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Single Idea 16866

[from 'Logic in Mathematics' by Gottlob Frege, in 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation ]

Full Idea

We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates.

Gist of Idea

Tracing inference backwards closes in on a small set of axioms and postulates

Source

Gottlob Frege (Logic in Mathematics [1914], p.204)

Book Reference

Frege,Gottlob: 'Posthumous Writings', ed/tr. Hermes/Long/White etc [Blackwell 1979], p.204


A Reaction

The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience.