Combining Texts

All the ideas for 'fragments/reports', 'Quaestiones de Potentia Dei' and 'Letter to Frege 29.12.1899'

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4 ideas

3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth

15716	If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
	Full Idea: If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence.
	From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind'
	A reaction: If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later.

9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates

17555	'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas]
	Full Idea: There are two sorts of one. There is the one which is convertible with being, which adds nothing to being except being undivided; and this deprives of multitude. Then there is the principle of number, which to the notion of being adds measurement.
	From: Thomas Aquinas (Quaestiones de Potentia Dei [1269], q3 a16 ad 3-um)
	A reaction: [From a lecture handout] I'm not sure I understand this. We might say, I suppose, that insofar as water is water, it is all one, but you can't count it. Perhaps being 'unified' and being a 'unity' are different?

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.