Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Mathematics without Numbers' and 'The Trouble with Possible Worlds'

unexpand these ideas     |    start again     |     specify just one area for these texts

10 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
21757 Philosophy is the conceptual essence of the shape of history [Hegel]
     Full Idea: Philosophy is the supreme blossom - the concept - of the entire shape of history, the consciousness and the spiritual essence of the whole situation, the spirit of the age as the spirit present and aware of itself in thought.
     From: Georg W.F.Hegel (Lectures on the History of Philosophy [1830], p.25), quoted by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This sees philosophy as intrinsically historical, which is a founding idea for 'continental' philosophy. Analysis is tied to science, in which the history of the subject is seen as irrelevant to its truth. Does this mean we can't go back to Aristotle?
2. Reason / B. Laws of Thought / 6. Ockham's Razor
15787 Maybe Ockham's Razor is a purely aesthetic principle [Lycan]
     Full Idea: It might be said that Ockham's Razor is a purely aesthetic principle.
     From: William Lycan (The Trouble with Possible Worlds [1979], 02)
     A reaction: I don't buy this, if it meant to be dismissive of the relevance of the principle to truth. A deep question might be, what is so aesthetically attractive about simplicity? I'm inclined to think that application of the Razor has delivered terrific results.
15784 The Razor seems irrelevant for Meinongians, who allow absolutely everything to exist [Lycan]
     Full Idea: A Meinongian has already posited everything that could, or even could not, be; how, then, can any subsequent brandishing of Ockham's Razor be to the point?
     From: William Lycan (The Trouble with Possible Worlds [1979], 02)
     A reaction: See the ideas of Alexius Meinong. Presumably these crazy Meinongians must make some distinction between what actually exists in front of your nose, and the rest. So the Razor can use that distinction too.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
     Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
     A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
     Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
     A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
     Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
     From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
     A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?
9. Objects / A. Existence of Objects / 4. Impossible objects
15792 Maybe non-existent objects are sets of properties [Lycan]
     Full Idea: Meinong's Objects have sometimes been construed as sets of properties.
     From: William Lycan (The Trouble with Possible Worlds [1979], 09)
     A reaction: [Lycan cites Castañeda and T.Parsons] You still seem to have the problem with any 'bundle' theory of anything. A non-existent object is as much intended to be an object as anything on my desk right now. It just fails to be.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
15795 Treating possible worlds as mental needs more actual mental events [Lycan]
     Full Idea: A mentalistic approach to possible worlds is daunted by the paucity of actual mental events.
     From: William Lycan (The Trouble with Possible Worlds [1979], 09)
     A reaction: Why do they have to be actual, any more than memories have to be conscious? The mental events just need to be available when you need them. They are never all required simultaneously. This isn't mathematical logic!
15796 Possible worlds must be made of intensional objects like propositions or properties [Lycan]
     Full Idea: I believe the only promising choice of actual entities to serve as 'worlds' is that of sets of intensional objects, such as propositions or properties with stipulated interrelations.
     From: William Lycan (The Trouble with Possible Worlds [1979], 12)
     A reaction: This is mainly in response to Lewis's construction of them out of actual concrete objects. It strikes me as a bogus problem. It is just a convenient way to think precisely about possibilities, and occasionally outruns our mental capacity.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
15794 If 'worlds' are sentences, and possibility their consistency, consistency may rely on possibility [Lycan]
     Full Idea: If a 'world' is understood as a set of sentences, then possibility may be understood as consistency, ...but this seems circular, in that 'consistency' of sentences cannot adequately be defined save in terms of possibility.
     From: William Lycan (The Trouble with Possible Worlds [1979], 09)
     A reaction: [Carnap and Hintikka propose the view, Lewis 'Counterfactuals' p.85 objects] Worlds as sentences is not, of course, the same as worlds as propositions. There is a lot of circularity around in 'possible' worlds.