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I am trying to understand the argument for the supposedly paradoxical nature of the verifiability criterion. The argument goes as follows:

Suppose that the principle of verifiability is itself verifiable. Then it follows that the contradictory of the principle must itself be a meaningful statement. For a statement can be said to be verifiable only if it has a significant contradictory. But the contradictory of the principle of veri- fiability asserts that there is some statement which is meaningful and which possesses no observable consequences. Hence it follows that it is significant to say: some statements are meaningful, and they don't have verifiable consequences. We must then conclude that the principle of verifiability is false. (Feuer, L. S. (1951). The Paradox of Verifiability)

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    The issue is that according to Logical Positivism. "A statement is meaningful if and only if it can be proved true or false, at least in principle, by means of the experience -- this assertion is called the verifiability principle [aka the "verifiability criterion of meaning"]. " Oct 4, 2021 at 7:21
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    But if the principle itself is meaningful, also its negation will be: "there is a statement which is meaningful but not 'testable' ". Thus, if we assert that the Verifiability Principle is a "regulatory" principle that is not empirical and thus not subject to verification/falsification, we have found a statement meaningful but not refutable (and thus not verifiable) and thus we are forced to reject the principle itself. Oct 4, 2021 at 7:31
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    See also Ayer: Meaning for discussion as well as Verificationism and the Critique of Metaphysics: "By 1950, in response to the troubles of Ayer’s two attempts to account for the indirect testing of theoretical statements via their consequences, Hempel conceded that it was “useless to continue to search for an adequate criterion of testability in terms of deductive relationships to observation sentences”." Oct 4, 2021 at 8:23
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    Per the truth-table definition of material conditional, disregarding the two vacuous true cases, to say we empirically verified p→q is to say if p is true, then q must be true. Once you get this result verified from whatever supposed empirical method, then immediately we also verified its contradiction p→¬q is false (check its truth table again). Then you arrive at a self-referential paradox of verifiability. Formally speaking the logical negation of p→¬q should be p∧q, so I'm using contradiction here informally. Oct 5, 2021 at 21:26
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    Another way to look at it is from Tarski's convention T. so the whole argument p→q has meaning when it's verified to be true. However, clearly p→q is not an analytic tautology here by its definition, so it's possible to be verified as false. When it's verified false, its contradiction p→¬q must be verified as true, then p→¬q acquires meaning, thus later you get self-referential paradox... Oct 6, 2021 at 2:33

2 Answers 2

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It follows from the principle of verifiability itself (because nothing counts under logical positivism unless it is verifiable). Under logical positivism, the only things that are verifiable are those that are falsifiable, but falsifications don't count unless they themselves are verifiable. It's a vicious circle.

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  • But if we supposed a statement like "a proposition is meaningless unless it can be empirically verified" is verifiable, why does the fact that its contradiction "a proposition is meaningful unless it can be empirically verified" being meaningful lead us to the conclusion that the verifiability criterion is false?
    – Nader
    Oct 4, 2021 at 15:54
  • If we assume there is emprirical evidence to verify the verifiablity criterion, then why can't we assume the same for its contradiction?
    – Nader
    Oct 4, 2021 at 15:56
  • The short answer is that if you're "supposing" then you're not "doing" logical positivism. Anyway, wouldn't empirically verifying the principle and its contradiction be more than "supposedly" paradoxical? Oct 5, 2021 at 4:19
  • Why does verification of a statement imply verifing its contradiction? Wouldn't that render all statments verified by the criterion paradoxical?
    – Nader
    Oct 5, 2021 at 4:31
  • Verification of a statement falsifies its contradiction. That's the whole problem. The principle of verifiability cannot accommodate the possibility that it could have a meaningful contradiction. I.e., it is unfalsifiable, ergo, it is unverifiable, ergo (according to itself), it is meaningless. Dec 8, 2021 at 14:42
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The meaning of a statement S is the difference it makes in the world, should it be true. A meaningful statement makes some difference.

But a difference is a comparison between two different conditions. Specifically, it is the comparison between the way the world would be if S is true (call that Consequences(S)), against the way the world would be if S is false (call that Consequences(not-S)).

For S to be meaningful means that Consequences(S) is different from Consequences(not-S).

By substituting, for not-S to be meaningful means that Consequences(not-S) is different from Consequences(not-not-S). But by double negation elimination, that's the same as saying Consequences(not-S) is different from Consequences(S). And that's the same condition as for S to be meaningful.

So, the condition for S to be meaningful is the same condition as the condition for not-S to be meaningful. Therefore, if S is meaningful, so is not-S, and vice versa.

Incidentally, the resolution to the paradox of the original question goes as follows.

Suppose that the principle of verifiability is itself verifiable. Then it follows that the contradictory of the principle must itself be a meaningful statement. For a statement can be said to be verifiable only if it has a significant contradictory. But the contradictory of the principle of verifiability asserts that there is some statement which is meaningful and which possesses no observable consequences. Hence it follows that it is significant to say: some statements are meaningful, and they don't have verifiable consequences. We must then conclude that the principle of verifiability is false. (Feuer, L. S. (1951). The Paradox of Verifiability)

The second to last line obtains the proposition, "it is significant to say: some statements are meaningful, and they don't have verifiable consequences." Let the sentence, "some statements are meaningful, and they don't have verifiable consequences" be named P. In order to obtain a counterexample to the principle of verifiability, we only have half the picture; we have shown that P is meaningful, but we have yet to show that P lacks verifiable consequences. Does it? The "paradox" fails to establish this.

In fact, there is evidence that P may have verifiable consequences. Namely, an intellectual community that believes P will behave differently from an intellectual community that believes not-P; the second community will reject as meaningless certain propositions that the first community will not. Belief in P influences behavior. And perhaps one of the communities will perform better, or worse, than the other, in regards to certain practical measures, such as the quality of technology produced by the community. The performance of the community, based on belief in P or not-P, could be considered a verifiable consequence of P. If P is true, we might expect the P-believing community would perform better, and if P is false, we might expect the not-P-believing community would perform better.

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