Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and the Continuum Hypothesis' and 'Sententia on 'Posterior Analytics''

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4 ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

14248	We could accept the integers as primitive, then use sets to construct the rest [Cohen]
	Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
	From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
	A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.

13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification

22109	The fullest knowledge places a conclusion within an accurate theory [Aquinas, by Kretzmann/Stump]
	Full Idea: Having 'scientia' is the fullest possible human cognition, by which one situates the fact expressed by a conclusion in an explanatory theory that accurately maps metaphysical or physical reality.
	From: report of Thomas Aquinas (Sententia on 'Posterior Analytics' [1269], 1.2.9, 1.5.7) by Kretzmann/Stump - Aquinas, Thomas 11
	A reaction: That is a perfect statement of my concept of knowledge. Explanatory theories must specify the essential natures of the entities involved. We don't aim for 'knowledge', we aim for the 'fullest possible cognition'. This account extend's Aristotle's.

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.