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    Sets and plural comprehension

    Hossack, Keith (2014) Sets and plural comprehension. Journal of Philosophical Logic 43 (2-3), pp. 517-539. ISSN 0022-3611.

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    Abstract

    The state of affairs of some things falling under a predicate is supposedly a single entity that collects these things as its constituents. But whether we think of a state of affairs as a fact, a proposition or a possibility, problems will arise if we adopt a plural logic. For plural logic says that any plurality include themselves, so whenever there are some things, the state of affairs of their plural self-inclusion should be a single thing that collects them all. This leads to paradoxes analogous to those that afflict naïve set theory. Here I suggest that they are the very same paradoxes, because sets can be reduced to states of affairs. However, to obtain a consistent theoretical reduction we must restrict the usual axiom scheme of Comprehension for plural logic to ‘stratified’ formulas, to avoid viciously circular definitions. I prove that with this modification to the background plural logic, the theory of states of affairs is consistent; moreover, it yields the axioms of the familiar set theory NFU.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): State of affairs, Set, Plural logic, Comprehension axiom scheme, Paradox, Vicious Circle Principle, NFU
    School: Birkbeck Schools and Departments > School of Social Sciences, History and Philosophy > Philosophy
    Depositing User: Administrator
    Date Deposited: 03 Jun 2013 08:00
    Last Modified: 24 Jun 2014 12:48
    URI: http://eprints.bbk.ac.uk/id/eprint/7187

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