Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'The Theory of Transfinite Numbers' and 'Oxford University Statutes'

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4 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.

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
	Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought.
	From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2
	A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896	Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
	Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections.
	From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
	A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue.

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

19347	Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
	Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates.
	From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1)
	A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that.