Single Idea 19292

[catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

Full Idea

All the propositions of logic are of equal status: it is not the case that some of them are essentially primitive propositions and others essentially derived propositions.

Gist of Idea

Logic doesn't split into primitive and derived propositions; they all have the same status

Source

Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.127)

Book Reference

Wittgenstein,Ludwig: 'Tractatus Logico-Philosophicus (Pears)', ed/tr. Pears,D. /McGuinness,B. [RKP 1961], p.64


A Reaction

So axioms are conventional. This specifically contradicts the claims of Frege and the earlier Russell. Their view is that logic has an explanatory essence, found in some core axioms or rules or concepts. I agree with them.

Related Ideas

Idea 17640 Finding the axioms may be the only route to some new results [Russell]

Idea 16866 Tracing inference backwards closes in on a small set of axioms and postulates [Frege]

Idea 16868 The essence of mathematics is the kernel of primitive truths on which it rests [Frege]