11 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. |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| Full Idea: It is clear the nominal essences really are the properties of the things which have them: they are (a subset of) the observable properties of the things. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: I think this is wrong. The surface characteristics are all that is available to us, so our classifications must be based on those, but it is on the ideas of them, not their intrinsic natures. That is empiricsm! What makes the properties 'essential'? |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| Full Idea: If the kinds there are depend not on the essences of the objects but on their observed distinguishing particulars, ...then for any kind that we think there is, it is possible that there are many underlying essences which are observably indistinguishable. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: Eagle is commenting on Locke's reliance on nominal essences. This seems to be the genuine problem with jadeite and nephrite (both taken to be 'jade'), or with 'fool's gold'. This isn't an objection to Locke; it just explains the role of science. |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| Full Idea: Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about. |
| 3570 | Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M] |
| Full Idea: Nozick suggests that knowledge is just belief which 'tracks the truth' (hence leaving out justification). | |
| From: report of Robert Nozick (Philosophical Explanations [1981]) by Michael Williams - Problems of Knowledge Ch. 2 |
| 2748 | A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J] |
| Full Idea: Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth"). | |
| From: report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1 | |
| A reaction: This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that. |
| 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. |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
| Full Idea: The natural thought is to think that real kinds are given only by classification on the basis of essential properties: properties that make an object the kind of thing that it is. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], II) | |
| A reaction: Circularity alert! Circularity alert! Essence gives a thing its kind - and hence we can see what the kind is? Test for a trivial property! Eagle is not unaware of these issues. Does he mean 'necessary' rather than 'essential'? |