Concept
Formal proof
Overview
establishment of a theorem using inference from the axioms
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Here and there in Germany men are beginning to alter the exposition of mathematics, and to proceed more in this analytical way. The greatest effort in this direction has been made by Herr Kosack, teacher of mathematics and physics in the Gymnasium at Nordhausen, who added a thorough attempt to teach geometry according to my principles to the programme of the school examination on the 6th of April 1852. In order to…
Arthur Schopenhauer, The World as Will and Idea
Close in meaning to Formal proof; the term itself is not named.
In a conception of inference in which both data and hypothesis are regarded as the tentative, experimental results of the processes of perception, memory, and constructive imagination engaged in the special task of removing conflict, ambiguity, and inhibition, and in which these processes are not conceived as the functions of a private mind nor of an equally private brain and nervous system, but as functions of…
John Dewey, Creative Intelligence
States what Formal proof is.
Until symbolic logic had acquired its present development, the principles upon which mathematics depends were always supposed to be philosophical, and discoverable only by the uncertain, unprogressive methods hitherto employed by philosophers. So long as this was thought, mathematics seemed to be not autonomous, but dependent upon a study which had quite other methods than its own. Moreover, since the nature of the…
Bertrand Russell, Mysticism and Logic and Other Essays
Close in meaning to Formal proof; the term itself is not named.
Related ideas
- Formal language
- Effective method
- Interpretation (logic)
- Proof theory
- Mathematics
- Reference
- Rule of inference
- Sequent calculus
- Set (mathematics)
- Semantics
- Theorem
- Symbol
- Formal system
- Well-formed formula
- Structure (mathematical logic)
- Logic
- Natural deduction
- Axiom
Opposing perspectives
Place in the tradition
Part of Inference.