Concept
Cardinal number
Overview
finite or infinite number that measures cardinality (size) of sets
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
We now define an irrational number as a certain class of ratios, thus constructing it logically by means of ratios, instead of arriving at it by a doubtful inference from them. Take again the case of cardinal numbers. Two equally numerous collections appear to have something in common: this something is supposed to be their cardinal number. But so long as the cardinal number is inferred from the collections, not…
Bertrand Russell, Mysticism and Logic and Other Essays
Names Cardinal number several times; states what Cardinal number is.
In so far as the cardinal number at least is concerned, the answer generally accepted by Dedekind, Peano, Russell, and such writers is this: the number is a "class of similar classes" (Whitehead and Russell, _Prin. Math._, Vol. II, p. 4). To the interpretation of this answer, Mr. Russell, the most self-consciously philosophical of these mathematicians, has devoted his full dialectic skill.
John Dewey, Creative Intelligence
Names Cardinal number several times; opens on Cardinal number.
And then the number of whole numbers, that of the points of space, etc., constitutes what he calls a _transfinite cardinal number_, that is to say a cardinal number greater than all the ordinary cardinal numbers. And he has occupied himself in comparing these transfinite cardinal numbers. In arranging in a proper order the elements of an aggregate containing an infinity of them, he has also imagined what he calls…
Henri Poincaré, The Foundations of Science
Names Cardinal number several times; opens on Cardinal number.
Philosophers who discussed Cardinal number
Related ideas
- Independence (mathematical logic)
- Finite set
- Georg Cantor
- Springer Science+Business Media
- Infinite set
- Zermelo–Fraenkel set theory
- Dana Scott
- Kurt Gödel
- Function (mathematics)
- Mathematics
- Rational number
- Model theory
- Real number
- Natural number
- Number
- Ordered pair
- Power set
- Principia Mathematica
- Set (mathematics)
- Set theory
- Topological space
- Arithmetic
- Hume's principle
- Uncountable set
Place in the tradition
Part of Analytic philosophy.