Symmetry as a Criterion for Comprehension Motivating Quine’s ‘New Foundations’

  title={Symmetry as a Criterion for Comprehension Motivating Quine’s ‘New Foundations’},
  author={M. Randall Holmes},
  journal={Studia Logica},
  • M. R. Holmes
  • Published 28 February 2008
  • Computer Science
  • Studia Logica
A common objection to Quine’s set theory “New Foundations” is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set (a kind of symmetry) which motivates NF. 
Invariance under permutations as a semantic motivation for Stratification
This article examines the notion of invariance under different kinds of permutations in a milieu of a theory of classes and sets, as a semantic motivation for Quine's new foundations "NF". TheExpand
Symmetry motivates a new consistent fragment of NF and an extension of NF with semantic motivation
A sequence of theories of sets and classes is presented, indexed by a natural number parameter k. The criterion for determining which classes are sets has to do with symmetry. The theories with k 2Expand
Normal subgroups of infinite symmetric groups, with an application to stratified set theory
If X is an infinite set with ∣X∣ = ∢X × X∣ then Symm(X) has no nontrivial normal subgroups of small index, and it is shown that every normal subgroup of Symm (X) (of small index) must contain every flexible permutation. Expand
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We studyExpand


The Axiom of Choice in Quine's New Foundations for Mathematical Logic.
  • E. Specker
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1953
The object of this note is to disprove the axiom of choice in Quine’s “New Foundations” by obtaining theAxiom of infinity as a corollary. Expand
On the Consistency of a Slight (?) Modification of Quine’s New Foundations
Quine’s system of set theory, New Foundations (NF), can be conveniently formalized as a first-order theory containing two predicates ≡ (identity) and e (set membership). One of the most attractiveExpand
The set-theoretical program of Quine succeeded, but nobody noticed
1. Abstract. The set theory "New Foundations" or MF introduced by W.V.O. Quine in 1935 is discussed, along with related systems. It is argued that, in spite of the fact that the consistency of NFExpand
Quine's Individuals
Publisher Summary This chapter focuses on the Quine's individuals. Professor Quine has suggested that in relation to the theories of membership, it can be possible to allow for the existence ofExpand
New Foundations for Mathematical Logic
(1937). New Foundations for Mathematical Logic. The American Mathematical Monthly: Vol. 44, No. 2, pp. 70-80.
A Set of Axioms for Logic
One of the preeminent problems confronting logicians is that of constructing a system of logic which will be adequate for mathematics, and the system of Quine's that this work is concerned is concerned. Expand
A System of Axiomatic Set Theory-Part VI
  • P. Bernays
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1948
This chapter defines a function to be a class of pairs in which different elements always have different first members such that, to every element a of its domain there is a unique element b of its converse domain determined by the condition 〈 a, b 〉 ηF . Expand
A System of Axiomatic Set Theory
The purpose of modifying the von Neumann system is to remain nearer to the structure of the original Zermelo system and at the same time, utilize some of the set-theoretic concepts of the Schroder Logic and of Principia Mathematica that have become familiar to logicians. Expand
Set Theory with a Universal Set
On the Consistency of an Impredicative Subsystem of Quine's NF