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Why did logical positivists struggle to create a criterion for meaningful statements?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Philosophy of science Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

Logical positivists struggled to create a criterion for meaningful statements primarily because the verifiability principle itself faced a fundamental self-referential challenge: it is not an empirical proposition, nor is it tautologically true, rendering it either meaningless or an arbitrary definition by its own standards.1

Additionally, the movement faced significant internal and external difficulties in defining the scope of "observable" conditions. Early attempts required statements to be logically entailed by finite observation reports, which proved too restrictive for scientific laws. Later efforts to shift toward "confirmability" or "probabilistic" support faced ongoing criticism regarding how to distinguish between meaningful scientific hypotheses and metaphysical or nonscientific claims.12

Furthermore, critics noted that positivists often conflated the truth conditions of a statement with the evidence used to confirm it, leading to conceptual errors. The lack of a precise, universally accepted criterion meant that even as the movement evolved, it remained unable to provide a definitive, non-arbitrary demarcation between meaningful and meaningless discourse.312