10 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. |
| 7260 | If there are intuited moral facts, why should we care about them? [Dancy,J] |
| Full Idea: Critics asked (of intuitionism) why, if moral facts are as the intuitionists say, we should care about them at all. | |
| From: Jonathan Dancy (Intuitionism [1991]) | |
| A reaction: It is a good question, as we don't care much about other a priori truths, such as the square root of 169. |
| 7261 | Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J] |
| Full Idea: There is an internalist view of intuitionism, saying that to accept that one's action is wrong is itself to be motivated not to do it. Externalists (like Ross) say that moral judgements need the help of an independent desire to motivate us. | |
| From: Jonathan Dancy (Intuitionism [1991]) | |
| A reaction: The internalists would be closer to Kant or Plato (for whom reason or pure ideas motivate), while externalist would favour Hume's belief/desire account of human actions. I like Kant and Plato, but Hume is more plausible. Dancy disagrees (Idea 7262). |
| 7262 | Obviously judging an action as wrong gives us a reason not to do it [Dancy,J] |
| Full Idea: It is ludicrous to say that we might accept an action is outrageously wrong and still think of this as not in itself giving us good reason to hold back. | |
| From: Jonathan Dancy (Intuitionism [1991]) | |
| A reaction: If we think of some dreadful man-made famine in a remote continent, our judgement may well give a reason to act, but apathy usually intervenes. We are discussing a purely theoretical motive on the one hand, and an actual motivator on the other. |
| 7265 | Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J] |
| Full Idea: I intend to suggest that moral facts are best thought of not as facts perceived but as reasons recognised in the exercise of practical moral judgement. | |
| From: Jonathan Dancy (Intuitionism [1991]) | |
| A reaction: I'm not convinced by this modified version. Why should the fact that someone is in pain be, in itself, a reason to prevent it? There are different cultural traditions for response to the pain of others. We are the squeamish tradition. |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |
| Full Idea: Primary matter is nothing if considered at rest. | |
| From: Gottfried Leibniz (Aristotle and Descartes on Matter [1671], p.90) | |
| A reaction: This goes with Leibniz's Idea 13393, that activity is the hallmark of existence. No one seems to have been able to make good sense of prime matter, and it plays little role in Aristotle's writings. |