8 ideas
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 17993 | Laws are relations of kinds, quantities and qualities, supervening on the essences of a domain [Vetter] |
| Full Idea: The laws of a domain are the fundamental, general explanatory relationships between kinds, quantities, and qualities of that domain, that supervene upon the essential natures of those things. | |
| From: Barbara Vetter (Dispositional Essentialism and the Laws of Nature [2012], 9.3) | |
| A reaction: Hm. How small can the domain be? Can it embrace the multiverse? Supervenience is a rather weak relationship. How about 'are necessitated/entailed by'? Are the relationships supposed to do the explaining? I would have thought the natures did that. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |