David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 11 (1):59-65 (1990)
Unrestricted use of the axiom schema of comprehension, ?to every mathematically (or set-theoretically) describable property there corresponds the set of all mathematical (or set-theoretical) objects having that property?, leads to contradiction. In set theories of the Zermelo?Fraenkel?Skolem (ZFS) style suitable instances of the comprehension schema are chosen ad hoc as axioms, e.g.axioms which guarantee the existence of unions, intersections, pairs, subsets, empty set, power sets and replacement sets. It is demonstrated that a uniform syntactic description may be given of acceptable instances of the comprehension schema, which include all of the axioms mentioned, and which in their turn are theorems of the usual versions of ZFS set theory. Well then, shall we proceed as usual and begin by assuming the existence of a single essential nature or Form for every set of things which we call by the same name? Do you understand? (Plato, Republic X.596a6; cf. Cornford 1966, 317)
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
References found in this work BETA
Joseph W. Dauben (1988). Cantorian Set Theory and Limitations of Size. British Journal for the Philosophy of Science 39 (4):541-550.
John Mayberry & Michael Hallett (1986). Cantorian Set Theory and Limitation of Size. Philosophical Quarterly 36 (144):429.
Willard V. Quine (1963). Set Theory and its Logic. Harvard University Press.
Citations of this work BETA
No citations found.
Similar books and articles
Richard Pettigrew (2009). On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame Journal of Formal Logic 50 (2):141-152.
Peter Aczel, Laura Crosilla, Hajime Ishihara, Erik Palmgren & Peter Schuster (2006). Binary Refinement Implies Discrete Exponentiation. Studia Logica 84 (3):361 - 368.
Andreas Blass (1981). The Model of Set Theory Generated by Countably Many Generic Reals. Journal of Symbolic Logic 46 (4):732-752.
Gregory H. Moore (1978). The Origins of Zermelo's Axiomatization of Set Theory. Journal of Philosophical Logic 7 (1):307 - 329.
Paul C. Gilmore (1986). Natural Deduction Based Set Theories: A New Resolution of the Old Paradoxes. Journal of Symbolic Logic 51 (2):393-411.
Michael Rathjen (2005). The Disjunction and Related Properties for Constructive Zermelo-Fraenkel Set Theory. Journal of Symbolic Logic 70 (4):1233 - 1254.
Masaru Shirahata (1996). A Linear Conservative Extension of Zermelo-Fraenkel Set Theory. Studia Logica 56 (3):361 - 392.
Andrzej Kisielewicz (1998). A Very Strong Set Theory? Studia Logica 61 (2):171-178.
Added to index2010-08-10
Total downloads6 ( #162,892 of 1,089,047 )
Recent downloads (6 months)1 ( #69,722 of 1,089,047 )
How can I increase my downloads?