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  1. Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.
  • Finsler Set Theory: Platonism and Circularity.D. Booth & R. Ziegler (eds.) - 1996 - Basel: Birkhaeuser.
    Paul Finsler (1894-1970) had already secured renown as a differential geometer when he first took up set theory. His work in this field is heir to the spirit of the set theory put forward by Cantor who, as Finsler, was an uncompromising Platonist. Finsler's papers on set theory are presented, here for the first time in English translation, in three parts. Each reflects one of the three central concerns of his investigations, namely the philosophical, the foundational and the combinatorial approach, (...)
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  • How to Be a Minimalist About Sets.Luca Incurvati - 2012 - Philosophical Studies 159 (1):69-87.
    According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...)
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  • The Philosophy of Bertrand Russell.Kurt Gödel - 1944 - Northwestern University Press.
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  • Non-Well-Founded Sets.Peter Aczel - 1988 - Csli Lecture Notes.
  • Philosophical Papers.Frank Plumpton Ramsey - 1925 - Cambridge University Press.
    Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The latter (...)
     
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  • Set Theory and its Philosophy: A Critical Introduction.Michael Potter - 2004 - Oxford University Press.
    Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...)
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  • Logic, Logic, and Logic.George Boolos - 1998 - Harvard University Press.
    This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...
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  • The Liar: An Essay on Truth and Circularity.Jon Barwise & John Etchemendy - 1987 - Oxford University Press USA.
    Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...)
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  • The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - Routledge & Kegan Paul.
  • The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
  • Sts: A Structural Theory Of Sets.A. Baltag - 1999 - Logic Journal of the IGPL 7 (4):481-515.
    We explore a non-classical, universal set theory, based on a purely 'structural' conception of sets. A set is a transfinite process of unfolding of an arbitrary binary structure, with identity of sets given by the observational equivalence between such processes. We formalize these notions using infinitary modal logic, which provides partial descriptions for set structures up to observational equivalence. We describe the comprehension and topological properties of the resulting set-theory, and we use it to give non-classical solutions to classical paradoxes, (...)
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  • Boolos on the Justification of Set Theory.Alexander Paseau - 2007 - Philosophia Mathematica 15 (1):30-53.
    George Boolos has argued that the iterative conception of set justifies most, but not all, the ZFC axioms, and that a second conception of set, the Frege-von Neumann conception (FN), justifies the remaining axioms. This article challenges Boolos's claim that FN does better than the iterative conception at justifying the axioms in question.
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  • Non-Wellfounded Set Theory.Lawrence S. Moss - 2008 - Stanford Encyclopedia of Philosophy.
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  • Logic, Logic and Logic.George Boolos & Richard C. Jeffrey - 1998 - Studia Logica 66 (3):428-432.
     
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  • An Argument for Finsler-Aczel Set Theory.Adam Rieger - 2000 - Mind 109 (434):241-253.
    Recent interest in non-well-founded set theories has been concentrated on Aczel's anti-foundation axiom AFA. I compare this axiom with some others considered by Aczel, and argue that another axiom, FAFA, is superior in that it gives the richest possible universe of sets consistent with respecting the spirit of extensionality. I illustrate how using FAFA instead of AFA might result in an improvement to Barwise and Etchemendy's treatment of the liar paradox.
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  • Non-Well-Founded Trees in Categories.Benno van den Berg & Federico De Marchi - 2007 - Annals of Pure and Applied Logic 146 (1):40-59.
    Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call M-types. We derive existence results for M-types in locally cartesian closed pretoposes with a natural numbers object, using their internal logic. These are then used to prove stability of such categories with M-types under various topos-theoretic constructions; namely, slicing, formation of coalgebras , and sheaves for an (...)
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  • New Foundations for Mathematical Logic.W. V. Quine - 1937 - Journal of Symbolic Logic 2 (2):86-87.
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  • The Liar, An Essay in Truth and Circularity.Jon Barwise & John Etchemendy - 1989 - Revue Philosophique de la France Et de l'Etranger 179 (1):108-108.
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  • Russell's Mathematical Logic.Kurt Gödel - 1944 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Northwestern University Press. pp. 119--141.
  • Hypersets.J. Barwise & L. Moss - 1991 - The Mathematical Intelligencer 13:31-41.
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