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Full Idea
Aristotelians treat mathematical facts as relations between properties. These properties, moreover, are abstracted from our experience of things. ...This view finds a natural companion in structuralism.
Gist of Idea
Mathematics is relations between properties we abstract from experience
Source
Edwin D. Mares (A Priori [2011], 11.7)
Book Ref
Mares,Edwin: 'A Priori' [Acumen 2011], p.182
A Reaction
This is the view of mathematics that I personally favour. The view that we abstract 'five' from a group of five pebbles is too simplistic, but this is the right general approach.
| 17700 | The most popular view is that coherent beliefs explain one another [Mares] |
| 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] |