6 ideas
| 8203 | All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine] |
| Full Idea: The arithmetic of ratios and irrational and imaginary numbers can all be reduced by definition to the theory of classes of positive integers, and this can in turn be reduced to pure set theory. | |
| From: Willard Quine (Vagaries of Definition [1972], p.53) | |
| A reaction: This summarises Quine's ontology of mathematics, which tries to eliminate virtually everything, but has to affirm the existence of sets. Can you count sets and their members, if the sets are used to define the numbers? |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| Full Idea: Let the incommunicable property of Plato be called 'Platonity'. For we can call this quality 'Platonity' by a fabricated word, in the way in which we call the quality of man 'humanity'. Therefore this Platonity is one man's alone - Plato's. | |
| From: Boethius (Librium de interpretatione editio secunda [c.516], PL64 462d), quoted by Alvin Plantinga - Actualism and Possible Worlds 5 | |
| A reaction: Plantinga uses this idea to reinstate the old notion of a haecceity, to bestow unshakable identity on things. My interest in the quotation is that the most shocking confusions about properties arose long before the invention of set theory. |
| 8202 | Meaning is essence divorced from things and wedded to words [Quine] |
| Full Idea: Meaning is essence divorced from the thing and wedded to the word. | |
| From: Willard Quine (Vagaries of Definition [1972], p.51) | |
| A reaction: Quine's strategy is that a demolition of essences will be a definition of meaning. Personally I would like to defend essences, though I admit to finding meaning tricky. That is because essences are external, but meanings are in minds. |
| 8201 | The distinction between meaning and further information is as vague as the essence/accident distinction [Quine] |
| Full Idea: The distinction between what belongs to the meaning of a word and what counts as further information is scarcely clearer than the distinction between the essence of a thing and its accidents. | |
| From: Willard Quine (Vagaries of Definition [1972], p.51) | |
| A reaction: In lots of cases the distinction between essence and accident strikes me as totally clear. Tricky borderline cases don't destroy a distinction. That bachelors are married is clearly not 'further information'. |
| 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. |