12 ideas
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
| From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
| A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
| 15990 | Every individual thing which exists has an essence, which is its internal constitution [Locke] |
| Full Idea: I take essences to be in everything that internal constitution or frame for the modification of substance, which God in his wisdom gives to every particular creature, when he gives it a being; and such essences I grant there are in all things that exist. | |
| From: John Locke (Letters to Edward Stillingfleet [1695], Letter 1), quoted by Simon Blackburn - Quasi-Realism no Fictionalism | |
| A reaction: This is the clearest statement I have found of Locke's commitment to essences, for all his doubts about whether we can know such things. Alexander says (ch.13) Locke was reacting against scholastic essence, as pertaining to species. |
| 15994 | If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke] |
| Full Idea: What reaches to knowledge, I think may be called certainty; and what comes short of certainty, I think cannot be knowledge. | |
| From: John Locke (Letters to Edward Stillingfleet [1695], Letter 2), quoted by Simon Blackburn - Quasi-Realism no Fictionalism | |
| A reaction: I much prefer that fallibilist approach offered by the pragmatists. Knowledge is well-supported belief which seems (and is agreed) to be true, but there is a small shadow of doubt hanging over all of it. |
| 7440 | Secondary qualities are microscopic primary qualities of physical things [Armstrong] |
| Full Idea: I argue for the direct identification of the secondary qualities with microscopic primary qualities of physical things. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xxii) | |
| A reaction: This sounds a bit like the eliminativism which Armstrong rejects. This seems in danger of mixing questions about the nature of mental events with questions about the nature of externally perceived objects. |
| 7437 | Consciousness and experience of qualities are not the same [Armstrong] |
| Full Idea: Consciousness and experience of qualities are often run together - a serious mistake, I think. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xvii) | |
| A reaction: A difficult claim to evaluate. Can we experience redness without being conscious of it? Could there be consciousness (e.g. of concepts) which didn't involve any qualities? I suspect that qualities are more basic than intentionality or consciousness. |
| 7434 | Behaviourism is false, but mind is definable as the cause of behaviour [Armstrong] |
| Full Idea: Behaviourism is false, but one is not far from the truth if one defines the mind as the cause of behaviour. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xvi) | |
| A reaction: As Putnam says, if you cut all the efferent (outgoing) nerves, you would have a mind with no behaviour at all. I would say my mind is full of stuff that never affects my behaviour. However, influencing behaviour is certainly the main function of a mind. |
| 7436 | The manifestations of a disposition need never actually exist [Armstrong] |
| Full Idea: The manifestations of a disposition have the particularly mysterious property (metaphysically speaking) that they need not exist - which makes them rather like intentional objects. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xvii) | |
| A reaction: His example is a brittle glass which never shatters. This problem seems to require the mention of conditional and counterfactual statements in the description of the actual world, which rather increases the workload for philosophers. |
| 7429 | Causal Functionalism says mental states are apt for producing behaviour [Armstrong] |
| Full Idea: I speak of my view as the Causal version of functionalism, which asserts that mental states are states apt for the production of certain ranges of behaviour and, in some cases, apt for being produced by certain ranges of stimuli. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xiv) | |
| A reaction: This effectively makes a mental state a place in a flowdiagram (and hence the mind is software). It says nothing about what qualities the mental states have which make them apt for this role. Full explanations need more than the function. |
| 7438 | A causal theory of mentality would be improved by a teleological element [Armstrong] |
| Full Idea: I now think, following Lycan, that my Causal theory of mentality would be strengthened (perhaps eliminating some potential counter-examples) by the addition of a teleological element. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xviii) | |
| A reaction: For Lycan, see Idea 6533. Armstrong has begun to realise that merely specifying the causal role of a mental state is too thin as an explanation. Teleology widens the notion of function. I also want to know about the properties that make it possible. |
| 7431 | The identity of mental states with physical properties is contingent, because the laws of nature are contingent [Armstrong] |
| Full Idea: Granted the contingency of the laws of nature, the identification of dispositions with their categorical bases can be contingent only. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xvi) | |
| A reaction: Personally I am not willing to grant the contingency of the laws of nature, but I suppose Armstrong is right about identity if he is right about laws. Presumably an identity could happen to be invariant across possible worlds, without being necessary. |
| 7432 | One mental role might be filled by a variety of physical types [Armstrong] |
| Full Idea: If the mental is just that which plays a causal role then there is the possibility, which may even be an empirical possibility, that the causal role of tokens of the same mental type should be filled by tokens of significantly different physical types. | |
| From: David M. Armstrong (Pref to new 'Materialist Theory' [1992], p.xiv) | |
| A reaction: This allows for multiple realisability in a physicalist framework. Fear has the same role in all animals, but may be realised in physically different ways. I go further, and say that two mental states could differ, while playing the same role. |