Citations of:
Wide Sets, ZFCU, and the Iterative Conception
Journal of Philosophy 111 (2):5783 (2014)
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The following barebones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in wellordered levels, and suffices for quasicategoricity. I show this by presenting Level Theory, a simplification of set theories (...) 

A new puzzle of modal recombination is presented which relies purely on resources of firstorder modal logic. It shows that naive recombinatorial reasoning, which has previously been shown to be inconsistent with various assumptions concerning propositions, sets and classes, leads to inconsistency by itself. The context sensitivity of modal expressions is suggested as the source of the puzzle, and it is argued that it gives us reason to reconsider the assumption that the notion of metaphysical necessity is in good standing. 

Philosophers often explain what could be the case in terms of what is, in fact, the case at one possible world or another. They may differ in what they take possible worlds to be or in their gloss of what is for something to be the case at a possible world. Still, they stand united by the threat of paradox. A family of paradoxes akin to the settheoretic antinomies seem to allow one to derive a contradiction from apparently plausible principles. (...) 

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents. 

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. / It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) 

In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification (...) 

The authors provide an objecttheoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent objecttheoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an (...) 

We study reflection principles in KelleyMorse set theory with urelements (KMU). We first show that FirstOrder Reflection Principle is not provable in KMU with Global Choice. We then show that KMU + Limitation of Size + SecondOrder Reflection Principle is mutually interpretable with KM + SecondOrder Reflection Principle. Furthermore, these two theories are also shown to be biinterpretable with parameters. Finally, assuming the existence of a κ+supercompact cardinal κ in KMU, we construct a model of KMU + SecondOrder Reflection Principle (...) 

Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some of the (...) 

This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle (...) 