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Prior to the development of the verifiability principle, Immanuel Kant classified statements into two categories, a set of analytic statements, and a set of synthetic statements [1]. For Kant, the truth of a mathematical statement had to be determined inside the mind, and he called any such statement analytic, in contrast to a synthetic statement like "the sky is blue", which requires the use of sensory perception to verify.
The classification terms analytic/synthetic have fallen into disuse, but the idea of a statement being empirically verifiable was taken up by the logical positivists of the twentieth century. In essence, Kant's synthetic statements are what are now called empirical statements. If an empirical statement is true, it might be empirically verifiable, and if an empirical statement is false, it might be empirically falsifiable. But, the verifiability priniciple itself is indeed an example of one of Kant's analytic statements, and hence is not a statement which is empirically verifiable. Hence, if the only kind of statements which are to be given meaning, are those statements which are empirically verifiable, then the verifiability principle is meaningless. Hence, the verifiability priniciple asserts its own meaninglessness. The verifiability theory of meaning is also closely related to the correspondence theory of truth.