Combining Texts

All the ideas for 'The Nature of Universals and Propositions', 'Presupposition and Conversational Implicature' and 'Mathematics without Numbers'

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6 ideas

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?

8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes

8511	Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K]
	Full Idea: In modern times, it was G.F. Stout who first explicitly made the proposal that properties and relations are as particular as the substances that they qualify.
	From: report of G.F. Stout (The Nature of Universals and Propositions [1923]) by Keith Campbell - The Metaphysic of Abstract Particulars §1
	A reaction: Note that relations will have to be tropes, as well as properties. Williams wants tropes to be parts of objects, but that will be tricky with relations. If you place two objects on a table, how does the 'to the left of' trope come into existence?

10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals

10990	Conditionals are truth-functional, but unassertable in tricky cases? [Grice, by Read]
	Full Idea: The 'conversational defence' of the truth-functional view of conditionals is that a conditional may not be assertible in difficult cases.
	From: report of H. Paul Grice (Presupposition and Conversational Implicature [1977]) by Stephen Read - Thinking About Logic Ch.3

19. Language / F. Communication / 5. Pragmatics / b. Implicature

10991	Key conversational maxims are 'quality' (assert truth) and 'quantity' (leave nothing out) [Grice, by Read]
	Full Idea: Grice particularly identified two maxims as guiding conversation: the maxim of 'quality' (that one should assert only what one believes to be true and justified), and of 'quantity' (one should not assert less than one can).
	From: report of H. Paul Grice (Presupposition and Conversational Implicature [1977]) by Stephen Read - Thinking About Logic Ch.3
	A reaction: I think it would be very foolish to boldly embrace the second maxim when talking to strangers. If white lies are occasionally acceptable, then what is the status of the first 'maxim'? Is it a moral maxim?