguage’. The object language is used to speak about facts, things and properties of the world, such as snow and its colour. Metalanguage is used to speak about both statements in object language, such as the statement in quotation marks ‘snow is white’, and about the facts of the world to which the statement refer. Footnote 1 In his comment Popper goes on to say that once the need for this metalanguage has been understood, it is not difficult to see how a statement can correspond to the facts, and it is also possible to explain the traps of everyday language, such as the classic ‘antinomy of the liar’, according to which the statement ‘I am lying’ is self-contradictory (the contradiction deriving from the fact that in everyday language no distinction is made between the levels of language and metalanguage).

Encouraged by Tarski’s results, Popper began to think that it might be possible to speak of objective truth, that is, of truth as correspondence to facts, without fear of falling into paradoxes, and that hence there was no longer any reason to abstain from speaking of the truth of science. One scientific theory could correspond to the facts better than another, that is, it could be closer to the truth. It would be rather unreasonable to think that Einstein’s physics, which had been successful in risky predictions, with precise measurements of phenomena not predicted by previous theories, did not contain something of the truth, or that it was no closer to the truth than all the rival theories that had preceded it [ 11 : pp. 1192–1193]. Popper became convinced that theories could come close to reality, and that it was also possible to recognise progress made towards the truth. If a theory had passed the tests that had been failed by a previous theory, then we have reason to believe that it is more verisimilar: we can therefore think that a highly corroborated theory is closer to the truth than one with a lower degree of corroboration.

Popper developed these concepts in the writings of his later years, and it is rather peculiar that his philosophy is known above all for its falsificationist methodology and much less known for these more articulated positions, in spite of these having been illustrated in lectures, talks and articles over the course of several decades. In one essay that joins two lectures given in the years 1960 and 1961, Popper himself wrote that, after having become aware of Tarski’s ideas on truth and becoming convinced that the idea of truth was not so ‘dangerously vague and metaphysical’ [ 8 : p. 314], he was able to contribute ‘essential further developments’ [ 8 : p. 291] to the ideas expressed in his Logic of Scientific Discovery . Footnote 2 According to this new outlook, science is something more than an incessant discovery of failures, and is not limited to revealing error and replacing erroneous theories. Scientific progress is not made only by means of conjectures and refutations; it is progress by means of conjectures, refutations and corroborations. Thus, corroborations, which were initially the point of departure for ulterior attempts at refutation [ 7 : Appendix IX, p. 419], became signs of progress and steps forward towards the truth, because a corroborated scientific theory, even if it can still be refuted, can be in the running as an approximately true theory and in any case contain a part of the truth. In this way Popper can also explain the possible paradox of false theories, such as Newtonian physics, which in any case function for centuries and continue to be used even after they have been falsified; this without taking refuge in pragmatism or instrumentalism, concepts according to which scientific theories are only convenient instruments for working without any pretext of aiding our understanding of the world. To the contrary, Popper states that the aim of science is precisely to search for the truth and that, in spite of difficulties and limited successes, it even manages to approach it.

3 Truth and approximation of truth

A further difficulty of the concept of truth derives from the conviction that a satisfying theory of truth must comprehend a criterion for believing in it in a way that is established and rational. According to Popper, this idea confuses what is true with what we know to be true, and does not take account of the fact that a theory can be true even if no one believes it. Popper maintains that truth must be separated from subjective experience of believing in it, and that the concepts of truth and certainty must not be confused. The aim of science cannot be to search for certainty, because all knowledge is fallible and thus uncertain, but the search for truth nevertheless remains. The theory of objective truth supported by Popper makes it possible to say that we search for the truth even if, as the ancient Greek philosopher Xenophanes (c.570–c.475 BCE) pointed out, we might not ever reach it, or recognise it when we do reach it. Using a famous metaphor, Popper compares the status of truth to a mountaintop wrapped in clouds. A climber might not only have trouble reaching it, but recognising it when he does: up in the clouds he might not be able to distinguish the main peak from the smaller peaks surrounding it. However, he can understand when he has not reached it, as when, for instance, he discerns one even higher, and he can consequently decide to continue on in that direction. As a rule we do not have a criterion of truth, that is, a procedure for recognising it, but we do have criteria for moving towards it.

However, the search for truth might also reveal itself to be a secondary ideal if it is limited to the trivial aspects of reality, because in science we seek something more than simple truth. Much in the same way as in mathematics, where we are not content with saying that two plus two equals four, in science as well we desire truths that are interesting and difficult to attain. We thus prefer a bold conjecture, even if it should turn out to be false, to a series of assertions that are true but uninteresting. From failure we can learn much about the truth; we can, eliminating our errors, come closer to it. Popper adds––and this is the new element––that to approach truth it is generally not sufficient to correct the errors of a previous theory. Certainly what is needed is a new theory that solves the difficulties of the earlier one, but this theory must also make it possible to predict facts never before observed, and to pass some of the tests regarding these new predictions. ‘An unbroken sequence of refuted theories would soon leave us bewildered and helpless’ [ 8 : p 330]: we need success and empirical corroboration in order to understand if we are on the right path, and also to appreciate the meaning of successful refutations.

All of these considerations take off from an intuitive base: the idea that scientific progress is made by means of a sequence of false (or presumably so) theories, ever closer to the truth, and that these can arise both by means of the correction of the aspects that are gradually falsified as well as by means of the support of new consequences or verified predictions. To explain precisely what he means, Popper considers two theories, A and B , both of which are false ( A can be considered an earlier theory and B a later one that replaced it) and states that B is closer to the truth than A if in the passage from A to B the set of false consequences is reduced without impairing the set of true consequences, or the set of true consequences is reinforced without incrementing at the same time the set of false consequences. This definition appears well posed logically: while a true theory has only true consequences, affirmations both true and false can follow from false premises. Moreover, common sense seems to agree with the idea that one false theory can contain fewer errors than another given the same amount of true information, or a greater amount of true information given equal false information. Unfortunately, a few years later some critics [ 5 , 14 ] showed that none of the conditions established by Popper for approaching truth can be verified, because the true consequences and false consequences of a theory increase and decrease together.

Given the importance of this negative result, which opened a new line of epistemological research, we want to expound on it in some detail. To this end, given the two false theories A and B , let A T indicate the truth-content (=the set of true logical consequences) of theory A , and A F its falsity-content (=the set of consequences of A that do not belong to A T ). Analogously, B T and B F are respectively the truth-content and falsity-content of theory B . Using these symbols, Popper’s comparative definition of verisimilitude or truthlikeness can be rewritten as follows: theory B is closer to the truth than theory A if and only if ( A T  ⊂  B T and B F  ⊆  A F ) or ( B F  ⊂  A F and A T  ⊆  B T ). Now let us show, following Tichý and Miller, that these two conditions cannot be satisfied if the theories are false and thus no false theory B can be closer to the truth than a false theory A on the basis of Popper’s criterion.

Let us first suppose that A T  ⊂  B T and that b is a true consequence of B but not of A (in the passage from A to B the truth-content is incremented, by example with the proposition b ). Since B is false, B F is not empty: I can thus consider a false consequence f of B and form the conjunction b&f . This conjunction is false (it would be true if and only if both b and f were true) and is a consequence of B (because b&f is a consequence of the propositions b and f , and moreover both b and f are consequences of B ): it therefore belongs to the falsity-content of B . The conjunction b&f cannot also belong to the falsity-content of A , because in that case both b and f would have to be consequences of A , contrary to our assumption that b is not. Therefore, if A T  ⊂  B T , there exists a proposition, b&f , which belongs to B F and not to A F , and there cannot be B F  ⊆  A F as required by Popper’s case 1. If the truth-content of the new theory B exceeds the truth-content of A , contemporarily the falsity-content of B also exceeds that of A .

Let us now suppose that B F  ⊂  A F and that g is a false consequence of A but not of B (in the passage from A to B the falsity-content is deprived of proposition g ). Let us consider a false proposition f of B to form the implication f  →  g . This implication is true (it would be false only for true f and false g ) and it is a consequence of A (because the implication f  →  g is a consequence of proposition g , and proposition g is a consequence of A ): it thus belongs to the truth-content of A . The statement f  →  g cannot also belong to the truth-content of B because in that case both f and g would have to be consequences of B , contrary to our assumption that g is not. Therefore, in the case where B F  ⊂  A F , there exists a statement, f  →  g , which belongs to A T and not to B T and there cannot be A T  ⊆  B T as required by case 2 of Popper’s definition. In the passage from A to B the falsity-content cannot diminish without at the same time also diminishing the truth-content.

This negative result, according to which two false scientific theories cannot be compared, might appear to be a mere logical artifice. Looking at the history of science, it seems reasonable to think that theories that are gradually falsified can still be considered increasingly better approximations to an unknown truth. The astronomical system of Copernicus has come to be considered better with respect to that of Ptolemy, and the theories of Newton and Einstein are considered even better. We might also cite trivial examples of false statements that we judge to be closer to the truth than others: the statement ‘There are ten planets in the solar system’ seems to be less false and thus closer to the truth than the statement ‘There are ten thousand planets in the solar system’.

