1. Since the encounter with Logical Positivism in Twentieth Century Western philosophy, testing a truth claim to see if it is self-referentially coherent has become standard fare for a beginning philosophy student.
("Logical positivism", Wikipedia): "Logical positivism and logical empiricism, which together formed neopositivism, was a movement in Western philosophy whose central thesis was verificationism, a theory of knowledge which asserted that only statements verifiable through empirical observation are cognitively meaningful."
Attempting to use science to rule out metaphysics and religion as meaningless, the logical positivists introduced the Verification Principle.
"Verificationism, also known as the verification principle or the verifiability criterion of meaning, is the philosophical doctrine that only statements that are empirically verifiable (i.e. verifiable through the senses) are cognitively meaningful, or else they are truths of logic (tautologies)."
"Verificationism thus rejects as cognitively 'meaningless' statements specific to entire fields such as metaphysics, theology, ethics and aesthetics. Such statements may be meaningful in influencing emotions or behavior, but not in terms of truth value, information or factual content. Verificationism was a central thesis of logical positivism, a movement in analytic philosophy that emerged in the 1920s by the efforts of a group of philosophers who sought to unify philosophy and science under a common naturalistic theory of knowledge."
"The verifiability criterion underwent various revisions throughout the 1920s to 1950s, but, by the 1960s, was deemed to be irreparably untenable. Its abandonment signaled the end of the entire movement launched by logical positivism."
The reason why the verification principle is irreparably untenable is simple: It suffered self-referential problems.
Verification Principle: Only statements that are empirically verifiable (i.e. verifiable through the senses) are cognitively meaningful, or else they are truths of logic (tautologies).
If we apply the Verification Principle to itself, we find that by its own standard the Verification Principle is cognitively meaningless.
The Verification Principle itself is not something that can be empirically verifiable through the senses and it is also not a truth of logic, so by its own criterion it is cognitively meaningless.
2. Many claims also suffered self-referential problems.
One such is a version of relativism which claims that there are no truths: all truth claims are interpretations only.
In the following brief quotation, which is part of a book review, Alvin Plantinga deftly disposes of this relativist claim.
(Plantinga 1987, 22):
"There is much to be said about this (most of it not flattering), but I won't take the time to say it. The basic idea here seems to be the notion, familiar in some varieties of continental philosophy, that whatever we think or believe is only a hermeneusis or interpretation, to which there are equally satisfactory alternatives. No matter what you believe on any important matter, there are alternatives to your belief that are quite as valid and acceptable. Indeed, for any belief you hold, its denial will be just as valid or satisfactory as it is."
"Of course if this is true, then Christianity, despite Sheehan's confident pronouncements, is as good an interpretation as any other. Thus Sheehan winds up (p.223) having to concede that Christianity is as acceptable an interpretation or hermeneusis as any other, and, indeed, as true as any other -- Sheehan's own interpretation, for example. (How we are to understand that is a bit puzzling, since Christianity and what Sheehan proposes are clearly inconsistent; but then Sheehan neither says nor suggests that ordinary logic is part of his interpretation.) Self-referential problems loom here. The fundamental claim seems to be that all we can ever have are equally acceptable if conflicting interpretations. But then, of course, if this claim is true, then it is itself just one more interpretation, and it is no better or closer to the truth than alternatives -- for example, its denial. If all is interpretation, then this idea itself has no more to be said for it than the contrary idea that some interpretations are vastly preferable and vastly closer to the truth than others. If all is interpretation to which there are equally satisfactory alternatives, then this very claim is an interpretation to which there are equally satisfactory alternatives: one can take it or leave it. As for me and my house, I think we'll leave it."
"Logical positivism", Wikipedia - The Free Encyclopedia,
"Verificationism", Wikipedia - The Free Encyclopedia,
Plantinga, Alvin. 1987. "Sheehan's Shenanigans: How theology becomes tomfoolery". The Reformed Journal 37, no.4 (April): 19-25.