Combining Texts

All the ideas for 'fragments/reports', 'Logical Analysis of Gestalt Concepts' 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).

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

12887	A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
	Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics.
	From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
	A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases.

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.