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2 ideas
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
| 21920 | No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB] |
| Full Idea: Schopenhauer dispenses with Kant's a priori categories, since all interrelations between representations are given through the principle of sufficient reason. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813]) by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: I'm not sure how Schopenhauer manages this move. Is it the stoic idea that reality has a logical structure, which can be inferred? Sounds good to me. Further investigation required. |