Sets and Plural Comprehension

Journal of Philosophical Logic 43 (2-3):517-539 (2014)
  Copy   BIBTEX

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

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 100,809

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

E pluribus unum: Plural logic and set theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
Critical Plural Logic.Salvatore Florio & Øystein Linnebo - 2020 - Philosophia Mathematica 28 (2):172-203.
Composition, identity and plural ontology.Roberto Loss - 2020 - Synthese 198 (10):9193-9210.
Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Consequences of collapse.Theodore Sider - 2014 - In Aaron J. Cotnoir & Donald L. M. Baxter (eds.), Composition as Identity. Oxford: Oxford University Press USA. pp. 211-221.
Much Ado About the Many.Jonathan Mai - 2021 - Principia: An International Journal of Epistemology 25 (1).

Analytics

Added to PP
2013-03-28

Downloads
168 (#139,770)

6 months
12 (#290,681)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Keith Hossack
Birkbeck College

Citations of this work

Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Can All Things Be Counted?Chris Scambler - 2021 - Journal of Philosophical Logic 50 (5):1079-1106.
When Do Some Things Form a Set?Simon Hewitt - 2015 - Philosophia Mathematica 23 (3):311-337.
Composition and Identities.Manuel Lechthaler - 2017 - Dissertation, University of Otago

Add more citations

References found in this work

Principles of mathematics.Bertrand Russell - 1931 - New York,: W.W. Norton & Company.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Introduction to mathematical logic.Elliott Mendelson - 1964 - Princeton, N.J.,: Van Nostrand.
Plural predication.Thomas McKay - 2006 - New York: Oxford University Press.

View all 39 references / Add more references