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
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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]
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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]
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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
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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]
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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)
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