Combining Texts

All the ideas for 'Events and Their Names', 'Mathematics without Numbers' and 'Philosophical Letters from England'

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

---

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?

7. Existence / B. Change in Existence / 4. Events / c. Reduction of events

8978	Events are made of other things, and are not fundamental to ontology [Bennett]
	Full Idea: Events are not basic items in the universe; they should not be included in any fundamental ontology...all the truths about them are entailed by and explained and made true by truths that do not involve the event concept.
	From: Jonathan Bennett (Events and Their Names [1988], p.12), quoted by Peter Simons - Events 3.1
	A reaction: Given the variable time spans of events, their ability to coincide, their ability to contain no motion, their blatantly conventional component, and their recalcitrance to individuation, I say Bennett is right.

23. Ethics / B. Contract Ethics / 2. Golden Rule

7844	The Golden Rule is accepted everywhere, and gives a fixed target for morality [Voltaire]
	Full Idea: Pascal asks where we can find a fixed point in morality. The answer is in that single maxim accepted by all nations: "Do not do to others what you would not like to have done to you".
	From: Francois-Marie Voltaire (Philosophical Letters from England [1733], 25)
	A reaction: Should I only offer to my guests foods which I myself like? If I don't mind a bit of pain, is it all right to inflict it? It is a sensible rule, but not precise enough for philosophy.

26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata

10364	Facts are about the world, not in it, so they can't cause anything [Bennett]
	Full Idea: Facts are not the sort of item that can cause anything. A fact is a true proposition (they say); it is not something in the world but is rather something about the world.
	From: Jonathan Bennett (Events and Their Names [1988], p.22), quoted by Jonathan Schaffer - The Metaphysics of Causation 1.1
	A reaction: Compare 10361. Good argument, but maybe 'fact' is ambiguous. See Idea 10365. Events are said to be more concrete, and so can do the job, but their individuation also seems to depend on a description (as Davidson has pointed out).