David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Synthese 27 (1-2):211 - 250 (1974)
In applied problems mathematics is used as language or as a metalanguage on which metatheories are built, E.G., Mathematical theory of experiment. The structure of pure mathematics is grammar of the language. As opposed to pure mathematics, In applied problems we must keep in mind what underlies the sign system. Optimality criteria-Axioms of applied mathematics-Prove mutually incompatible, They form a mosaic and not mathematical structures which, According to bourbaki, Make mathematics a unified science. One of the peculiarities of applied mathematical language is a variety of dialects: a problem can be presented in terms of various mathematical notions. Another peculiarity is polysemy: a problem can be presented in the framework of one dialect by a set of various models with equal right to exist. The pragmatic sense of distinction between applied and pure mathematics must lead to specific training in each case
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References found in this work BETA
Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.
Ernest Nagel (1958). Gödel's Proof. [New York]New York University Press.
A. Heyting (1956). Intuitionism an Introduction. North-Holland.
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