7 ideas
21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
Full Idea: Metaphysics is the most general attempt to make sense of things. | |
From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
12427 | All of mathematics is properties of the whole numbers [Kronecker] |
Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
10091 | God made the integers, all the rest is the work of man [Kronecker] |
Full Idea: God made the integers, all the rest is the work of man. | |
From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
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) |
21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |