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# Falsifiability

This page discusses how a theory or assertion is "falsifiable" ("disprovable" opp: "verifiable"), rather than the non-philosophical use of "falsification", meaning "counterfeiting." The idea comes from the work of the philosophers Sir Karl Popper and Ernest Gellner.

Falsifiability is an important concept in the philosophy of science that amounts to the apparently paradoxical idea that a proposition or theory cannot be scientific if it does not admit consideration of the possibility of its being false.

"Falsifiable" does not mean "false". For a proposition to be falsifiable, it must be possible in principle to make an observation that would show the proposition to be false, even if that observation has not been made. For example, the proposition "All crows are black" would be falsified by observing one white crow.

Any theory that is not falsifiable is said to be unscientific. Psychoanalytic theory, for example, is held up by followers of Popper as an example of an ideology rather than a science. A patient regarded by his psychoanalyst as "in denial" about his sexual orientation may be viewed as confirming he is homosexual simply by denying that he is; and if he has sex with women, he may be accused of trying to buttress his denials. In other words, there is no way the patient could convincingly demonstrate his heterosexuality to his analyst. This is an example of what Popper called a "closed circle ". The proposition that the patient is homosexual is not falsifiable.

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## Naïve falsification

Falsifiability was first developed by Karl Popper in the 1930s. Popper noticed that two types of statements are of particular value to scientists. The first are statements of observations, such as 'this is a white swan'. Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x which is a swan and is white.

The second type of statement of interest to scientists categorizes all instances of something, for example "All swans are white". Logicians call these statements universal. They are usually parsed in the form For all x, if x is a swan then x is white.

Scientific laws are commonly supposed to be of this form. Perhaps the most difficult question in the methodology of science is: how does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from ‘this is a white swan', “that is a white swan”, and so on, to a universal statement such as 'all swans are white'. This method is clearly logically invalid, since it is always possible that there may be a non-white swan that has somehow avoided observation. Yet some philosophers of science claim that science is based on such an inductive method.

Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the problem of induction. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false. In logic this is modus tollens. 'There is a black swan' implies 'there is a non-white swan' which in turn implies 'there is something which is a swan and which is not white'.

Although the logic of naïve falsification is valid, it is rather limited. Popper drew attention to these limitations in The Logic of Scientific Discovery, in response to anticipated criticism from Duhem and Carnap. W. V. Quine is also well-known for his observation in his influential essay, "Two Dogmas of Empiricism" (which is reprinted in From a Logical Point of View), that nearly any statement can be made to fit with the data, so long as one makes the requisite "compensatory adjustments". In order to logically falsify a universal, one must find a true falsifying singular statement. But Popper pointed out that it is always possible to change the universal statement or the existential statement so that falsification does not occur. On hearing that a black swan has been observed in Australia, one might introduce ad hoc hypothesis, 'all swans are white except those found in Australia'; or one might adopt another, more cynical view about some observers, 'Australian ornithologists are incompetent'. As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.

In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories which can account for the phenomena which falsified the prior theory, that is, with greater explanatory power. Thus, Aristotelian mechanics explained observations of objects in everyday situations, but was falsified by Galileo’s experiments, and was itself replaced by Newtonian which accounted for the phenomena noted by Galileo (and others). Newtonian mechanics' reach included the observed motion of the planets and the mechanics of gases. Or at least most of them; the motion of Mercury wasn't predicted by Newtonian mechanics, but was by Einstein's general relativity. The Youngian wave theory of light (i.e., waves carried by the luminiferous ether) replaced Newton's (and many of the Classical Greeks') particles of light but in its turn was falsified by the Michelson-Morley experiment, whose results were eventually understood as incompatible with an ether and was superseded by Maxwell's electrodynamics and Einstein's special relativity, which did account for the new phenomena. At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found which had greater 'explanatory power' (i.e., could account for the previously unexplained phenomena), and as a result provided greater opportunity for its own falsification.

Naïve falsificationism is an unsuccessful attempt to prescribe a rationally unavoidable method for science. Falsificationism proper, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice.

## Popper's swan argument

A white mute swan, common to Eurasia and North America

One notices a white swan, from this one can conclude:

Some swans are white.

