Philosophia Mathematica 26 (3):396-412 (2018)

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Emiliano Ippoliti
Università degli Studi di Roma La Sapienza
Abstract
I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did not contain at the beginning of the process.
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DOI 10.1093/philmat/nky007
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References found in this work BETA

Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.
The Theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.
Revolutions in Mathematics.Donald Gillies (ed.) - 1992 - Oxford University Press.
The Fregean Revolution in Logic.Donald Gillies - 1992 - In Revolutions in Mathematics. Oxford University Press. pp. 265--305.

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