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How did logical positivism use the verification principle to evaluate meaningful claims?

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Four colored straws in a glass of water appear bent at the water's surface, visually demonstrating the refraction of light. — Epistemology The refraction (bending) of light as it passes from air into water causes an optical illusion: straws in the glass of water appear broken or bent at the water's surface.

In logical positivism, the verifiability principle serves as a criterion to distinguish between meaningful and meaningless statements. According to this doctrine, a non-tautological statement is considered cognitively meaningful only if it is empirically verifiable—meaning there are observable conditions relevant to determining its truth or falsity.12

The principle functions by categorizing statements into two types:
* Analytic: Statements that are true or false by virtue of their definitions (e.g., logic and mathematics), which are considered meaningful but provide no factual information about the world.12
* Synthetic: Statements that purport to express matters of material fact. For these, the principle requires that one be able to identify what evidence would count for or against their truth.2

If a statement—such as those found in metaphysics, ethics, or religion—cannot be verified through experience or observation, logical positivists dismiss it as cognitively meaningless. While such statements may influence emotions or conduct, they do not impart knowledge because they are compatible with any possible state of affairs, rendering them devoid of factual significance.123