22 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). |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| Full Idea: To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story. |
| 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. |
| 15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
| Full Idea: Pure, extreme nominalism sees all classification as the product of arbitrary convention. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I'm not sure what the word 'arbitrary' is doing there. Nominalists are not daft, and if they can classify any way they like, they are not likely to choose an 'arbitrary' system. Pragmatism tells the right story here. |
| 15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
| Full Idea: The naturalness of a class depends as essentially on the nature of the observers who classify as it does on the nature of the objects that they classify. ...It depends on our perceptual apparatus, and on our relatively mutable needs and interests. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: This seems to translate 'natural' as 'natural for us', which is not much use to scientists, who spend quite a lot of effort combating folk wisdom. Do desirable sports cars constitute a natural class? |
| 9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
| Full Idea: To say there are properties is to say there are natural classes, classes introduction to some of whose members enables people to pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: Aristotle would like this approach, but it doesn't find many friends among modern logician/philosophers. We should go on to ask why people agree on these things. Causal powers will then come into it. |
| 15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
| Full Idea: Properties that have no concrete instances must be defined in terms of those that have. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I wonder what the dodo used to smell like? |
| 8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |
| Full Idea: Quinton proposes that an individual is a union of a group of qualities and a position. | |
| From: report of Anthony Quinton (The Nature of Things [1973], Pt I) by Keith Campbell - The Metaphysic of Abstract Particulars §5 | |
| A reaction: This seems the obvious defence of a bundle account of objects against the charge that indiscernibles would have to be identical. It introduces, however, 'positions' into the ontology, but maybe that price must be paid. Materialism needs space. |
| 20189 | Belief is a feeling, independent of the will, which arises from uncontrolled and unknown causes [Hume] |
| Full Idea: Belief consists merely in a certain feeling or sentiment; in something, that depends not on the will, but must arise from certain determinate causes and principles, of which we are not master. | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], Appen p.2) | |
| A reaction: This is the opposite of Descartes' 'doxastic voluntarism' (i.e. we choose what to believe). If you want to become a Christian, steep yourself in religious literature, and the company of religious people. It will probably work. |
| 21309 | A proposition cannot be intelligible or consistent, if the perceptions are not so [Hume] |
| Full Idea: No proposition can be intelligible or consistent with regard to objects, which is not so with regard to perceptions. | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], Appendix) | |
| A reaction: An interesting variant on expressions of the empiricist principle. Presumably one can say intelligible things about Escher drawings. |
| 15755 | Hume needs a notion which includes degrees of resemblance [Shoemaker on Hume] |
| Full Idea: Hume needs a notion of resemblance where some things resemble a given thing more than other things do, and some may resemble exactly, and some hardly at all. | |
| From: comment on David Hume (Treatise of Human Nature, + Appendix [1740]) by Sydney Shoemaker - Causality and Properties §02 | |
| A reaction: An astute and simple point. Once you admit degrees of resemblance, of course, then resemblance probably ceases to be a primitive concept in your system, and Hume would be well stuck. |
| 5323 | Experiences are logically separate, but factually linked by simultaneity or a feeling of continuousness [Ayer on Hume] |
| Full Idea: Our experiences are logically independent, but they may be factually connected. What unites them is that either they are experienced together, or (if at separate times) they are separated by a stream of experience which is felt to be continuous. | |
| From: comment on David Hume (Treatise of Human Nature, + Appendix [1740], Bk 3 App.) by A.J. Ayer - The Central Questions of Philosophy §VI.A | |
| A reaction: A strict empiricist cannot deny that the feeling of continuity could be false, though that invites the Cartesian question of what exactly is experiencing the delusion. Hume denies that we experience any link between simultaneous experiences. |
| 21311 | Are self and substance the same? Then how can self remain if substance changes? [Hume] |
| Full Idea: Is the self the same with substance? If it be, how can that question have place concerning the subsistence of self, under a change of substance? If they be distinct, what is the difference between them? | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], Appendix) | |
| A reaction: Locke seems to think there is a characterless substance which supports momories, and the latter constitute the self. So if my substance acquires Nestor's memories, I become Nestor. Hume, the stricter empiricist, cares nothing for characterless things. |
| 21312 | Perceptions are distinct, so no connection between them can ever be discovered [Hume] |
| Full Idea: If perceptions are distinct existences, they form a whole only by being connected together. But no connexions among distinct existences are ever discoverable. We only feel a connexion ...to pass from one object to another. | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], Appendix) | |
| A reaction: This first part of this is a problem for any 'bundle' theory of objects or self. This is why Hume abandons all hope for his theory of personal identity based on association. You infer the associations, but don't perceive them. |
| 21308 | We have no impression of the self, and we therefore have no idea of it [Hume] |
| Full Idea: Every idea is derived from preceding impressions; and we have no impression of self or substance, as something simple and individual. We have, therefore, no idea of them in that sense. | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], Appendix) | |
| A reaction: This spells out with beautiful simplicity how his empiricist assumptions lead him to this sceptical view. No logical positivist could reject this thought. Personally I favour empiricism with added inference to the best explanation. |
| 21310 | Does an oyster with one perception have a self? Would lots of perceptions change that? [Hume] |
| Full Idea: Suppose an oyster to have only one perception, as of thirst or hunger. Do you consider any thing but merely that perception? Have you any notion of self or substance? If not, the addition of other perceptions can never give you that notion. | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], Appendix) | |
| A reaction: A splendid addition to his earlier sceptical thinking. We could form a different conclusion. Suppose I do have a self. If my multitudinous perceptions were reduced to a single perception of agonising pain, would that remove the self? |
| 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. |
| 23115 | We have no natural love of mankind, other than through various relationships [Hume] |
| Full Idea: It may be affirm'd, that there is no such passion in human minds, as the love of mankind, merely as such, independent of personal qualities, of services, or of relation to ourself. | |
| From: David Hume (Treatise of Human Nature, + Appendix [1740], p.481), quoted by John Kekes - Against Liberalism 9.4 | |
| A reaction: Hume says this is for the best. I can't imagine spontaneous love of human beings we have never met. It takes the teachings of some sort of doctrine - religious or political - to produce such an attitude. I see it as a distortion of love. A hijacking. |
| 16946 | Causation is just invariance, as long as it is described in general terms [Quine on Hume] |
| Full Idea: Hume explained cause as invariable succession, and this makes sense as long as the cause and effect are referred to by general terms. … This account leaves singular causal statements unexplained. | |
| From: comment on David Hume (Treatise of Human Nature, + Appendix [1740]) by Willard Quine - Natural Kinds p.131 | |
| A reaction: A nice 20th century linguistic point made against a good 18th century theory. |
| 15250 | If impressions, memories and ideas only differ in vivacity, nothing says it is memory, or repetition [Whitehead on Hume] |
| Full Idea: Hume confuses 'repetition of impressions' with 'impression of repetitions of impressions'. ...In order of 'force and vivacity' we have: impressions, memories, ideas. This omits the vital fact that memory is memory; the notion of repetition is lost. | |
| From: comment on David Hume (Treatise of Human Nature, + Appendix [1740]) by Alfred North Whitehead - Process and Reality V.II | |
| A reaction: [compressed; Harré and Madden spotted this idea] This seems to pinpoint rather nicely the hopeless thinness of Hume's account. He is so desperate to get it down to minimal empirical experience that his explanations are too thin. One big idea.... |