Group: mathematics
Group: program proving
Topic: embedded systems
Topic: limitations of formalism
Topic: mathematical proof
Topic: mathematics by proofs and refutations
Topic: meaning by social context
Topic: number and arithmetic as part of language
Topic: private language argument for skepticism about meaning
Topic: problems with analytic truth
Topic: program proving is infeasible
Topic: scientific paradigms and research programs
 
Summary
Mathematics is essentially a social process instead of an isolated formal one. Its theorems, proofs, and mathematical constructs become known and used through social interaction in a community. Engineers take mathematical results and build models for testing new designs. Mathematics, despite its formal foundation, is embedded within other systems and processes. (cbb 5/80)
Subtopic: mathematical truth requires support
Quote: a mathematician regards any discovered truth as a mere probability; confidence is gained through the approbation of friends and the learned world [»humeD_1739, OK]
 Quote: the truth of a theorem is established through transformations, generalizations, use, and connections [»demiRA5_1979]
 Quote: a believable theorem gets used [»demiRA5_1979]
 Subtopic: arithmetic as social process
Quote: a person is an adder if the community agrees about his additions and procedures; those who deviate are corrected [»kripSA_1982]
 Subtopic: authority and public testimony
Quote: facts are supported by the great weight of authority and of public testimony; it is not credible that many should conspire to deceive
 Subtopic: proof as communication
Quote: a proof is a construction that can be understood, reviewed , and verified by a mathematician [»tymoT2_1979]
 Quote: proofs are convincing to an arbitrary mathematician. This is why proofs are the arbiter of judgment in mathematics [»tymoT2_1979]
 Quote: mathematical theorems are believed because of social processes; reading, publishing, generalizing, using, etc. [»demiRA_1977]
 Quote: when a mathematician grasps a proof, he tries it out on his colleagues; it is not absolute [»demiRA5_1979]
 Quote: mathematicians' errors are corrected by other mathematicians, not by formal logic [»demiRA5_1979]
 Quote: if a mathematical proof is believed, it is internalized, paraphrased [»demiRA5_1979]

Related Topics
Group: mathematics (23 topics, 560 quotes)
Group: program proving (10 topics, 311 quotes)
Topic: embedded systems (26 items)
Topic: limitations of formalism (93 items)
Topic: mathematical proof (23 items)
Topic: mathematics by proofs and refutations (31 items)
Topic: meaning by social context (33 items)
Topic: number and arithmetic as part of language (30 items)
Topic: private language argument for skepticism about meaning (34 items)
Topic: problems with analytic truth (20 items)
Topic: program proving is infeasible (47 items)
Topic: scientific paradigms and research programs (30 items)
