Combining Texts

All the ideas for 'fragments/reports', 'Identity and Reference' and 'Proof that every set can be well-ordered'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
     Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory.
     From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I
18. Thought / B. Mechanics of Thought / 5. Mental Files
16362 An identity statement aims at getting the hearer to merge two mental files [Lockwood]
     Full Idea: The purpose of an identity statement is to get the hearer to merge these files or bodies of information into one.
     From: Michael Lockwood (Identity and Reference [1971], p.209), quoted by François Recanati - Mental Files 4.1
     A reaction: Lockwood is a pioneer, in seeing 'Hesperus is Phosphorus' and 'Scott is the author of 'Waverley'' in terms of how the mind works. Mental files seem to me to explain a huge amount. Recanati proposes 'linking' rather than 'merging'.
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.