Quine's confirmational holism entails that mathematical statements share empirical content with the physical hypotheses they help confirm, directly contradicting Carnap's formalist insulation of mathematics.
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Willard Van Orman Quine was a 20th-century American philosopher who wrote about how we know things and how language works. In this statement, we're discussing one of his specific ideas about observation.
confirmational holism(Attributed to Quine; used to extend empirical confirmation to mathematical theories)
The thesis that empirical evidence does not confirm any single individual hypothesis but rather globally confirms the theory in which the hypothesis is embedded
empirical content(Used by Popper to equate informational richness with falsifiability.)
The amount of empirical information conveyed by a theory.
physical hypotheses(the assumptions being tested in the argument)
Proposed explanations about how the natural world works, based on the idea that everything follows physical laws.