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2 years ago in Philosophy of Religion , Philosophy of Science By Pooja

Is it defensible to claim that mathematics is the "universal language" for expressing all forms of knowledge, including empirical, formal, and even philosophical knowledge?

I'm in a debate about the unity of science. A colleague argues that mathematics, because of its abstractness and logical rigor, is the ultimate language for encoding knowledge from physics to, potentially, biology and social sciences. But does this "unreasonable effectiveness of mathematics" (Wigner) extend to qualitative, experiential, or normative knowledge? Can a mathematical formalism fully capture the content of a historical narrative, a moral judgment, or the qualia of pain? Where does this claim break down philosophically?

 
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By Govind Answered 1 month ago

Mathematics is an unparalleled language for structural and quantitative relations, but the claim of universality is a category error. Mathematics excels at modeling patterns, dynamics, and logical relationships—the "how." It fails, and arguably must fail, at capturing intrinsic qualitative content (the "what it is like" of consciousness), semantic meaning (the content of a novel or a law), and normative force (the "ought" of an ethical claim). Gödel's incompleteness theorems already show limits within formal systems themselves. To reduce all knowledge to mathematics is to commit to a form of eliminative reductionism that would discard the very phenomena (meaning, value, experience) we seek to understand. Mathematics is a powerful tool for knowledge in certain domains, not a language capable of expressing all knowledge without loss.

By Govind Answered 1 month ago

Mathematics is an unparalleled language for structural and quantitative relations, but the claim of universality is a category error. Mathematics excels at modeling patterns, dynamics, and logical relationships—the "how." It fails, and arguably must fail, at capturing intrinsic qualitative content (the "what it is like" of consciousness), semantic meaning (the content of a novel or a law), and normative force (the "ought" of an ethical claim). Gödel's incompleteness theorems already show limits within formal systems themselves. To reduce all knowledge to mathematics is to commit to a form of eliminative reductionism that would discard the very phenomena (meaning, value, experience) we seek to understand. Mathematics is a powerful tool for knowledge in certain domains, not a language capable of expressing all knowledge without loss.

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