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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 Ref
'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]
| 10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
| 9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
| 9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| 9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
| 22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
| 17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
| 12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| 12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |