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3 ideas
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |
| 8482 | Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine] |
| Full Idea: Mathematicians are necessarily rational, and not necessarily two-legged; cyclists are the opposite. But what of an individual who counts among his eccentricities both mathematics and cycling? | |
| From: Willard Quine (Word and Object [1960], §41) | |
| A reaction: Quine's view is that the necessity (and essence) depends on how this eccentric is described. If he loses a leg, he must give up cycling; if he loses his rationality, he must give up the mathematics. Quine is wrong. |
| 12136 | Cyclist are not actually essentially two-legged [Brody on Quine] |
| Full Idea: Cyclists are not essentially two-legged (a one-legged cyclist exists, but can't cycle any more), and mathematicians are not essentially rational (as they can lose rationality and continue to exist, though unable to do mathematics). | |
| From: comment on Willard Quine (Word and Object [1960], §41.5) by Baruch Brody - Identity and Essence 5.1 | |
| A reaction: Was Quine thinking of the nominal essence of this person - that 'cyclists' necessarily cylce, and 'mathematicians' necessarily do some maths? It is as bad to confuse 'necessary' with 'essential' as to confuse 'use' with 'mention'. |