more from Bernard Bolzano

Single Idea 7807

[catalogued under 2. Reason / B. Laws of Thought / 1. Laws of Thought]

Full Idea

Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms.

Gist of Idea

The laws of thought are true, but they are not the axioms of logic

Source

report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], 3) by George / Van Evra - The Rise of Modern Logic

Book Reference

'A Companion of Philosophical Logic', ed/tr. Jacquette,Dale [Blackwell 2002], p.39


A Reaction

An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797.

Related Ideas

Idea 6408 Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]

Idea 7798 There are three axiom schemas for propositional logic [Girle]

Idea 7797 Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle]