5 ideas
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) | |
| A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'. |
| 17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
| Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3) |
| 17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
| Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) |
| 9155 | An a priori proof is independent of experience [Leibniz] |
| Full Idea: An a priori proof is a proof independent of experience. | |
| From: Gottfried Leibniz (Primary Truths [1686]) | |
| A reaction: Burge says Leibniz gave the first modern account of a priori knowledge. There may be no explicit reference to experience involved, but it would beg many questions to deny that implicit experience may be at the root of the proof. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |