Combining Texts

All the ideas for 'Mathematics without Numbers', 'Oxford University Statutes' and 'Lectures on the Philosophy of Religion'

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6 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought

8074	There is a five shilling fine for each point of divergence from the thinking of Aristotle [Oxford Univ 1350]
	Full Idea: Bachelors and Masters of Arts who do not follow Aristotle's philosophy are subject to a fine of five shillings for each point of divergence, as well as for infractions of the rules of the Organon.
	From: Oxford Univ 1350 (Oxford University Statutes [1350]), quoted by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: Lovely quotation! We may defend the medieval period as a genuinely philosophical age, but this sort of statement suggests otherwise, and shows what intellectual heroes the few independent thinkers like William of Ockham really were.

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?

29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity

21798	To universalise 'give everything to the poor' leads to absurdity [Hegel]
	Full Idea: If everyone gave everything to the poor, then soon there would be no more poor to give anything to, or no more persons who would have anything to give.
	From: Georg W.F.Hegel (Lectures on the Philosophy of Religion [1827], III: 152), quoted by Stephen Houlgate - An Introduction to Hegel 10 'Faith'
	A reaction: Matthew 5:8, 19:21. Beautifully clear. [I always believed that I had thought of this idea - but not so]. If the logic is that it is better to be poor than to be rich, then the implication is that all excess wealth should be thrown into the sea.

29. Religion / D. Religious Issues / 2. Immortality / a. Immortality

21797	Immortality does not come at a later time, but when pure knowing Spirit fully grasps the universal [Hegel]
	Full Idea: The immortality of the soul must not be imagined as though it first emerges into actuality at some later time; rather it is a present quality. ...As pure knowing or as thinking, Spirit has the universal for its object - this is eternity.
	From: Georg W.F.Hegel (Lectures on the Philosophy of Religion [1827], III: 208), quoted by Stephen Houlgate - An Introduction to Hegel 10 'Death'
	A reaction: An unusual view of immortality, which challenges orthodoxy. The idea seems to be that 'pure knowing' is a grasping of the pure reason which embodies nature, which in turn is the nature of God. You enter eternity, rather than reside in it?