From this, one may wish to infer that:

All swans are white.

However, to prove this, one must find all the swans in the world and verify that they are white. This is nigh impossible, and extensions such as, All swans have always been white would require a time machine as would all swans will always be white. Therefore, this cannot be proven.

Two black swans, native to Australia

As it turns out, not all swans are white. By finding a black swan, one has falsified the statement all swans are white; it is not true. We have to refine our paradigm to a more specific statement, thus

All swans except Cygnus atratus are white; C. atratus is black.

## Formal logical arguments

The explication of falsification by Popper perhaps is responsible for the formulation of the two main objections to empirical positivism. Falsification of some theory occurs through Modus tollens, via some observation. Suppose some theory T, implies an observation O:

$T \rightarrow O$

But the required observation is not made, so

$\sim O$

So by Modus Tollens,

$\sim T$

### Theory-dependence of observation

All observations make use of prior assumptions; so

$O \equiv \left( p_1 \wedge p_2 \wedge p_3 \cdots p_n \right)$

and so,

$\sim O \equiv \sim \left( p_1 \wedge p_2 \wedge p_3 \cdots \wedge p_n \right)$

but

$\sim \left( p_1 \wedge p_2 \wedge p_3 \cdots \wedge p_n \right) \equiv \left( \sim p_1 \vee \sim p_2 \vee \sim p_3 \cdots \vee \sim p_n \right)$

In words, failure to make some observation only implies the failure of at least one of the prior assumptions that went into making the observation. It is always possible to reject an apparently falsifying observation by claiming that some one of its underlying assumptions is false; since there are an indeterminate number of such assumptions, any observation can potentially be made compatible with any theory. So it is quite valid to use a theory to reject an observation.

### Indeterminacy of theory by evidence

Similarly, a theory consists of some indeterminate conjunction of hypotheses,

$T \equiv \left( h_1 \wedge h_2 \wedge h_3 \cdots \wedge h_n \right)$

and so,

$\sim T \equiv \sim \left( h_1 \wedge h_2 \wedge h_3 \cdots \wedge h_n \right)$

but

$\sim \left( h_1 \wedge h_2 \wedge h_3 \cdots \wedge h_n \right) \equiv \left( \sim h_1 \vee \sim h_2 \vee \sim h_3 \cdots \vee \sim h_n \right)$

In words, failure of some theory implies only failure of at least one of the underlying hypotheses of the theory. It is always possible to resurrect a falsified theory by claiming that some one of its underlying hypotheses is false; again, since there are an indeterminate number of such hypotheses, any theory can potentially be made compatible with any particular observation. So it is not possible to determine the falsity of a theory by reference to the evidence.

## The criterion of demarcation

Popper proposed falsification as a way of determining if a theory is scientific or not. If a theory is falsifiable, then it is scientific; if it is not falsifiable, then it is not science. Popper uses this criterion of demarcation to draw a sharp line between scientific and unscientific theories. Some have taken this principle to an extreme to cast doubt on the scientific validity of many disciplines (such as macroevolution and Cosmology). Falsifiability was one of the criteria used by Judge William Overton to determine that 'creation science' was not scientific and should not be taught in Arkansas public schools.

In the philosophy of science, verificationism (also known as the verifiability theory of meaning) held that a statement must be in principle empirically verifiable in order to be both meaningful and scientific. This was an essential feature of the logical empiricism of the so-called Vienna Circle that featured such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neutrath and Hans Reichenbach. After Popper, verifiability came to be replaced by falsifiability as the criterion of demarcation. In other words, in order to be scientific, a statement had to be, in principle, falsifiable. Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, and had accordingly given a single solution to both of them: verificationism. In opposition to this view, Popper emphasized that a theory might well be meaningful without being scientific, and that, accordingly, a criterion of meaningfulness may not necessarily coincide with a criterion of demarcation. His own falsificationism, thus, is not only an alternative to verificationism; it is also an acknowledgment of the conceptual distinction that previous theories had ignored.

