Hossack, Keith (2014) Sets and plural comprehension. Journal of Philosophical Logic 43 (2-3), pp. 517-539. ISSN 0022-3611.
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 Faculties and Schools > Faculty of Humanities and Social Sciences > School of Historical Studies |
| Depositing User: | Administrator |
| Date Deposited: | 03 Jun 2013 08:00 |
| Last Modified: | 02 Aug 2023 17:05 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/7187 |
Statistics
Additional statistics are available via IRStats2.
Archive Staff Only (login required)
