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Full Idea
The Axiom of Infinity means that there are an infinity of distinguishable individuals, which is an empirical proposition.
Gist of Idea
Infinity: there is an infinity of distinguishable individuals
Source
Frank P. Ramsey (The Foundations of Mathematics [1925], §5)
Book Ref
Ramsey,Frank: 'Philosophical Papers', ed/tr. Mellor,D.H. [CUP 1990], p.222
A Reaction
The Axiom sounds absurd, as a part of a logical system, but Ramsey ends up defending it. Logical tautologies, which seem to be obviously true, are rendered absurd if they don't refer to any objects, and some of them refer to infinities of objects.
Related Idea
Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]
| 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
| 22328 | I just confront the evidence, and let it act on me [Ramsey] |
| 22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |