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How did logical positivists connect meaning with empirical verification?

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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. — Truth Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

Logical positivists connected meaning to empirical verification through the verifiability principle, which posits that a non-tautological statement is meaningful only if it can be empirically verified, at least in principle.12

For the logical positivists, the meaning of a statement is defined by the set of conditions under which it would be true—specifically, the method of its verification. They categorized meaningful statements into two types:132
* Analytic propositions: Statements that are necessarily true or false based solely on the meanings of their terms (e.g., logic and mathematics), which are considered tautological.13
* Synthetic propositions: Statements that express matters of material fact, which must be supported or rendered probable by empirical observation to possess cognitive meaning.13

By this standard, the positivists argued that metaphysical, ethical, and religious assertions are literally meaningless because they cannot be verified through experience. While some positivists, such as A.J. Ayer, acknowledged that these statements might have "emotive" significance, they insisted they lack genuine cognitive or factual content.13452