# Falsifiability

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Falsifiability, or defeasibility, is an important concept in the philosophy of science. It is the principle that in hypothesis testing a proposition or theory cannot be considered scientific if it does not admit the possibility of being shown to be false.

Falsifiable does not mean false. For a proposition to be falsifiable, it must - at least in principle - be possible to make an observation that would show the proposition to be false, even if that observation has not actually been made. For example, the proposition "All crows are black" would be falsified by observing one white crow. A falsifiable proposition or theory must define in some way what is, or will be, forbidden by that proposition or theory (e.g., in this case a white crow is forbidden). The possibility, in principle, of observing a white crow to disprove this proposition thus makes it falsifiable.

## 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 x 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 the second type. 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 called 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', hence 'all swans are white' is false, because that is the same as 'there is nothing 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 the 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.

## Falsificationism

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 mechanics 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 size of the precession of the orbit 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

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

At least one swan is 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.

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.

## Formal logical arguments

The falsification of theories occurs through modus tollens, via some observation. Suppose some theory T implies an observation O:

$T \rightarrow O$

An observation conflicting with O, however, is made:

$\neg O$

So by Modus Tollens,

$\neg T$

## 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 Neurath, 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, namely 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. Much that would be considered meaningful and useful, however, 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 that 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 hypotheses as unscientific, Lakatos accepted their place in the development of new theories.

Lakatos also brought the notion of falsifiability to bear on the discipline of mathematics in Proofs and Refutations. The long-standing debate over whether mathematics is a science depends in part on the question of whether proofs are fundamentally different from experiments. Lakatos argued that mathematical proofs and definitions evolve through criticism and counterexample in a manner very similar to how a scientific theory evolves in response to experiments.

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.

Following from Feyerabend, the whole "Popper project" to define science around one particular methodology—which accepts nothing except itself—is a perverse example of what he supposedly decried: a closed circle argument. The Popperian criterion itself is not falsifiable.

Moreover, it makes Popper effectively a philosophical nominalist, which has nothing to do with empirical sciences at all.

Although Popper's claim of the singular characteristic of falsifiability does provide a way to replace invalid inductive thinking (empiricism) with deductive, falsifiable reasoning, it appeared to Feyerabend that doing so is neither necessary for, nor conducive to, scientific progress.

### Case Studies

Multiple universes from the Anthropic Principle and the existence of intelligent life (see SETI) beyond Earth are potentially non-falsifiable ideas. They are "true-ifiable" because they are potentially detectable. Lack of detection does not mean other universes or non-human intelligent life does not exist; it only means they have not been detected. Yet, both of these ideas are generally considered scientific ideas. Some suggest that an idea has to be only one of falsifiable or "true-ifiable", but not both to be considered a scientific idea. That is, it must be at least one of confirmable or deniable.

### From scientists

Many actual physicists, including Nobel Prize winner Steven Weinberg and Alan Sokal (Fashionable Nonsense), have criticized falsifiability on the grounds that it does not accurately describe the way science really works. Take astrology, an example most would agree is not science. Astrology constantly makes falsifiable predictions -- a new set is printed every day in the newspapers -- yet few would argue this makes it scientific.

One might respond that astrological claims are rather vague and can be excused or reinterpreted. But the same is true of actual science: a physical theory predicts that performing a certain operation will result in a number in a certain range. Nine times out of ten it does; the tenth the physicists blame on a problem with the machine -- perhaps someone slammed the door too hard or something else happened that shook the machine. Falsifiability does not help us decide between these two cases.

In reality, of course, theories are used because of their successes, not because of their failures. As Sokal writes, "When a theory successfully withstands an attempt at falsification, a scientist will, quite naturally, consider the theory to be partially confirmed and will accord it a greater likelihood or a higher subjective probability. ... But Popper will have none of this: throughout his life he was a stubborn opponent of any idea of 'confirmation' of a theory, or even of its 'probability'. ... [but] the history of science teaches us that scientific theories come to be accepted above all because of their successes."

## Some examples

Claims about verifiability and falsifiability have been used to criticize various controversial views. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise 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 to what extent 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, not much credence can be given to such a statement.

### 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 "all objects follow a parabolic path when thrown into the air" is falsifiable (and, in fact, false; think of a feather—a better statement would be: "all objects follow a parabolic path when thrown in a vacuum and acted upon by gravity", which is itself falsified when considering paths that are a measureable proportion of the planet's radius).

### 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. If God is a transcendental being that can escape the realm of the observable, claims about God's non-existence can not be supported by a lack of 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 because the theist claims to have presentable evidence that verifies the existence of God. This is, of course, a matter of interest for anyone who places stock in witnesses who claim to have seen God or ideas like 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 and eye-witness accounts, rather than the existence, of God may be falsifiable. See nontheism for further information.

### Conspiracy theories

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 T. 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.

### Memetics

The model of cultural evolution known as memetics is as of yet unfalsifiable, as its practitioners have been unable to determine what constitutes a single meme, and more importantly, what determines the survival of a meme. For the theory to be falsifiable, more exact accounts of this are needed, as currently every outcome of cultural evolution can be explained memetically by suitable choice of competing memes. This does not, however, mean that all epidemological theories of social and cultural spread are unscientific, as some of them have (mostly due to smaller scope) more exact terms of transmission and survival.

### 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 scepticism, 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 a 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 without the gland but with the hormone occurring naturally in their body, the hypothesis is falsified.

The range of available testing apparatus is also sometimes an issue - when Galileo showed Roman 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 observing 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.