In any case, even if the results of Tichý and Miller seem rather counter-intuitive, Popper acknowledged his logical error and attempted to correct the initial definitions of verisimilitude, and so did some of his students and other scholars in the years that followed. One idea might be that of placing a few restrictions on the classes of logical consequences that might work for or against the verisimilitude of theories, for example, comparing only the truth contents or privileging atomic or elementary propositions. This search for an approach to truth can be conducted, as Popper suggested, ‘in a kind of metrical or at least topological space’ [ 8 : p. 314] but, in spite of a great plethora of approaches, the search has not produced results that are unanimously shared. Thus the intuitive idea of a progressive approach to truth is not easily captured by formal definitions and the problem of verisimilitude remains an open one. Footnote 3

4 Concluding observations and a glance at ulterior problems

In an autobiographical note about his youthful interests, Popper wrote that in the autumn of 1919, when he tackled his first problem of the philosophy of science, he was not worried about the truth of theories: ‘My problem was different: I wished to distinguish between science and pseudo-science, knowing very well that science often errs and that pseudo-science may happen to stumble on the truth’ [ 9 : p. 44]. Be that as it may, already at the origin of all of Popper’s discourse, and his efforts to distinguish science from other forms of knowledge, it is possible to recognise an undeclared assumption: the basic idea that the requirement of falsifiability in any case renders science superior to metaphysics and pseudo-science. Imprecise theories, such as astrology and psychoanalysis, or theories that resort to continual correction to render them immune from failure, such as Marxism, can add nothing to our knowledge: if the search for counter-examples is not practical, then neither can we have any clue as to their provisional reliability. Further, even if one metaphysical theory or another should by some chance speak the truth, it would in any case be a truth that was static and without progress. To the contrary, it is the falsifiable aspects of theories, the refutations and successes in resisting the attempts at refutation, that are capable of contributing to progress towards the truth. These ideas, not yet clarified in Popper’s youthful work, would be elaborated, as we have seen, in the later development of his thinking.

Pavel Tichý, one of the logicians who criticised the Popperian definitions of verisimiltude, defines Popper’s mature conception as ‘optimistic scepticism’ [ 14 : p. 155]: the scepticism comes from the statement that we can never prove the truth of a scientific theory; the optimism derives from another of his statements, that our theories, presumably false, can be improved by approaching the truth. It was Popper himself who empowered these definitions of Tichý’s, speaking of his position as halfway between a pessimistic and an optimistic conception of scientific knowledge [ 12 : pp. 3–10], tending to be closer to optimism than to sceptical pessimism. This is because, while we might be sceptical about our capability to recognise the truth, we have no reason to be so towards the notion of approaching the truth and the fact that our science can grow and progress.

The middle road between scepticism and optimism sought by Popper seems problematical in any case: from the technical point of view there remains the problem of an acceptable formalization of the notion of verisimilitude; from the epistemological point of view Popper had to recognise that in order to justify his rediscovered optimism he needs a ‘whiff’ of inductivism [ 11 : p. 1193] to be able to state (taking the history of science as his point of departure) that the theories best corroborated are those closest to the truth. We can see that in this way Popper, after having kicked induction out the door, lets it back in through the window, and further that his inductive argument, weak nevertheless, needs notions that do not seem objective in the strict sense. Popper says that science progresses by means of risky predictions and results that are unexpected, surprising and sometimes spectacular; he also tells us that science seeks truths that are difficult and interesting. In either case, it appears that (aside from Popper’s intentions) other elements, of a subjective, psychological or perhaps aesthetic nature, must be introduced into the scientific enterprise. Recently some scholars of the problem of verisimilitude have begun to consider, albeit with a great deal of caution, the possibility of introducing a principle of aesthetic induction into the evaluation of scientific theories. Footnote 4 But this is another story.

Translated from the Italian by Kim Williams.

On the concept of truth as conformity with (or correspondence to) reality or as conformity with the “existing state of affairs”, see [ 13 ].

Among the essays of Popper’s optimistic phase, Imre Lakatos particularly remarks the ‘Addendum’ to The Open Society and its Enemies [ 10 ], even while reproaching Popper for not having ‘fully exploited the possibilities opened up by his Tarskian turn’ [ 2 : p. 159].

For a survey of the studies on verosimiltude, see [ 6 ].

The discussion on aesthetic induction is introduced in [ 3 ]. On the relationship between aesthetic induction and truth, see [ 1 ] and [ 4 ].

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Veronesi, C. Falsifications and scientific progress: Popper as sceptical optimist. Lett Mat Int 1 , 179–184 (2014). https://doi.org/10.1007/s40329-014-0031-7

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Published : 30 January 2014

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4.14: Experiments and Hypotheses

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Now we’ll focus on the methods of scientific inquiry. Science often involves making observations and developing hypotheses. Experiments and further observations are often used to test the hypotheses.

A scientific experiment is a carefully organized procedure in which the scientist intervenes in a system to change something, then observes the result of the change. Scientific inquiry often involves doing experiments, though not always. For example, a scientist studying the mating behaviors of ladybugs might begin with detailed observations of ladybugs mating in their natural habitats. While this research may not be experimental, it is scientific: it involves careful and verifiable observation of the natural world. The same scientist might then treat some of the ladybugs with a hormone hypothesized to trigger mating and observe whether these ladybugs mated sooner or more often than untreated ones. This would qualify as an experiment because the scientist is now making a change in the system and observing the effects.

Forming a Hypothesis

When conducting scientific experiments, researchers develop hypotheses to guide experimental design. A hypothesis is a suggested explanation that is both testable and falsifiable. You must be able to test your hypothesis, and it must be possible to prove your hypothesis true or false.

For example, Michael observes that maple trees lose their leaves in the fall. He might then propose a possible explanation for this observation: “cold weather causes maple trees to lose their leaves in the fall.” This statement is testable. He could grow maple trees in a warm enclosed environment such as a greenhouse and see if their leaves still dropped in the fall. The hypothesis is also falsifiable. If the leaves still dropped in the warm environment, then clearly temperature was not the main factor in causing maple leaves to drop in autumn.

In the Try It below, you can practice recognizing scientific hypotheses. As you consider each statement, try to think as a scientist would: can I test this hypothesis with observations or experiments? Is the statement falsifiable? If the answer to either of these questions is “no,” the statement is not a valid scientific hypothesis.

Practice Questions

Determine whether each following statement is a scientific hypothesis.

• No. This statement is not testable or falsifiable.
• No. This statement is not testable.
• No. This statement is not falsifiable.
• Yes. This statement is testable and falsifiable.

[reveal-answer q=”429550″] Show Answers [/reveal-answer] [hidden-answer a=”429550″]

• d: Yes. This statement is testable and falsifiable. This could be tested with a number of different kinds of observations and experiments, and it is possible to gather evidence that indicates that air pollution is not linked with asthma.
• a: No. This statement is not testable or falsifiable. “Bad thoughts and behaviors” are excessively vague and subjective variables that would be impossible to measure or agree upon in a reliable way. The statement might be “falsifiable” if you came up with a counterexample: a “wicked” place that was not punished by a natural disaster. But some would question whether the people in that place were really wicked, and others would continue to predict that a natural disaster was bound to strike that place at some point. There is no reason to suspect that people’s immoral behavior affects the weather unless you bring up the intervention of a supernatural being, making this idea even harder to test.

[/hidden-answer]

Testing a Vaccine

Let’s examine the scientific process by discussing an actual scientific experiment conducted by researchers at the University of Washington. These researchers investigated whether a vaccine may reduce the incidence of the human papillomavirus (HPV). The experimental process and results were published in an article titled, “ A controlled trial of a human papillomavirus type 16 vaccine .”

Preliminary observations made by the researchers who conducted the HPV experiment are listed below:

• Human papillomavirus (HPV) is the most common sexually transmitted virus in the United States.
• There are about 40 different types of HPV. A significant number of people that have HPV are unaware of it because many of these viruses cause no symptoms.
• Some types of HPV can cause cervical cancer.
• About 4,000 women a year die of cervical cancer in the United States.

Practice Question

Researchers have developed a potential vaccine against HPV and want to test it. What is the first testable hypothesis that the researchers should study?

• HPV causes cervical cancer.
• People should not have unprotected sex with many partners.
• People who get the vaccine will not get HPV.
• The HPV vaccine will protect people against cancer.

