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Full Idea
Deductivism is a good account of large parts of mathematics, but stumbles where mathematics is directly applicable to the world. It fails to explain how we detach the antecedent so as to arrive at unconditional conclusions.
Clarification
'Deductrivism' also known as 'if-thenism'
Gist of Idea
Deductivism can't explain how the world supports unconditional conclusions
Source
Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Deduc')
Book Ref
Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.127
A Reaction
I suppose the reply would be that we have designed deductive structures which fit our understanding of reality - so it is all deductive, but selected pragmatically.
| 10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
| 10055 | Mathematical proofs work, irrespective of whether the objects exist [Locke] |
| 10056 | At bottom eternal truths are all conditional [Leibniz] |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| 24137 | Mathematics is just accurate inferences from definitions, and doesn't involve objects [Nietzsche] |
| 10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
| 10064 | Quine quickly dismisses If-thenism [Quine, by Musgrave] |
| 10066 | Putnam coined the term 'if-thenism' [Putnam, by Musgrave] |
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |