Falsification (Falsifiability)

Falsifiability is a standard of evaluation of scientific theories and hypotheses that was introduced by the philosopher of science Karl Popper in his book ''The Logic of Scientific Discovery'' (1934). He proposed it as the cornerstone of a solution to both the problem of induction and the problem of demarcation. A theory or hypothesis is falsifiable (or refutable) if it can be ''logically'' contradicted by an empirical test that can potentially be executed with existing technologies. Popper insisted that, as a logical criterion, it is distinct from the related concept "capacity to be proven wrong" discussed in Lakatos' falsificationism. Even being a logical criterion, its purpose is to make the theory predictive and testable, thus useful in practice.

Popper opposed falsifiability to the intuitively similar concept of verifiability. Verifying the claim "All swans are white" would theoretically require observing all swans, which in actuality, is not possible. In contrast, observing a single black swan is theoretically reasonable and sufficient to logically falsify the claim. On the other hand, the Duhem–Quine thesis says that definitive experimental falsifications are impossible and that no scientific hypothesis is by itself capable of making predictions, because an empirical test of the hypothesis requires one or more background assumptions.

According to Popper there is a clean asymmetry on the logical side and falsifiability does not have the Duhem problem because it is a logical criterion. Experimental research has the Duhem problem and other problems, such as induction, but, according to Popper, statistical tests can still be useful within a critical discussion when a theory can be falsified. Philosophers such as Deborah Mayo consider that Popper "comes up short" in his description of the scientific role of statistical and data models.

As a key notion in the separation of science from non-science and pseudo-science, falsifiability has featured prominently in many scientific controversies and applications, even being used as legal precedent.

The problem of induction and demarcation

One of the questions in scientific method is: how does one move from observations to scientific laws? This is the problem of induction. Suppose we want to put the hypothesis that all swans are white to the test. We come across a white swan. We cannot validly argue (or ''induce'') from "here is a white swan" to "all swans are white"; doing so would require a logical fallacy such as, for example, affirming the consequent.

Popper's idea to solve this problem is that while it is impossible to verify that every swan is white, finding a single black swan shows that ''not'' every swan is white. We might tentatively accept the proposal that every swan is white, while looking out for examples of non-white swans that would show our conjecture to be false. Falsification uses the valid inference ''modus tollens'': if from a law $L$ we logically deduce $Q$, but what is observed is $\neg Q$, we infer that the law $L$ is false. For example, given the statement $L =$ "all swans are white", we can deduce $Q =$ "the specific swan here is white", but if what is observed is $\neg Q =$ "the specific swan here is not white" (say black), then "all swans are white" is false. More accurately, the statement $Q$ that can be deduced is broken into an initial condition and a prediction as in $C \Rightarrow P$ in which $C =$ "the thing here is a swan" and $P =$ "the thing here is a white swan". If what is observed is C being true while P is false (formally, $C \wedge \neg P$), we can infer that the law is false.

For Popper, induction is actually never needed in science. Instead, in Popper's view, laws are conjectured in a non-logical manner on the basis of expectations and predispositions. This has led David Miller, a student and collaborator of Popper, to write "the mission is to classify truths, not to certify them". In contrast, the logical empiricism movement, which included such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath and A.J. Ayer wanted to formalize the idea that, for a law to be scientific, it must be possible to argue on the basis of observations either in favor of its truth or its falsity. There was no consensus among these philosophers about how to achieve that, but the thought expressed by Mach's dictum that "where neither confirmation nor refutation is possible, science is not concerned" was accepted as a basic precept of critical reflection about science.

Popper said that a demarcation criterion was possible, but we have to use the ''logical possibility'' of falsifications, which is falsifiability. He cited his encounter with psychoanalysis in the 1910s. It did not matter what observation was presented, psychoanalysis could explain it. Unfortunately, the reason why it could explain everything is that it did not exclude anything also. For Popper, this was a failure, because it meant that it could not make any prediction. From a logical standpoint, if one finds an observation that does not contradict a law, it does not mean that the law is true. A verification has no value in itself. But, if the law makes risky predictions and these are corroborated, Popper says, there is a reason to prefer this law over another law that makes less risky predictions or no predictions at all. In the definition of falsifiability, contradictions with observations are not used to support eventual falsifications, but for ''logical'' "falsifications" that show that the law makes risky predictions, which is completely different.