[reveal-answer q=”20917″] Show Answer [/reveal-answer] [hidden-answer a=”20917″]Hypothesis A is not the best choice because this information is already known from previous studies. Hypothesis B is not testable because scientific hypotheses are not value statements; they do not include judgments like “should,” “better than,” etc. Scientific evidence certainly might support this value judgment, but a hypothesis would take a different form: “Having unprotected sex with many partners increases a person’s risk for cervical cancer.” Before the researchers can test if the vaccine protects against cancer (hypothesis D), they want to test if it protects against the virus. This statement will make an excellent hypothesis for the next study. The researchers should first test hypothesis C—whether or not the new vaccine can prevent HPV.[/hidden-answer]

Experimental Design

You’ve successfully identified a hypothesis for the University of Washington’s study on HPV: People who get the HPV vaccine will not get HPV.

The next step is to design an experiment that will test this hypothesis. There are several important factors to consider when designing a scientific experiment. First, scientific experiments must have an experimental group. This is the group that receives the experimental treatment necessary to address the hypothesis.

The experimental group receives the vaccine, but how can we know if the vaccine made a difference? Many things may change HPV infection rates in a group of people over time. To clearly show that the vaccine was effective in helping the experimental group, we need to include in our study an otherwise similar control group that does not get the treatment. We can then compare the two groups and determine if the vaccine made a difference. The control group shows us what happens in the absence of the factor under study.

However, the control group cannot get “nothing.” Instead, the control group often receives a placebo. A placebo is a procedure that has no expected therapeutic effect—such as giving a person a sugar pill or a shot containing only plain saline solution with no drug. Scientific studies have shown that the “placebo effect” can alter experimental results because when individuals are told that they are or are not being treated, this knowledge can alter their actions or their emotions, which can then alter the results of the experiment.

Moreover, if the doctor knows which group a patient is in, this can also influence the results of the experiment. Without saying so directly, the doctor may show—through body language or other subtle cues—his or her views about whether the patient is likely to get well. These errors can then alter the patient’s experience and change the results of the experiment. Therefore, many clinical studies are “double blind.” In these studies, neither the doctor nor the patient knows which group the patient is in until all experimental results have been collected.

Both placebo treatments and double-blind procedures are designed to prevent bias. Bias is any systematic error that makes a particular experimental outcome more or less likely. Errors can happen in any experiment: people make mistakes in measurement, instruments fail, computer glitches can alter data. But most such errors are random and don’t favor one outcome over another. Patients’ belief in a treatment can make it more likely to appear to “work.” Placebos and double-blind procedures are used to level the playing field so that both groups of study subjects are treated equally and share similar beliefs about their treatment.

The scientists who are researching the effectiveness of the HPV vaccine will test their hypothesis by separating 2,392 young women into two groups: the control group and the experimental group. Answer the following questions about these two groups.

• This group is given a placebo.
• This group is deliberately infected with HPV.
• This group is given nothing.
• This group is given the HPV vaccine.

[reveal-answer q=”918962″] Show Answers [/reveal-answer] [hidden-answer a=”918962″]

• a: This group is given a placebo. A placebo will be a shot, just like the HPV vaccine, but it will have no active ingredient. It may change peoples’ thinking or behavior to have such a shot given to them, but it will not stimulate the immune systems of the subjects in the same way as predicted for the vaccine itself.
• d: This group is given the HPV vaccine. The experimental group will receive the HPV vaccine and researchers will then be able to see if it works, when compared to the control group.

Experimental Variables

A variable is a characteristic of a subject (in this case, of a person in the study) that can vary over time or among individuals. Sometimes a variable takes the form of a category, such as male or female; often a variable can be measured precisely, such as body height. Ideally, only one variable is different between the control group and the experimental group in a scientific experiment. Otherwise, the researchers will not be able to determine which variable caused any differences seen in the results. For example, imagine that the people in the control group were, on average, much more sexually active than the people in the experimental group. If, at the end of the experiment, the control group had a higher rate of HPV infection, could you confidently determine why? Maybe the experimental subjects were protected by the vaccine, but maybe they were protected by their low level of sexual contact.

To avoid this situation, experimenters make sure that their subject groups are as similar as possible in all variables except for the variable that is being tested in the experiment. This variable, or factor, will be deliberately changed in the experimental group. The one variable that is different between the two groups is called the independent variable. An independent variable is known or hypothesized to cause some outcome. Imagine an educational researcher investigating the effectiveness of a new teaching strategy in a classroom. The experimental group receives the new teaching strategy, while the control group receives the traditional strategy. It is the teaching strategy that is the independent variable in this scenario. In an experiment, the independent variable is the variable that the scientist deliberately changes or imposes on the subjects.

Dependent variables are known or hypothesized consequences; they are the effects that result from changes or differences in an independent variable. In an experiment, the dependent variables are those that the scientist measures before, during, and particularly at the end of the experiment to see if they have changed as expected. The dependent variable must be stated so that it is clear how it will be observed or measured. Rather than comparing “learning” among students (which is a vague and difficult to measure concept), an educational researcher might choose to compare test scores, which are very specific and easy to measure.

In any real-world example, many, many variables MIGHT affect the outcome of an experiment, yet only one or a few independent variables can be tested. Other variables must be kept as similar as possible between the study groups and are called control variables . For our educational research example, if the control group consisted only of people between the ages of 18 and 20 and the experimental group contained people between the ages of 30 and 35, we would not know if it was the teaching strategy or the students’ ages that played a larger role in the results. To avoid this problem, a good study will be set up so that each group contains students with a similar age profile. In a well-designed educational research study, student age will be a controlled variable, along with other possibly important factors like gender, past educational achievement, and pre-existing knowledge of the subject area.

What is the independent variable in this experiment?

• Sex (all of the subjects will be female)
• Presence or absence of the HPV vaccine
• Presence or absence of HPV (the virus)

[reveal-answer q=”68680″]Show Answer[/reveal-answer] [hidden-answer a=”68680″]Answer b. Presence or absence of the HPV vaccine. This is the variable that is different between the control and the experimental groups. All the subjects in this study are female, so this variable is the same in all groups. In a well-designed study, the two groups will be of similar age. The presence or absence of the virus is what the researchers will measure at the end of the experiment. Ideally the two groups will both be HPV-free at the start of the experiment.

List three control variables other than age.

[practice-area rows=”3″][/practice-area] [reveal-answer q=”903121″]Show Answer[/reveal-answer] [hidden-answer a=”903121″]Some possible control variables would be: general health of the women, sexual activity, lifestyle, diet, socioeconomic status, etc.

What is the dependent variable in this experiment?

• Sex (male or female)
• Rates of HPV infection
• Age (years)

[reveal-answer q=”907103″]Show Answer[/reveal-answer] [hidden-answer a=”907103″]Answer b. Rates of HPV infection. The researchers will measure how many individuals got infected with HPV after a given period of time.[/hidden-answer]

Contributors and Attributions

• Revision and adaptation. Authored by : Shelli Carter and Lumen Learning. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
• Scientific Inquiry. Provided by : Open Learning Initiative. Located at : https://oli.cmu.edu/jcourse/workbook/activity/page?context=434a5c2680020ca6017c03488572e0f8 . Project : Introduction to Biology (Open + Free). License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike

Law of Falsifiability

The Law of Falsifiability is a rule that a famous thinker named Karl Popper came up with. In simple terms, for something to be called scientific, there must be a way to show it could be incorrect. Imagine you’re saying you have an invisible, noiseless, pet dragon in your room that no one can touch or see. If no one can test to see if the dragon is really there, then it’s not scientific. But if you claim that water boils at 100 degrees Celsius at sea level, we can test this. If it turns out water does not boil at this temperature under these conditions, then the claim would be proven false. That’s what Karl Popper was getting at – science is about making claims that can be tested, possibly shown to be false, and that’s what keeps it trustworthy and moving forward.

Examples of Law of Falsifiability

• Astrology – Astrology is like saying certain traits or events will happen to you based on star patterns. But because its predictions are too general and can’t be checked in a clear way, it doesn’t pass the test of falsifiability. This means astrology cannot be considered a scientific theory since you can’t show when it’s wrong with specific tests.
• The Theory of Evolution – In contrast, the theory of evolution is something we can test. It says that different living things developed over a very long time. If someone were to find an animal’s remains in a rock layer where it should not be, such as a rabbit in rock that’s 500 million years old, that would challenge the theory. Since we can test it by looking for evidence like this, evolution is considered falsifiable.

Why is it Important?

The Law of Falsifiability matters a lot because it separates what’s considered scientific from what’s not. When an idea can’t be tested or shown to be wrong, it can lead people down the wrong path. By focusing on theories we can test, science gets stronger and we learn more about the world for real. For everyday people, this is key because it means we can rely on science for things like medicine, technology, and understanding our environment. If scientists didn’t use this rule, we might believe in things that aren’t true, like magic potions or the idea that some stars can predict your future.

Implications and Applications

The rule of being able to test if something is false is basic in the world of science and is used in all sorts of subjects. For example, in an experiment, scientists try really hard to see if their guess about something can be shown wrong. If their guess survives all the tests, it’s a good sign; if not, they need to think again or throw it out. This is how science gets better and better.

