6 ideas
| 19043 | Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine] |
| Full Idea: It is in the spirit of bivalence not just to treat each closed sentence as true or false; as Frege stressed, each general term must be definitely true or false of each object, specificiable or not. | |
| From: Willard Quine (What Price Bivalence? [1981], p.36) | |
| A reaction: But note that this is only the 'spirit' of the thing. If you had (as I do) doubts about whether predicates actually refer to genuine 'properties', you may want to stick to the whole sentence view, and not be so fine-grained. |
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
| From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
| From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
| A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
| 19042 | Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine] |
| Full Idea: A term is apt to be vague if it is to be learned by ostension, since its applicability must admit of being judged on the spot and so cannot hinge of fine distinctions laboriously drawn. | |
| From: Willard Quine (What Price Bivalence? [1981], p.32) | |
| A reaction: [Quine cites C. Wright for this] Presumably precision can steadily increased by repeated ostension. After the first 'dog' it's pretty vague; after hundreds of them we are pretty clear about it. Long observation of borderline 'clouds' could do the same. |
| 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. |
| 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. |