Combining Texts

All the ideas for 'fragments/reports', 'Intro to 2nd ed of Principia Mathematica' and 'On Plural Reference and Set Theory'

unexpand these ideas     |    start again     |     specify just one area for these texts

4 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10670 A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack]
     Full Idea: Helen Cartwright calls 'a number of' a 'singulariser', an expression whose linguistic function is to convert to a syntactically neutral form an expression whose semantic value remains plural. It is a great convenience grammatically.
     From: report of Helen Cartwright (On Plural Reference and Set Theory [1993]) by Keith Hossack - Plurals and Complexes 2
     A reaction: Compare Hofweber's Idea 10004, suggesting it is a crucial psychological convenience for reasoning, as well as a 'grammatical' convenience.
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
21681 Given all true atomic propositions, in theory every other truth can thereby be deduced [Russell]
     Full Idea: Given all true atomic propositions, together with the fact that they are all, every other true proposition can theoretically be deduced by logical methods.
     From: Bertrand Russell (Intro to 2nd ed of Principia Mathematica [1925], p.xv)
     A reaction: This is evidently his strongest statement of the ideal underlying logical atomism. The atoms were initially sense-date, but then became atomic propositions saying an object has a property.
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.