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Single Idea 13892

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers ]

Full Idea

Someone could be clear about number identities, and distinguish numbers from other things, without conceiving them as ordered in a progression at all. The point of them would be to make comparisons between sizes of groups.

Gist of Idea

One could grasp numbers, and name sizes with them, without grasping ordering

Source

Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv)

Book Ref

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.118

A Reaction

Hm. Could you grasp size if you couldn't grasp which of two groups was the bigger? What's the point of noting that I have ten pounds and you only have five, if you don't realise that I have more than you? You could have called them Caesar and Brutus.

Related Ideas

Idea 13893 It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]

Idea 13894 Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]

The 19 ideas with the same theme [which type of numbers is the most fundamental?]:

11044 One is prior to two, because its existence is implied by two [Aristotle]
10091 God made the integers, all the rest is the work of man [Kronecker]
10090 Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
7524 Order, not quantity, is central to defining numbers [Dedekind, by Monk]
17452 Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
9983 Cantor took the ordinal numbers to be primary [Cantor, by Tait]
18256 Quantity is inconceivable without the idea of addition [Frege]
13510 Could a number just be something which occurs in a progression? [Russell, by Hart,WD]
14128 Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell]
14129 Ordinals presuppose two relations, where cardinals only presuppose one [Russell]
14132 Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell]
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
18255 Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
13411 If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
9151 Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K]
18102 A cardinal is the earliest ordinal that has that number of predecessors [Bostock]
13892 One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
8661 The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend]