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Full Idea
The epistemological burden of showing that the axioms are true is removed if we are only studying pure mathematics. If, however, we want to look at applied mathematics, then this burden returns.
Gist of Idea
The truth of the axioms doesn't matter for pure mathematics, but it does for applied
Source
Edwin D. Mares (A Priori [2011], 11.4)
Book Ref
Mares,Edwin: 'A Priori' [Acumen 2011], p.178
A Reaction
One of those really simple ideas that hits the spot. Nice. The most advanced applied mathematics must rest on counting and measuring.
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| 17701 | Possible worlds semantics has a nice compositional account of modal statements [Mares] |
| 17702 | Unstructured propositions are sets of possible worlds; structured ones have components [Mares] |
| 17704 | Operationalism defines concepts by our ways of measuring them [Mares] |
| 17703 | Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares] |
| 17705 | Empiricists say rationalists mistake imaginative powers for modal insights [Mares] |
| 17706 | The essence of a concept is either its definition or its conceptual relations? [Mares] |
| 17708 | Maybe space has points, but processes always need regions with a size [Mares] |
| 17710 | Aristotelian justification uses concepts abstracted from experience [Mares] |
| 17713 | After 1903, Husserl avoids metaphysical commitments [Mares] |
| 17714 | Aristotelians dislike the idea of a priori judgements from pure reason [Mares] |
| 17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares] |
| 17716 | Mathematics is relations between properties we abstract from experience [Mares] |