Comparison with Related Axioms

• Verifiability : This means checking if a statement or idea is true. Both verifiability and falsifiability have to do with testing, but falsifiability is seen as more important because things that can be proven wrong are usually also things we can check for truth.
• Empiricism : This is the belief that knowledge comes from what we can sense – like seeing, hearing, or touching. Falsifiability and empiricism go hand in hand because both involve using real evidence to test out ideas.
• Reproducibility : This idea says that doing the same experiment in the same way should give you the same result. To show something is falsifiable, you should be able to repeat a test over and over, with the chance that it might fail.

Karl Popper brought the Law of Falsifiability into the world in the 1900s. He didn’t like theories that seemed to answer everything because, to him, they actually explained nothing. By making this law, he aimed to make a clear line between what could be taken seriously in science and what could not. It was his way of making sure scientific thinking stayed sharp and clear.

Controversies

Not everyone agrees that falsifiability is the only way to tell if something is scientific. Some experts point out areas in science, like string theory from physics, which are really hard to test and so are hard to apply this law to. Also, in science fields that look at history, like how the universe began or how life changed over time, it’s not always about predictions that can be tested, but more about understanding special events. These differences in opinion show that while it’s a strong part of scientific thinking, falsifiability might not work for every situation or be the only thing that counts for scientific ideas.

Related Topics

• Scientific Method : This is the process scientists use to study things. It involves asking questions, making a hypothesis, running experiments, and seeing if the results support the hypothesis. Falsifiability is part of this process because scientists have to be able to test their hypotheses.
• Peer Review : When scientists finish their work, other experts check it to make sure it was done right. This involves reviewing if the experiments and tests were set up in a way that they could have shown the work was false if it wasn’t true.
• Logic and Critical Thinking : These are skills that help us make good arguments and decisions. Understanding falsifiability helps people develop these skills because it teaches them to always look for ways to test ideas.

In conclusion, the Law of Falsifiability, as brought up by Karl Popper, is like a key part of a scientist’s toolbox. It makes sure that ideas need to be able to be tested and possibly shown to be not true. By using this rule, we avoid believing in things without good evidence, and we make the stuff we learn about the world through science stronger and more reliable.

Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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September 7, 2020

The Idea That a Scientific Theory Can Be ‘Falsified’ Is a Myth

It’s time we abandoned the notion

By Mano Singham

Transit of Mercury across the Sun; Newton's theory of gravity was considered to be "falsified" when it failed to account for the precession of the planet's orbit.

Getty Images

J.B.S. Haldane, one of the founders of modern evolutionary biology theory, was reportedly asked what it would take for him to lose faith in the theory of evolution and is said to have replied, “Fossil rabbits in the Precambrian.” Since the so-called “Cambrian explosion” of 500 million years ago marks the earliest appearance in the fossil record of complex animals, finding mammal fossils that predate them would falsify the theory.

But would it really?

The Haldane story, though apocryphal, is one of many in the scientific folklore that suggest that falsification is the defining characteristic of science. As expressed by astrophysicist Mario Livio in his book Brilliant Blunders : "[E]ver since the seminal work of philosopher of science Karl Popper, for a scientific theory to be worthy of its name, it has to be falsifiable by experiments or observations. This requirement has become the foundation of the ‘scientific method.’”

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But the field known as science studies (comprising the history, philosophy and sociology of science) has shown that falsification cannot work even in principle. This is because an experimental result is not a simple fact obtained directly from nature. Identifying and dating Haldane's bone involves using many other theories from diverse fields, including physics, chemistry and geology. Similarly, a theoretical prediction is never the product of a single theory but also requires using many other theories. When a “theoretical” prediction disagrees with “experimental” data, what this tells us is that that there is a disagreement between two sets of theories, so we cannot say that any particular theory is falsified.

Fortunately, falsification—or any other philosophy of science—is not necessary for the actual practice of science. The physicist Paul Dirac was right when he said , "Philosophy will never lead to important discoveries. It is just a way of talking about discoveries which have already been made.” Actual scientific history reveals that scientists break all the rules all the time, including falsification. As philosopher of science Thomas Kuhn noted, Newton's laws were retained despite the fact that they were contradicted for decades by the motions of the perihelion of Mercury and the perigee of the moon. It is the single-minded focus on finding what works that gives science its strength, not any philosophy. Albert Einstein said that scientists are not, and should not be, driven by any single perspective but should be willing to go wherever experiment dictates and adopt whatever works .

