Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine's NF

It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of . Everything here holds also for NFU if the permutations are taken to fix all urelemente. NF is Quine's system of set theory, axiomatised by extensionality and those instances of the na

• Type: Journal
• Year: 2006
• Where: JSYML
• Authors: Thomas Forster
• Keywords: JSYML 2006, Label, Ordinal Arithmetic, ZF-style Meanings