Falsifiability is a property of statements and theories, and is itself neutral. As a demarcation criterion, it seeks to take this property and make it a base for affirming the superiority of falsifiable theories over non-falsifiable ones as a part of science, in effect setting up a political position that might be called falsificationism. However, much that would be considered meaningful and useful is not falsifiable. Certainly non-falsifiable statements have a role in scientific theories themselves. The Popperian criterion provides a definition of science that excludes much that is of value; it does not provide a way to distinguish meaningful statements from meaningless ones.

It is nevertheless very useful to know if a statement or theory is falsifiable, if for no other reason than it provides us with an understanding of the ways in which one might assess the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable.

## Criticism

Thomas Kuhn’s influential book The Structure of Scientific Revolutions argued that scientists work within a conceptual paradigm that determines the way in which they view the world. Scientists will go to great length to defend their paradigm against falsification, by the addition of ad hoc hypotheses to existing theories. Changing one's 'paradigm' is not easy, and only through some pain and angst does science (at the level of the individual scientist) change paradigms.

Some falsificationists saw Kuhn’s work as a vindication, since it showed that science progressed by rejecting inadequate theories. More commonly, it has been seen as showing that sociological factors, rather than adherence to a strict, logically obligatory method, play the determining role in deciding which scientific theory is accepted. This was seen as a profound threat to those who seek to show that science has a special authority in virtue of the methods that it employs.

Imre Lakatos attempted to explain Kuhn’s work in falsificationist terms by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naïve falsification. In Lakatos' approach, a scientist works within a research program that corresponds roughly with Kuhn's 'paradigm'. Whereas Popper rejected the use of ad hoc hypothesis as unscientific, Lakatos accepted their place in the development of new theories.

Paul Feyerabend examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He went beyond Lakatos’ argument for ad hoc hypothesis, to say that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method. Rather, he claimed, ironically, that if one is keen to have a universally valid methodological rule, anything goes would be the only candidate. For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method.

Although falsifiability does provide a way to replace invalid inductive thinking with deductive, falsifiable reasoning, it appeared to Feyerabend that doing so is neither necessary for, nor conducive to, scientific progress.

## Some examples

Claims about verifiability and falsifiability have been used to criticize various controversial views. Examination of these examples shows the usefulness of falsifiability in showing us where to look when criticising a theory.

Non-falsifiable theories can usually be reduced to a simple uncircumscribed existential statement, such as there exists a green swan. It is entirely possible to verify that the theory is true, simply by producing the green swan. But since this statement does not specify when or where the green swan exists, it is simply not possible to show that the swan does not exist, and so it is impossible to falsify the statement.

That such theories are unfalsifiable says nothing about either their validity or truth. But it does assist us in determining how such statements might be evaluated. If evidence cannot be presented to support a case, and yet the case cannot be shown to be indeed false, how much credence should it be given?

### Mathematics

Mathematical and logical statements are typically regarded as unfalsifiable, since they are tautologies, not existential or universal statements. For example, "all bachelors are male" and "all green things are green" are necessarily true (or given) without any knowledge of the world; given the meaning of the terms used, they are tautologies.

Proving mathematical theorems involves reducing them to tautologies, which can be mechanically proven as true given the axioms of the system or reducing the negative to a contradiction. Mathematical theorems are unfalsifiable, since this process, coupled with the notion of consistency, eliminates the possibility of counterexamples - a process that the philosophy of mathematics studies in depth as a separate matter.

How a mathematical formula might apply to the physical world, however (as a model), is a physical question, and thus testable, within certain limits. For example, the theory that "an object will follow a parabolic path when thrown into the air" is falsifiable (and, in fact, false; think of a feather).

### Ethics

Many philosophers have held that claims about morality (such as "murder is evil" and "John was wrong to steal that money") are not part of scientific inquiry; their function in language is not even to state facts, but simply to express certain moral sentiments. Hence they are not falsifiable.

