Combining Texts

All the ideas for 'Mathematics without Numbers', 'God and Human Attributes' and 'talk'

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

---

5 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?

15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality

7272	Maybe lots of qualia lead to intentionality, rather than intentionality being basic [Gildersleve]
	Full Idea: A common modern reductive view of the mind is that a hierarchy of intentional systems eventually produce qualia, but it might be the other way around. The mind is 'qualia-upon-qualia', with units of minimal qualia building up into intentional thought.
	From: Harry Gildersleve (talk [2005]), quoted by PG - Db (ideas)
	A reaction: If qualia are seen as existing at the most basic level of the brain, this may well imply panpsychism. It certainly says that basic brain cells are capable of minimal experiences. The idea that thought is essentially qualitative is very intriguing.

28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument

20713	God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B]
	Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God.
	From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality'
	A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist?