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Proofs and mistakes: Their syntactics, semantics, and pragmatics
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Solomon Marcus,
Published/Copyright:
February 18, 2012
Abstract
We point out the syntactic, semantic, and pragmatic levels of proofs and of mistakes in mathematics and the increasing difficulties in checking the correctness of a proof. We analyze the role of mistakes in mathematical creativity and we point out the frequency of mistakes (malign or benign) in works opening new ways in science. Significant examples are provided.
Keywords:: proof; mistake; error; syntactic; semantic; pragmatic; creativity; correctness; pioneering works
Published Online: 2012-02-18
Published in Print: 2012-February
© 2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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- Semiotics and logic: Pragmatization of the common ground
- Meaning between sense and reference: Impacts of semiotics on philosophy of science
- Where does logic meet semiotics?
- The correspondence theory of truth
- The intent to lie
- Reasoning in belief contexts
- Pragmatic constraints of meaning: An inferentialist approach
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- Proofs and mistakes: Their syntactics, semantics, and pragmatics
- Object realism versus mathematical structuralism
- Indeterministic tense operators and the concept of time as a substance
- Counterfactual semantics and quantum physics
- The ultimate strengthening of the Turing Test?
- Is computation based on interpretation?
- The troubles with ontological primacy
- Some remarks on the word “be” and other existential expressions
- The evolution of scientific languages in Ajdukiewicz and Kuhn
- The core of grammar
- The grammar of philosophical discourse
- Semantic bounds for everyday language
- Demonstrative descriptions and conventional implicatures
- Does the Twin-Earth argument rest on a fallacy of equivocation?
Keywords for this article
proof;
mistake;
error;
syntactic;
semantic;
pragmatic;
creativity;
correctness;
pioneering works
Articles in the same Issue
- Prelims
- Semiotics and logic: Pragmatization of the common ground
- Meaning between sense and reference: Impacts of semiotics on philosophy of science
- Where does logic meet semiotics?
- The correspondence theory of truth
- The intent to lie
- Reasoning in belief contexts
- Pragmatic constraints of meaning: An inferentialist approach
- On common knowledge in conversation
- Proofs and mistakes: Their syntactics, semantics, and pragmatics
- Object realism versus mathematical structuralism
- Indeterministic tense operators and the concept of time as a substance
- Counterfactual semantics and quantum physics
- The ultimate strengthening of the Turing Test?
- Is computation based on interpretation?
- The troubles with ontological primacy
- Some remarks on the word “be” and other existential expressions
- The evolution of scientific languages in Ajdukiewicz and Kuhn
- The core of grammar
- The grammar of philosophical discourse
- Semantic bounds for everyday language
- Demonstrative descriptions and conventional implicatures
- Does the Twin-Earth argument rest on a fallacy of equivocation?
