| The verification principle is essentially invalid. This was the problem with positivism and the whole vienna circle. This is probably best represented by Ayer and forms a substantive critique of all 'objectivist' philosophies.
Basically, positivism argued that the meaning (truth) of a statement lies in the method of verification. It generally splits into two classes -- necessary and empirical statements. Mathematical equations are example of a necessary statement, where you can prove the truth of the statement within the axioms of mathematics. Empirical statements can be tested against experience for their truth value. The verifiability principle is simply: no statement can make a claim to truth unless that claim can be verified.
There are several problems with this -- and I'm not really aware of all of them.
The first and simplest one is that experience is necessarily subjective and the logical leap from subjective to objective knowledge is never satisfactorily argued (in fact, positivism tends to assume that experience is objective, which is necessarily false).
Secondly, positivism rests on a strict materialist ontology. Unfortunately, one cannot verify materialism (or any other metaphysical system for that matter). So, according to positivism, one should reject the materialist onotology -- but doing so means that positivist notions of verification are no longer sensible. For positivism to work, one has to assume a particular metaphysical position; but this gives basis for not assuming a different metaphysical position -- such as Cartesean dualism.
Thirdly, the verification principle itself cannot be verified. Because it cannot be verified, one must reject it. Take out the verification principle and positivism has no basis upon which to establish truth.
Fourthly, Hume's critique of inductive logic is never addressed. The problem of induction lies in the making the leap from a number of singular observations to a general statement of truth. Hume pointed out that one cannot be certain that the future will resemble the past. It is an unproven assumption that is not subject to verification (more specifically, he shows that all of the arguments for inductive certainty are necessarily circular).
All of these problems are related and basically end up at the same point: any thesis of verification cannot be verified. Verification is not capable of producing certain knowledge.
The most common modern answer to this is the falsification principle, made popular by Karl Popper. He argued that any claim to scientific knowledge must be able to be proven untrue. This can be illustrated by the statement "all swans are white." To prove this true, I would have to find ever swan that ever lived (or would ever live) and see that it was white. However, observing one black swan would prove it false. Any scienific statement cannot be said to be true with certainty, but merely that it has not yet been falsified. Statements that cannot be falsified are not science (whether they are knowledge or not is another question). |