8 ideas
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 15391 | A substance is, roughly, a basic being or subject at the foundation of reality [Robb] |
| Full Idea: A substance is a basic being, something at reality's foundation. What exactly this means is a matter of some controversy. Some philosophers think of substance as an ultimate subject, something that has properties but isn't a property. | |
| From: David Robb (Substance [2009], 'Intro') | |
| A reaction: This seems to capture the place of 'substance' in contemporary metaphysics. I think of 'substance' as a placeholder for some threatened account, even in Aristotle. |
| 15392 | If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb] |
| Full Idea: Sometimes a whole can survive a loss of parts: the chair would still exist if it lost one of its legs. This seems to give complex objects a sort of autonomy over their parts. | |
| From: David Robb (Substance [2009], 'Ident') | |
| A reaction: There is then a puzzle as to how much loss of parts the whole can survive, and why. The loss of a major part could be devastating, so why do all wholes not exhibit this relation to all their parts? I demand rules, now! |
| 7444 | Type-type psychophysical identity is combined with a functional characterisation of pain [Lewis] |
| Full Idea: The materialist theory Armstrong and I proposed joins claims of type-type psychophysical identity with a behaviourist or functionalist way of characterising mental states such as pain. | |
| From: David Lewis (Mad Pain and Martian Pain [1980], §III) | |
| A reaction: Armstrong has backed off from 'type-type' identity, because the realisations of a given mental state might be too diverse to be considered of the same type. Putnam's machine functionalism allows the possibility of dualism. |
| 7445 | The application of 'pain' to physical states is non-rigid and contingent [Lewis] |
| Full Idea: The word 'pain' is a non-rigid designator; it is a contingent matter what state the concept and the word apply to. (Note: so the sort of theory Kripke argues against is not what we propose). | |
| From: David Lewis (Mad Pain and Martian Pain [1980], §III) | |
| A reaction: I like the view that a given quale is necessarily identical to a given mental state, but that many mental states might occupy a given behavioural role. The smell of roses might occupy the behavioural role of pain. Frog pain isn't quite like ours. |
| 7443 | A theory must be mixed, to cover qualia without behaviour, and behaviour without qualia [Lewis, by PG] |
| Full Idea: To pass our test it seems that our theory will have to be a 'mixed' theory, to account for the Madman (whose pain has odd causes, and odd effects) and also for the Martian (who has normal causes and effects, but an odd physical state). | |
| From: report of David Lewis (Mad Pain and Martian Pain [1980], §II) by PG - Db (ideas) | |
| A reaction: A statement that 'pain' is ambiguous (qualia/causal role) would help a lot here. Martians have the causal role but no qualia, and the madman has the qualia but lacks the causal role. I say lots of different qualia might have the same causal role. |