display all the ideas for this combination of texts
8 ideas
9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
Full Idea: The existence of abstract objects is a pseudo-problem. | |
From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
Full Idea: Cratylus was appalled that Heraclitus said you could not step twice into the same river, because it was already going too far to admit stepping into the same river once. | |
From: report of Cratylus (fragments/reports [c.425 BCE]) by Aristotle - Metaphysics 1010a | |
A reaction: Compare Idea 427. |
9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |