In the early twentieth century, the logical positivists put forth what came to be known as the verifiability theory of meaning. The verifiability theory was based upon the verifiability principle, which states that for a statement to have meaning, the statement must be empirically verifiable. However, the verifiability principle is not empirically verifiable, hence if it is true then it is meaningless, and if it is meaningless, then it cannot be true, hence it cannot be true.

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] (http://plato.stanford.edu/entries/analytic-synthetic/). 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 in contemporary formal logic, but the idea of a statement being empirically verifiable was taken up by in the twentieth century by the logical positivists of the Vienna Circle, who used it to build upon the theory of language that Ludwig Wittgenstein had introduced in his Logisch-Philosophische Abhandlung. 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.