Against a Universal Definition of 'Type'

Abstract

What is the definition of 'type'? Having a clear and precise answer to this question would avoid many misunderstandings and prevent meaningless discussions that arise from them. But having such clear and precise answer to this question would also hurt science, "hamper the growth of knowledge" and "deflect the course of investigation into narrow channels of things already understood". In this essay, I argue that not everything we work with needs to be precisely defined. There are many definitions used by different communities, but none of them applies universally. A brief excursion into philosophy of science shows that this is not just tolerable, but necessary for progress. Philosophy also suggests how we can think about this imprecise notion of type.

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Against Method.P. Feyerabend - 1975 - British Journal for the Philosophy of Science 26 (4):331-342.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
A formulation of the simple theory of types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.

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