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All the ideas for 'Mathematics without Numbers', 'Intention' and 'works'

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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?

20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions

20041	Intentional actions are those which are explained by giving the reason for so acting [Anscombe]
	Full Idea: Intentional actions are those to which a certain sense of the question 'Why?' is given application; the sense is of course that in which the answer, if positive, gives a reason for acting.
	From: G.E.M. Anscombe (Intention [1957], p.9), quoted by Rowland Stout - Action 2 'Two kinds'
	A reaction: This works better for grand large-scale actions than for small ones, like taking the knife out of the drawer before the fork. Kahnemann nowadays tells us that the reasons we articulate might not be the ones that are operative.

25. Social Practice / E. Policies / 2. Religion in Society

20723	Only when working people are poor do they remain obedient to God [Calvin, by Weber]
	Full Idea: Calvin made the much-quoted statement that only when the people, i.e. the mass of labourers and craftsmen, were poor did they remain obedient to God.
	From: report of Jean Calvin (works [1549]) by Max Weber - The Protestant Ethic and the Spirit of Capitalism 5
	A reaction: This is only one aspect of Christian influence. The alternative is John Wesley's exhortation to work diligently, live modestly, save, invest and get rich. Most people want a comfortable intermediate state, but who proclaims that?