Philosophy of Science

Ayer

"A further distinction which we must make is the distinction between the "strong" and the "weak" sense of the term "verifiable." A proposition is said to be verifiable, in the strong sense of the term, if, and only if, its truth could be conclusively established in experience. But it is verifiable, in the weak sense, if it is possible for experience to render it probable. In which sense are we using the term when we say that a putative proposition is genuine only if it is verifiable? "It seems to me that if we adopt conclusive verifiability as our criterion of significance, as some positivists have proposed, our argument will prove too much. Consider, for example, the case of general propositions of law - such propositions, namely, as "arsenic is poisonous"; "all men are mortal"; "a body tends to expand when it is heated." It is of the very nature of these propositions that their truth cannot be established with certainty by any finite series of observations. But if it is recognized that such general proopositions of law are designed to cover an infinite number of cases, then it must be admitted that they cannot, even in principle, be verified conclusively. And then, if we adopt conclusive verifiability as our criterion of significance, we are logically obliged to treat these general propositions of law in the same fashion as we treat the statements of the metaphysician."

- A. J. Ayer, The Elimination of Metaphysics

Ayer then states that statements about what has happened historically cause the same difficulty, and that some "heroically" take this to the extreme and say that historical statements are just nonsense - but "important" nonsense.

"For it must surely be admitted that, however strong the evidence in favor of historical statements may be, their truth can never become more than highly probable. And to maintain that they also constituted an important, or unimportant, type of nonsense would be implausible... no proposition, other than a tautology, can possibly be anything more than a probable hypothesis."

- A. J. Ayer, The Elimination of Metaphysics

Popper

Popper's attitude toward a definition of science, a discrimination between science and pseudo-science, is that of falsifiability, or refutability, or testability. The examples of theories given are Einstein's theory of relativity, the Marxist theory of history, and Freudian psycho-analysis. He presents the latter two as theories that can be applied to anything, as opposed to the former, which "risks" predictions about reality that can be proven wrong.

Popper gives a list of 9 conclusions:

1. It is easy to obtain confirmations, or verifications, for nearly every theory - if we look for confirmations.

2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory - an event which would have refuted the theory.

3. Every 'good' scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.

4. A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.

5. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.

6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of 'corroborating evidence'.)

7. Some genuinely testable theories, when found to be false, are still upheld by their admirers - for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later described such a rescuing operation as a conventionalist twist or a conventionalist stratagem.)

- Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (1963)