6 ideas
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 21354 | It may be that internal relations like proportion exist, because we directly perceive it [MacBride] |
| Full Idea: Some philosophers maintain that we literally perceive proportions and other internal relations. These relations must exist, otherwise we couldn't perceive them. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: [He cites Mulligan 1991, and Hochberg 2013:232] This seems a rather good point. You can't perceive the differing heights of two people, yet fail to perceive that one is taller. You also perceive 'below', which is external. |
| 21353 | Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride] |
| Full Idea: Internal relations are determined either by the mere existence of the things they relate, or by their intrinsic characters, or they supervene on the intrinsic characters of the things they relate. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: Suggesting that they 'supervene' doesn't explain anything (and supervenience never explains anything). I vote for the middle one - the intrinsic character. It has to be something about the existence, and not the mere fact of existence. |
| 21352 | 'Multigrade' relations are those lacking a fixed number of relata [MacBride] |
| Full Idea: A 'unigrade' relation R has a definite degree or adicity: R is binary, or ternary....or n-ary (for some unique n). By contrast a relation is 'multigrade' if it fails to be unigrade. Causation appears to be multigrade. | |
| From: Fraser MacBride (Relations [2016], 1) | |
| A reaction: He also cites entailment, which may have any number of premises. |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red. | |
| From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5 | |
| A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts. |