Combining Texts

All the ideas for 'fragments/reports', 'The Nature of Universals and Propositions' and 'Mathematics: Form and Function'

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4 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

18189	ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
	Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
	From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
	A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).

8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes

8511	Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K]
	Full Idea: In modern times, it was G.F. Stout who first explicitly made the proposal that properties and relations are as particular as the substances that they qualify.
	From: report of G.F. Stout (The Nature of Universals and Propositions [1923]) by Keith Campbell - The Metaphysic of Abstract Particulars §1
	A reaction: Note that relations will have to be tropes, as well as properties. Williams wants tropes to be parts of objects, but that will be tricky with relations. If you place two objects on a table, how does the 'to the left of' trope come into existence?

25. Social Practice / E. Policies / 5. Education / b. Education principles

13304	Learned men gain more in one day than others do in a lifetime [Posidonius]
	Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
	From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
	A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.

27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure

20820	Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
	Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
	From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
	A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.