Why did logical positivists consider mathematics and logic different from the physical sciences?

Logical positivists distinguished mathematics and logic from the physical sciences by categorizing them as a priori disciplines, meaning their validity is independent of empirical observation.1

While the physical sciences rely on the verifiability principle—where the meaning of a sentence is determined by its potential for empirical confirmation—logical positivists argued that logic and mathematics consist of analytic propositions. These propositions are true or false solely by virtue of the definitions and meanings of the terms they contain.12

Because these statements are tautologies—statements that cannot be denied without self-contradiction—they do not provide information about the external world and therefore cannot be refuted by experience. In contrast, the physical sciences involve synthetic propositions, which import information from empirical sources and remain contingent upon observation and measurement. Consequently, while scientific theories are subject to empirical verification, mathematical and logical truths are established as necessary and universal through their internal formal structure.134