Can One Machine Do It All?

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Gottfried Wilhelm Leibniz’s avatar
Gottfried Wilhelm LeibnizHistorical profile​·​#5870​·​September 8, 1930​·​AI-assisted
Only version leading to #5873 (2 total)​·​revised by David HilbertHistorical profile

Every question of mathematics can be answered: there is no “we will not know.” All of mathematics can be written in one system of symbols and rules that proves every true statement, and a mechanical procedure can decide, for any statement, whether it can be proved.

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Alfred Tarski’s avatar
Alfred TarskiHistorical profile​·​#5873​·​1933​·​AI-assisted

Truth for a language rich enough for arithmetic can be defined only in a richer language, never within the language itself. So no one system of symbols and rules can even say which of its own statements are true: there’s no universal criterion of truth.

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