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  1. A Renaissance of Empiricism in the Recent Philosophy of Mathematics.Imre Lakatos - 1976 - British Journal for the Philosophy of Science 27 (3):201-223.
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  • Conceptions and Paradoxes of Sets.G. Aldo Antonelli - 1999 - Philosophia Mathematica 7 (2):136-163.
    This paper is concerned with the way different axiom systems for set theory can be justified by appeal to such intuitions as limitation of size, predicativity, stratification, etc. While none of the different conceptions historically resulting from the impetus to provide a solution to the paradoxes turns out to rest on an intuition providing an unshakeable foundation,'each supplies a picture of the set-theoretic universe that is both useful and internally well motivated. The same is true of more recently proposed axiom (...)
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  • Conceptual Realism Versus Quine on Classes and Higher-Order Logic.Nino B. Cocchiarella - 1992 - Synthese 90 (3):379 - 436.
    The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...)
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  • Inception of Quine's Ontology.Lieven Decock - 2004 - History and Philosophy of Logic 25 (2):111-129.
    This paper traces the development of Quine's ontological ideas throughout his early logical work in the period before 1948. It shows that his ontological criterion critically depends on this work in logic. The use of quantifiers as logical primitives and the introduction of general variables in 1936, the search for adequate comprehension axioms, and problems with proper classes, all forced Quine to consider ontological questions. I also show that Quine's rejection of intensional entities goes back to his generalisation of Principia (...)
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  • NF at (Nearly) 75.Thomas Forster - 2010 - Logique Et Analyse 53 (212):483.
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  • Systems of Combinatory Logic Related to Predicative and ‘Mildly Impredicative’ Fragments of Quine's ‘New Foundations’.M. Randall Holmes - 1993 - Annals of Pure and Applied Logic 59 (1):45-53.
    This paper extends the results of an earlier paper by the author . New subsystems of the combinatory logic TRC shown in that paper to be equivalent to NF are introduced; these systems are analogous to subsystems of NF with predicativity restrictions on set comprehension introduced and shown to be consistent by Crabbé. For one of these systems, an exact equivalence in consistency strength and expressive power with the analogous subsystem of NF is established.
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  • Automorphisms of Models of Set Theory and Extensions of NFU.Zachiri McKenzie - 2015 - Annals of Pure and Applied Logic 166 (5):601-638.
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