8 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) |
| 22320 | An 'object' is just what can be referred to without possible non-existence [Wittgenstein] |
| Full Idea: What I once called 'objects', simples, were simply what I could refer to without running the risk of their possible non-existence. | |
| From: Ludwig Wittgenstein (Philosophical Remarks [1930], p.72), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 52 'Simp' | |
| A reaction: For most of us, you can refer to something because you take it to be an object. For these Fregean influenced guys (e.g. Hale) something is an object because you can refer to it. Why don't they use 'object*' for their things? |
| 18283 | Language pictures the essence of the world [Wittgenstein] |
| Full Idea: The essence of language is a picture of the essence of the world. | |
| From: Ludwig Wittgenstein (Philosophical Remarks [1930], p.85), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 17 | |
| A reaction: Hence for a long time the study of language seemed to be the way to do metaphysics. Now they study mathematical logic, with the same hope. |
| 18282 | You can't believe it if you can't imagine a verification for it [Wittgenstein] |
| Full Idea: It isn't possible to believe something for which you cannot imagine some kind of verification. | |
| From: Ludwig Wittgenstein (Philosophical Remarks [1930], p.200), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 13 'Constr' | |
| A reaction: In 1930 LW was calling this his 'old principle'. As it stands here it is too vague to assert very much. |
| 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. |