6 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) |
| 23900 | Chance is compatible with necessity, and the two occur together [Weil] |
| Full Idea: Chance is not the contrary of necessity; it is not incompatible with necessity. On the contrary, it never appears except at the same time as necessity. | |
| From: Simone Weil (The Scientific Image [1941], p.175) | |
| A reaction: She illustrates it with the six terminating results of a die throw, and the innumerabe ways the throw can occur. This thought strikes me as relevant to discussions of free will. …But I'm not sure I fully understand it. |
| 23899 | The secret of art is that beauty is a just blend of unity and its opposite [Weil] |
| Full Idea: A just blend of unity and that which opposes it is the condition of the beautiful, and it is the secret of art. | |
| From: Simone Weil (The Scientific Image [1941], p.169) | |
| A reaction: Rather sweeping, but the observation strikes me as fairly accurate. It seems to work for most novels, paintings and music, though more recent art may provide counterexamples. |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
| From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
| A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |