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### 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

#### [general ideas concerning numbers]

25 ideas
 1729 We perceive number by the denial of continuity [Aristotle]
 13273 Pluralities divide into discontinous countables; magnitudes divide into continuous things [Aristotle]
 10958 Perhaps numbers are substances? [Aristotle]
 13152 We can talk of 'innumerable number', about the infinite points on a line [Newton]
 16920 Numbers are formed by addition of units in time [Kant]
 9823 Numbers are free creations of the human mind, to understand differences [Dedekind]
 13412 Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
 13413 We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
 9901 Numbers can't be sets if there is no agreement on which sets they are [Benacerraf]
 9912 There are no such things as numbers [Benacerraf]
 12335 Numbers are for measuring and for calculating (and the two must be consistent) [Badiou]
 12334 There is no single unified definition of number [Badiou]
 10599 For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P]
 13861 Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
 10027 Mathematics is higher-order modal logic [Hodes]
 8958 In Field's version of science, space-time points replace real numbers [Field,H, by Szabó]
 8865 If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
 9923 We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
 9622 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
 17453 The meaning of a number isn't just the numerals leading up to it [Heck]
 12238 The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg]
 9998 What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
 10002 '2 + 2 = 4' can be read as either singular or plural [Hofweber]
 21644 Numbers are used as singular terms, as adjectives, and as symbols [Hofweber]
 21646 The Amazonian Piraha language is said to have no number words [Hofweber]