Combining Texts

All the ideas for 'Purifications (frags)', 'Universal Arithmetick' and 'Probability and Logic of Rational Belief'

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

2 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / e. The Lottery paradox
6368 If my ticket won't win the lottery (and it won't), no other tickets will either [Kyburg, by Pollock/Cruz]
     Full Idea: The Lottery Paradox says you should rationally conclude that your ticket will not win the lottery, and then apply the same reasoning to all the other tickets, and conclude that no ticket will win the lottery.
     From: report of Henry E. Kyburg Jr (Probability and Logic of Rational Belief [1961]) by J Pollock / J Cruz - Contemporary theories of Knowledge (2nd) §7.2.8
     A reaction: (Very compressed by me). I doubt whether this is a very deep paradox; the conclusion that I will not win is a rational assessment of likelihood, but it is not the result of strict logic.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17783 A number is not a multitude, but a unified ratio between quantities [Newton]
     Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity.
     From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2
     A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern.