Combining Texts

All the ideas for 'Reportatio', 'Mathematics without Numbers' and 'On 'Physics''

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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?

9. Objects / E. Objects over Time / 6. Successive Things

16695	Successive entities are in flux, flowing in existence, with different parts at different times [Oresme]
	Full Idea: For any time, some of a successive entity exists in one of its parts, and a totally different such exists in another part. …It is in continuous flux and transition, ..and flows in existence if it does not have the same existence over a whole time.
	From: Nicole Oresme (On 'Physics' [1346], III.6, dist.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.1
	A reaction: Pasnau says the successive entity is the whole made up of these changing parts, so it sounds very like the temporal stages view of Sider and Hawley.

28. God / A. Divine Nature / 3. Divine Perfections

9111	God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham]
	Full Idea: God is not wise, but more-than-wise; God is not good, but more-than-good.
	From: William of Ockham (Reportatio [1330], III Q viii)
	A reaction: [He is quoting 'Damascene'] I quote this for interest, but I very much doubt whether Damascene or William knew what it meant, and I certainly don't. There seems to have been a politically correct desire to invent super-powers for God.

28. God / C. Attitudes to God / 4. God Reflects Humanity

9112	We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham]
	Full Idea: What we abstract is said to belong to perfection in so far as it can be predicated of God and can stand for Him. For if such a concept could not be abstracted from a creature, then in this life we could not arrive at a cognition of God's wisdom.
	From: William of Ockham (Reportatio [1330], III Q viii)
	A reaction: This seems to be the germ of an important argument. Without the ability to abstract from what is experienced, we would not be able to apply general concepts to things which are beyond experience. It is a key idea for empiricism.