Unfortunately, some scientists have disparaged the entire field of science studies, claiming that it was undermining public confidence in science by denying that scientific theories were objectively true. This is a mistake since science studies play vital roles in two areas. The first is that it gives scientists a much richer understanding of their discipline. As Einstein said : "So many people today—and even professional scientists—seem to me like somebody who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth." The actual story of how science evolves results in inspiring more confidence in science, not less.

The second is that this knowledge equips people to better argue against antiscience forces that use the same strategy over and over again, whether it is about the dangers of tobacco, climate change, vaccinations or evolution. Their goal is to exploit the slivers of doubt and discrepant results that always exist in science in order to challenge the consensus views of scientific experts. They fund and report their own results that go counter to the scientific consensus in this or that narrow area and then argue that they have falsified the consensus. In their book Merchants of Doubt, historians Naomi Oreskes and Erik M. Conway say that for these groups “[t]he goal was to fight science with science—or at least with the gaps and uncertainties in existing science, and with scientific research that could be used to deflect attention from the main event.”

Science studies provide supporters of science with better arguments to combat these critics, by showing that the strength of scientific conclusions arises because credible experts use comprehensive bodies of evidence to arrive at consensus judgments about whether a theory should be retained or rejected in favor of a new one. These consensus judgments are what have enabled the astounding levels of success that have revolutionized our lives for the better. It is the preponderance of evidence that is relevant in making such judgments, not one or even a few results.

So, when anti-vaxxers or anti-evolutionists or climate change deniers point to this or that result to argue that they have falsified the scientific consensus, they are making a meaningless statement. What they need to do is produce a preponderance of evidence in support of their case, and they have not done so.

Falsification is appealing because it tells a simple and optimistic story of scientific progress, that by steadily eliminating false theories we can eventually arrive at true ones. As Sherlock Holmes put it, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.” Such simple but incorrect narratives abound in science folklore and textbooks. Richard Feynman in his book QED , right after “explaining” how the theory of quantum electrodynamics came about, said, "What I have just outlined is what I call a “physicist’s history of physics,” which is never correct. What I am telling you is a sort of conventionalized myth-story that the physicists tell to their students, and those students tell to their students, and is not necessarily related to the actual historical development which I do not really know!"

But if you propagate a “myth-story” enough times and it gets passed on from generation to generation, it can congeal into a fact, and falsification is one such myth-story.

It is time we abandoned it.

5 Falsifiability

Textbook chapters (or similar texts).

• Deductive Logic
• Persuasive Reasoning and Fallacies
• The Falsifiability Criterion of Science
• Understanding Science

Journal articles

• Why a Confirmation Strategy Dominates Psychological Science

*******************************************************

Inquiry-based Activity:  Popular media and falsifiability

Introduction : Falsifiability, or the ability for a statement/theory to be shown to be false, was noted by Karl Popper to be the clearest way to distinguish science from pseudoscience. While incredibly important to scientific inquiry, it is also important for students to understand how this criterion can be applied to the news and information they interact with in their day-to-day lives. In this activity, students will apply the logic of falsifiability to rumors and news they have heard of in the popular media, demonstrating the applicability of scientific thinking to the world beyond the classroom.

Question to pose to students : Think about the latest celebrity rumor you have heard about in the news or through social media. If you cannot think of one, some examples might include, “the CIA killed Marilyn Monroe” and “Tupac is alive.” Have students get into groups, discuss their rumors, and select one to work with.

Note to instructors: Please modify/update these examples if needed to work for the students in your course. Snopes is a good source for recent examples.

Students form a hypothesis : Thinking about that rumor, decide what evidence would be necessary to prove that it was correct. That is, imagine you were a skeptic and automatically did not believe the rumor – what would someone need to tell or show you to convince you that it was true?

Students test their hypotheses : Each group (A) should then pair up with one other group (B) and try to convince them their rumor is true, providing them with the evidence from above. Members of group B should then come up with any reasons they can think of why the rumor may still be false. For example – if “Tupac is alive” is the rumor and “show the death certificate” is a piece of evidence provided by group A, group B could posit that the death certificate was forged by whoever kidnapped Tupac. Once group B has evaluated all of group A’s evidence, have the groups switch such that group B is now trying to convince group A about their rumor.

Do the students’ hypotheses hold up? : Together, have the groups work out whether the rumors they discussed are falsifiable. That is, can it be “proven?” Remember, a claim is non-falsifiable if there can always be an explanation for the absence of evidence and/or an exhaustive search for evidence would be required. Depending on the length of your class, students can repeat the previous step with multiple groups.

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