Combining Texts

All the ideas for 'fragments/reports', 'Letters to Leibniz' 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.

8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence

12750	The question is whether force is self-sufficient in bodies, and essential, or dependent on something [Lenfant]
	Full Idea: The whole question is to know if the force to act in bodies is in matter something distinct and independent of everything else that one conceives there. Without that, this force cannot be its essence, and will remain the result of some primitive quality.
	From: Jacques Lenfant (Letters to Leibniz [1693], 1693.11.07), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 8
	A reaction: This challenge to Leibniz highlights the drama of trying to simultaneously arrive at explanations of things, and to decide the nature of essence. Leibniz replied that force is primitive, because it is the 'principle' of behaviour and dispositions.

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.