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The Emergence of First-Order Logic

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[New Entry by William Ewald on November 17, 2018.] For anybody schooled in modern logic, first-order logic can seem an entirely natural object of study, and its discovery inevitable. It is semantically complete; it is adequate to the axiomatization of all ordinary mathematics; and Lindstrom's theorem shows that it is the maximal logic satisfying the compactness and Lowenheim-Skolem properties. So it is not surprising that first-order logic has long been regarded as the "right" logic for investigations into the foundations of mathematics. It...

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News source: Stanford Encyclopedia of Philosophy

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