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Bibliographic Item (1.0)
- Frank Plumpton Ramsey (ed R B Braithwaite)
- Foundations of mathematics and other Logical Essays
- Littlefield Adams, Paterson NJ 1960
- =ESSAYS PHILOSOPHY LOGIC MATHEMATICS TYPES PROBABILITY
- Essays, papers, reviews, and notes dating from the 1920s.
- The Foundations of Mathematics 1925
- Mathematical Logic 1926
- On a Problem of Formal Logic 1928
- Note on the preceeding paper 1926
- Facts and Propositions 1927
- Truth and probability 1926
- Further Considerations 1928
- Last Papers 1928
- Appendix: Critical Notice of L Wittgenstein's "Tractatus Logico-Philosophicus"
- PM::="Principia Mathematica",
- Dispenses with PM's pphilosophical
axiom of reducibility
by using Wittgenstein's Tractatus Logico-Philosophicus.
- PM gives a syntactic definition set of special predicative truth functions to avoid paradoxes and then has to assume that all sets (for example) of objects of a given type can be expressed using one of these functions.
- Ramsey uses a semantic definition from Wittgenstein that makes any truth function predicative.
- Argues for the need for a theory of types.
- Does not discard axioms of infinity and selection.
Axiom of infinity
asserts the existence of an infinite domain, Needed to define infinite numbers.
Because, in PM, numbers measure the size of sets of objects of a particular type.
Indeed a number is a set of all sets with the same size of that type.
So the largest number for a given type is = to the size of the type.
Axiom of selection
is equivalent to the Axiom of Choice
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