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2 ideas
| 4044 | Rat behaviour reveals a considerable ability to count [Goldman] |
| Full Idea: Rats can determine the number of times they have pressed a lever up to at least twenty-four presses,…and can consistently turn down the fifth tunnel on the left in a maze. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.58) | |
| A reaction: This seems to encourage an empirical view of maths (pattern recognition?) rather than a Platonic one. Or numbers are innate in rat brains? |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |