Wikipedia: Falsifiability

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Falsifiability is an essential concept in the [philosophy of science]?. To convey the concept roughly, we can say that for an assertion to be falsifiable, it must be in principle possible to make an observation or do a physical experiment? that would show the assertion to be false. For example, the assertion "All crows are black" could be falsified by observing a red crow.

The basic concept of falsifiability is simple, but, like all basic concepts in philosophy, its precise definition has been a matter of considerable disagreement. In particular, there has been great disagreement among the [logical empiricists]? and philosophers of science who learned from them about when to consider a statement falsified. W. V. Quine is 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." Hence, in the above example, one could say, for example, that it was in fact not a crow at all but some other kind of bird that was observed, or that the observer was mistaken that the color of the crow was in fact red (perhaps it was only painted red), etc.

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 meaningful. This was an essential feature of the [logical empiricism]? of the so-called [Vienna Circle]? that featured and essentially influenced such philosophers as [Moritz Schlick]?, [Rudolph Carnap]?, [Otto Neutrath]?, [Hans Reichenbach]?, Ludwig Wittgenstein, A. J. Ayer, and Karl Popper. Later, the leading theory of meaningfulness posited not verifiability but falsifiability as the criterion of meaningfulness (also known as [cognitive significance]?). In other words, in order to be meaningful at least in a strict sense, it had to be in principle possible (but it has been a vexed question how "in principle possible" should be cashed out) that we might produce some data that would show (or perhaps only tend to show) the proposition to be false.

Falsifiability has also been importantly connected not only with meaningfulness but also with scientific method: Karl Popper, for example, stressed that falsifiability is critical to the scientific method. If a hypothesis offered in explanation of some empirical phenomenon cannot be falsified, then the hypothesis is "unscientific" and should not be tested (all results will be, necessarily, positive, which proves nothing).

Claims about verifiability and falsifiability have been used to criticize various controversial views. On the view of some, for example A. J. Ayer, theism is not falsifiable; since God is typically alleged to be a transcendental being, beyond the realm of the observable, claims about the existence of God can neither be supported nor undermined by observation. This is, of course, a matter of controversy for anyone who places stock in natural theology--the [argument from design]? and other [a posterior]? arguments for the existence of God.

The existence or non-existence of God. For any test we might devise, it can be argued that God in his omnipotence chose for the test for fail, or chose for us to perceive that it failed, so there is no possible test that would prove His non-existence.
Many conspiracy theories. These are unfalsifiable because the nature of most conspiracy theories require that the conspiracy to be strong enough to generate evidence that shows the conspiracy does not exist. Specifically, anyone who denies the conspiracy can simply be made one of the conspirators, and his denial explained as deception.
Solipsism?. The belief that the rest of the Universe is only a figment of one's own imagination is not falsifiable, because to a solipsist, there is no evidence that can prove anything.
Definitions and Tautologies? such as "all green things are green" are necessarily true (or given) without any knowledge of the world. 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. These are unfalsifiable, because any evidence given is ignored in the proof process. How a mathematical formula might apply the the physical world, however, is testable.
Supernatural? creation of the world, such as the Omphalos hypothesis, in which the world is created suddenly in all its detail, including people, memories, records, tree rings, and other signs of age. Any experiment that suggests age can be explained away as the work of a supernatural creator.

Examples of falsifiable theories:

Laws of physics. At any time, some experiment may behave in a way that violates known "laws" of such things as gravity, electromagnetism, or nuclear interactions. Indeed, Isaac Newton's original laws of motion in their original form were falsified by experiments in the twentieth century, and replaced by more exact theories that hold under more conditions (though Newton's theories are still close enough to be used practically without the modern updates).
Modern theories of evolution. The theory as a whole could be falsified by finding an anomalous fossil of an advanced life form in rocks dated before that life form or its ancestors could have evolved (for example, finding a mammal in pre-Cambrian sediment). The theory of common descent could be falsified by finding a unique form of Earthly life that was totally unrelated to any existing or fossil form (for example, one not using RNA or proteins). The theory of sexual selection could be falsified by finding an organism with colorful sexual selection markings that was blind.

Any theory based upon a non-falsifiable premise is itself non-falsifiable. For example, a physical theory that posits multiple parallel universes with which we cannot interact is necessarily non-flasifiable. If the premise is changed to allow some theoretical mechanism by which we can see or change something in those universes, then it might theoretically become testable.

It should be noted that while the criterion of falsifiability is a foundation of modern science, many scientists and educators are lax in its application to their beliefs in general. For example, many scientists hold and express strong opinions about the existence of God or the non-existence of God, even though such beliefs are not falsifiable and thus not scientific. Likewise, scientists may often speculate or extend analogies to offer explanations for things that are not yet easily testable, and thus not falsifiable. For example, some theories like evolutionary psychology are offered as explanations for human behavior even though we presently lack the technology to rigorously test what causes human behavior. These theories are only falsifiable and "scientific" to the degree that they predict some future means of being able to test them, or that individual facts predicted by the theory might be testable on their own.

There are also degrees of falsifiability, and scientific hypotheses are considered superior if they are more falsifiable than competing ones. For example, a hypothesis for which there are many presently available tests (such as most physical laws) is superior to one that may only be testable in the future with some new technology (such as some psychological theories), and those are in turn superior to hypotheses that can never be tested because they are fundamentally untestable by their very nature (such as the existence or non-existence of God).