On the basic philosophical side of this issue, Popper said that some philosophers of the Vienna Circle had mixed two different problems, that of meaning and that of demarcation, and had proposed in verificationism a single solution to both: a statement that could not be verified was considered meaningless. In opposition to this view, Popper said that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.

From Hume's problem to non problematic induction

The problem of induction is often called Hume's problem. David Hume studied how human beings obtain new knowledge that goes beyond known laws and observations, including how we can discover new laws. He understood that deductive logic could not explain this learning process and argued in favour of a mental or psychological process of learning that would not require deductive logic. He even argued that this learning process can not be justified by any general rules, deductive or not. Popper accepted Hume's argument and therefore viewed progress in science as the result of quasi-induction, which does the same as induction, but has no inference rules to justify it. Philip N. Johnson-Laird, professor of psychology, also accepted Hume's conclusion that induction has no justification. For him induction does not require justification and therefore can exist in the same manner as Popper's quasi-induction does.

When Johnson-Laird says that no justification is needed, he does not refer to a general method of justification that, to avoid a circular reasoning, would not itself require any justification. On the contrary, in agreement with Hume, he refers to the fact that there is no general method of justification for induction and that's ok, because the induction steps do not require justification. Instead, these steps use patterns of induction that may or may not be applicable depending on the background knowledge. Johnson-Laird wrote: " ilosophers have worried about which properties of objects warrant inductive inferences. The answer rests on knowledge: we don't infer that all the passengers on a plane are male because the first ten off the plane are men. We know that this observation doesn't rule out the possibility of a woman passenger." The reasoning pattern that was not applied here is enumerative induction.

Popper was interested in the overall learning process in science, to quasi-induction, which he also called the "path of science". However, Popper did not show much interest in these reasoning patterns, which he globally referred to as psychologism. He did not deny the possibility of some kind of psychological explanation for the learning process, especially when psychology is seen as an extension of biology, but he felt that these biological explanations were not within the scope of epistemology. Popper proposed an evolutionary mechanism to explain the success of science, which is much in line with Johnson-Laird's view that "induction is just something that animals, including human beings, do to make life possible", but Popper did not consider it a part of his epistemology. He wrote that his interest was mainly in the ''logic'' of science and that epistemology should be concerned with logical aspects only. Instead of asking why science succeeds he considered the pragmatic problem of induction. This problem is not how to justify a theory or what is the global mechanism for the success of science but only what methodology do we use to pick one theory among theories that are already conjectured. His methodological answer to the latter question is that we pick the theory that is the most tested with the available technology: "the one, which in the light of our ''critical discussion'', appears to be the best so far". By his own account, because only a negative approach was supported by logic, Popper adopted a negative methodology.: "The fundamental difference between my approach and the approach for which I long ago introduced the label 'inductivist' is that I lay stress on negative arguments, such as negative instances or counter-examples, refutations, and attempted refutations—in short, criticism". The purpose of his methodology is to prevent "the policy of immunizing our theories against refutation". It also supports some "dogmatic attitude" in defending theories against criticism, because this allows the process to be more complete. This negative view of science was much criticized and not only by Johnson-Laird.

In practice, some steps based on observations can be justified under assumptions, which can be very natural. For example, Bayesian inductive logic is justified by theorems that make explicit assumptions. These theorems are obtained with deductive logic, not inductive logic. They are sometimes presented as steps of induction, because they refer to laws of probability, even though they do not go beyond deductive logic. This is yet a third notion of induction, which overlap with deductive logic in the following sense that it is supported by it. These deductive steps are not really inductive, but the overall process that includes the creation of assumptions is inductive in the usual sense. In a fallibilism perspective, a perspective that is widely accepted by philosophers, including Popper, every learning step only creates or reinforces an assumption—that is all what science does.

Basic statements and the definition of falsifiability

Popper distinguished between the logic of science and its applied ''methodology''. For example, Newton's law of gravitation is falsifiable—it is falsified by "The brick fell upwards when released". An explanation for this imaginary state of affairs such as some hidden force other than gravity acting on the brick would make it more intuitive, but is not needed for falsifiability, because it is a logical criterion. The empirical requirement on the potential falsifier, also called the ''material requirement'', is only that it is observable inter-subjectively with existing technologies. The logical part consists of theories, statements and their purely logical relationship together with this material requirement, which is needed for a connection with the methodological part.

The methodological part consists, in Popper's view, of informal rules, which are used to guess theories, accept observation statements as factual, etc. These include statistical tests: Popper is aware that observation statements are accepted with the help of statistical methods and that these involve methodological decisions. When this distinction is applied to the term "falsifiability", it corresponds to a distinction between two completely different meanings of the term. The same is true for the term "falsifiable". Popper said that he only uses "falsifiability" or "falsifiable" in reference to the logical side and that, when he refers to the methodological side, he speaks instead of "falsification" and its problems.

Popper said that methodological problems require proposing methodological rules. For example, one such rule is that, if one refuses to go along with falsifications, then one has retired oneself from the game of science. The logical side does not have such methodological problems, in particular with regard to the falsifiability of a theory, because basic statements are not required to be possible. Methodological rules are only needed in the context of actual falsifications.

So observations have two purposes in Popper's view. On the methodological side, observations can be used to show that a law is false, which Popper calls falsification. On the logical side, observations, which are purely logical constructions, do not show a law to be false, but contradict a law to show its falsifiability. Unlike falsifications and ''free from the problems of falsification'', these contradictions establish the value of the law, which may eventually be corroborated. He wrote that an entire literature exists because this distinction was not observed.

Basic statements

In Popper's view of science, statements of observation can be analyzed within a logical structure independently of any factual observations. The set of all purely logical observations that are considered constitutes the empirical basis. Popper calls them the ''basic statements'' or ''test statements''. They are the statements that can be used to show the falsifiability of a theory. Popper says that basic statements do not have to be possible in practice. It is sufficient that they are accepted by convention as belonging to the empirical language, a language that allows intersubjective verifiability: "they must be testable by intersubjective observation (the material requirement)". See the examples in section .

In more than twelve pages of ''The Logic of Scientific Discovery'', Popper discusses informally which statements among those that are considered in the logical structure are basic statements. A logical structure uses universal classes to define laws. For example, in the law "all swans are white" the concept of swans is a universal class. It corresponds to a set of properties that every swan must have. It is not restricted to the swans that exist, existed or will exist. Informally, a basic statement is simply a statement that concerns only a finite number of specific instances in universal classes. In particular, an existential statement such as "there exists a black swan" is not a basic statement, because it is not specific about the instance. On the other hand, "this swan here is black" is a basic statement. Popper says that it is a singular existential statement or simply a singular statement. So, basic statements are singular (existential) statements.

The definition of falsifiability

Thornton says that basic statements are statements that correspond to particular "observation-reports". He then gives Popper's definition of falsifiability:

As in the case of actual falsifiers, decisions must be taken by scientists to accept a logical structure and its associated empirical basis, but these are usually part of a background knowledge that scientists have in common and, often, no discussion is even necessary. The first decision described by Lakatos is implicit in this agreement, but the other decisions are not needed. This agreement, if one can speak of agreement when there is not even a discussion, exists only in principle. This is where the distinction between the logical and methodological sides of science becomes important. When an actual falsifier is proposed, the technology used is considered in detail and, as described in section , an actual agreement is needed. This may require using a deeper empirical basis, hidden within the current empirical basis, to make sure that the properties or values used in the falsifier were obtained correctly ( gives some examples).

Popper says that despite the fact that the empirical basis can be shaky, more comparable to a swamp than to solid ground, the definition that is given above is simply the formalization of a natural requirement on scientific theories, without which the whole logical process of science would not be possible.

Initial condition and prediction in falsifiers of laws

In his analysis of the scientific nature of universal laws, Popper arrived at the conclusion that laws must "allow us to deduce, roughly speaking, more ''empirical'' singular statements than we can deduce from the initial conditions alone." A singular statement that has one part only can not contradict a universal law. A falsifier of a law has always two parts: the initial condition and the singular statement that contradicts the prediction.

However, there is no need to require that falsifiers have two parts in the definition itself. This removes the requirement that a falsifiable statement must make prediction. In this way, the definition is more general and allows the basic statements themselves to be falsifiable. Criteria that require that ''a law'' must be predictive, just as is required by falsifiability (when applied to laws), Popper wrote, "have been put forward as criteria of the meaningfulness of sentences (rather than as criteria of demarcation applicable to theoretical systems) again and again after the publication of my book, even by critics who pooh-poohed my criterion of falsifiability."

Falsifiability in model theory

Scientists such as the Nobel laureate Herbert A. Simon have studied the semantic aspects of the logical side of falsifiability. These studies were done in the perspective that a logic is a relation between formal sentences in languages and a collection of mathematical structures. The relation, usually denoted $\models \phi$, says the formal sentence $\phi$ is true when interpreted in the structure $$—it provides the semantic of the languages.This perspective can be found in any text on model theory. For example, see . According to Rynasiewicz, in this semantic perspective, falsifiability as defined by Popper means that in some observation structure (in the collection) there exists a set of observations which refutes the theory. An even stronger notion of falsifiability was considered, which requires, not only that there exists one structure with a contradicting set of observations, but also that all structures in the collection that cannot be expanded to a structure that satisfies $\phi$ contain such a contradicting set of observations.

Examples of demarcation and applications

Newton's theory

In response to Lakatos who suggested that Newton's theory was as hard to show falsifiable as Freud's psychoanalytic theory, Popper gave the example of an apple that moves from the ground up to a branch and then starts to dance from one branch to another. It is clearly impossible, yet a basic statement that is a valid potential falsifier for Newton's theory, because the position of the apple at different times can be measured.

Einstein's equivalence principle

Another example of a basic statement is "The inert mass of this object is ten times larger than its gravitational mass." This is a basic statement because the inert mass and the gravitational mass can both be measured separately, even though it never happens that they are different. It is, as described by Popper, a valid falsifier for Einstein's equivalence principle.

Evolution

Industrial melanism

In a discussion of the theory of evolution, Popper mentioned industrial melanism as an example of a falsifiable law. A corresponding basic statement that acts as a potential falsifier is "In this industrial area, the relative fitness of the white-bodied peppered moth is high." Here "fitness" means "reproductive success over the next generation".For example, see , or It is a basic statement, because it is possible to separately determine the kind of environment, industrial vs natural, and the relative fitness of the white-bodied form (relative to the black-bodied form) in an area, even though it never happens that the white-bodied form has a high relative fitness in an industrial area.

Precambrian rabbit

A famous example of a basic statement from J. B. S. Haldane is " hese arefossil rabbits in the Precambrian era." This is a basic statement because it is possible to find a fossil rabbit and to determine that the date of a fossil is in the Precambrian era, even though it never happens that the date of a rabbit fossil is in the Precambrian era. Despite opinions to the contrary, some times wrongly attributed to Popper, this shows the scientific character of paleontology or the history of the evolution of life on Earth, because it contradicts the hypothesis in paleontology that all mammals existed in a much more recent era. Richard Dawkins adds that any other modern animal, such as a hippo, would suffice.

Simple examples of unfalsifiable statements

A simple example of a non-basic statement is "this angel does not have large wings". It is not a basic statement, because though the absence of large wings can be observed, no technology (independent of the presence of wings) exists to identify angels. Even if it is accepted that angels exist, the sentence "All angels have large wings" is not falsifiable.

Another example from Popper of a non-basic statement is "This human action is altruistic." It is not a basic statement, because no accepted technology allows us to determine whether or not an action is motivated by self-interest. Because no basic statement falsifies it, the statement that "All human actions are egotistic, motivated by self-interest" is thus not falsifiable.

Omphalos hypothesis

Some adherents of young-Earth creationism make an argument (called the Omphalos hypothesis after the Greek word for navel) that the world was created with the appearance of age; e.g., the sudden appearance of a mature chicken capable of laying eggs. This ad hoc hypothesis introduced into young-Earth creationism is unfalsifiable because it says that the time of creation (of a species) measured by the accepted technology is illusory and no accepted technology is proposed to measure the claimed "actual" time of creation. Moreover, if the ad hoc hypothesis says that the world was created as we observe it today without stating further laws, by definition it cannot be contradicted by observations and thus is not falsifiable. This is discussed by Dienes in the case of a variation on the Omphalos hypothesis, which, in addition, specifies that God made the creation in this way to test our faith.

Useful metaphysical statements

discussed statements such as "All men are mortal". This is not falsifiable, because it does not matter how old a man is, maybe he will die next year. Maxwell said that this statement is nevertheless useful, because it is often corroborated. He coined the term "corroboration without demarcation". Popper's view is that it is indeed useful, because Popper considers that metaphysical statements can be useful, but also because it is indirectly corroborated by the corroboration of the falsifiable law "All men die before the age of 150." For Popper, if no such a falsifiable law exists, then the metaphysical law is less useful, because it is not indirectly corroborated. This kind of non-falsifiable statements in science was noticed by Carnap as early a