### Theism

On the view of some, theism is not falsifiable, since the existence of God is typically asserted without sufficient conditions to allow a falsifying observation. God being a transcendental being, beyond the realm of the observable, claims about its existence can neither be supported nor undermined by observation. It is quite consistent for a theist to agree that the existence of God is unfalsifiable, and that the proposition is not scientific, but to still claim that God exists. This is, of course, a matter of interest for anyone who places stock in natural theology--the argument from design and other a posteriori arguments for the existence of God. (See non-cognitivism.) However, arguments relating to alleged actions, rather than the existence, of God may be falsifiable. See nontheism for further information.

### Conspiracy theories

There are other examples of theories, however, that are much less controversial as examples of unfalsifiable claims. Some so-called "conspiracy theories," at least as defended by some people, are essentially unfalsifiable because of their logical structure. Conspiracy theories usually take the form of uncircumscribed existential statements, alleging the existence of some action or object without specifying the place or time at which it can be observed. Failure to observe the phenomenon can then always be the result of looking in the wrong place or looking at the wrong time. Conspiracy theorists can, and often do, defend their position by claiming that lying and other forms of fabrication are, in fact, a common tool of governments and other powerful players and that evidence suggesting that a conspiracy did not occur has been fabricated.

### Economics

Many viewpoints in economics are often accused of not being falsifiable, mainly by sociologists and other social scientists in general.

The most common argument is made against rational expectations theories, which work under the assumption that people act to maximize their utility. However, under this viewpoint, it is impossible to disprove the fundamental theory that people are utility-maximizers. The political scientist Graham Allison , in his book Essence of Decision, attempted to both quash this theory and substitute other possible models of behavior.

### Historicism

Theories of history or politics which allegedly predict the future course of history have a logical form that renders them neither falsifiable nor verifiable. They claim that for every historically significant event, there exists an historical or economic law that determines the way in which events proceeded. Failure to identify the law does not mean that it does not exist, yet an event that satisfies the law does not prove the general case. Evaluation of such claims is at best difficult. On this basis, Popper himself argued that neither Marxism nor psychoanalysis were science, although both made such claims. Again, this does not mean, that any of these types of theories are necessarily invalid. Popper considered falsifiability a test of whether theories are scientific, not of whether theories are valid.

### Solipsism

In philosophy, solipsism is, in essence, non-falsifiable. Solipsism claims that the Universe exists entirely in one's own mind. This can straightforwardly be seen not to be falsifiable, because whatever evidence one might adduce that is contrary to solipsism can be, after all, dismissed as something that is "in one's mind." In other words, there is no evidence that one could possibly adduce that would be inconsistent with the proposition that everything that exists, exists in one's own mind. This view is somewhat similar to Cartesian skepticism , and indeed, Cartesian skepticism has been rejected as unfalsifiable as well by many philosophers.

### Physical laws

The laws of physics are an interesting case. Occasionally it is suggested that the most fundamental laws of physics, such as "force equals mass times acceleration" (F=ma), are not falsifiable because they are definitions of basic physical concepts (in the example, of "force"). More usually, they are treated as falsifiable laws, but it is a matter of considerable controversy in the philosophy of science what to regard as evidence for or against the most fundamental laws of physics. Isaac Newton's laws of motion in their original form were falsified by experiments in the twentieth century (eg, the anomaly of the motion of Mercury, the behavior of light passing sufficiently close to a star, the behavior of particle being accelerated in a cyclotron, etc), and replaced by a theory which predicted those phenomena, General Relativity, though Newton's account of motion is still a good enough approximation for most human needs. In the case of less fundamental laws, their falsifiability is much easier to understand. If, for example, a biologist hypothesizes that, as a matter of scientific law (though practising scientists will rarely actually state it as such), only one certain gland produces a certain hormone, when someone discovers an individual with the hormone but lacking the gland, the hypothesis is falsified.

The range of available testing apparatus is also sometimes an issue - when Galileo showed Catholic Church scholars the moons of Jupiter, there was only one telescope on hand, and telescopes were a new technology, so there was some debate about whether the moons were real or possibly an artifact of the telescope or of the type of telescope. Fortunately, this type of problem can usually be resolved in a short time, as it was in Galileo's case, by the spread of technical improvements. Diversity of apparatus is quite important to concepts of falsifiability, because presumably any observer with any appropriate apparatus should be able to make the same observation and so prove a thesis false.

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