David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 55 (1): 79 - 90 (2014)
A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky worlds for certain weak set theories. Second, the paradox of Burali-Forti shows that according to the Zermelo-Fraenkel set theory ZF, junky worlds are possible. Finally, it is shown that set theories are not the only sources for designing plausible models of junky worlds: Topology (and possibly other "algebraic" mathematical theories) may be used to construct models of junky worlds. In sum, junkyness is a relatively widespread feature among possible worlds.
|Keywords||Junky worlds Principle of universal fusion Zermelo natural numbers von Neumann ordinal numbers Burali-Forti paradox Topological junky worlds|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Einar Duenger Bohn (2010). The Necessity of Universalism Versus the Possibility of Junky Worlds: A Rejoinder. Analysis 70 (2):296-298.
Greg Restall (1997). Ways Things Can't Be. Notre Dame Journal of Formal Logic 38 (4):583-596.
Patrick Dehornoy (1996). Another Use of Set Theory. Bulletin of Symbolic Logic 2 (4):379-391.
Colin McLarty (1990). The Uses and Abuses of the History of Topos Theory. British Journal for the Philosophy of Science 41 (3):351-375.
Thomas Mormann (1997). Topological Aspects of Combinatorial Possibility. Logic and Logical Philosophy 5:75 - 92.
J. Robert G. Williams (2007). The Possibility of Onion Worlds: Rebutting an Argument for Structural Universals. Australasian Journal of Philosophy 85 (2):193 – 203.
D. M. Armstrong (1989). A Combinatorial Theory of Possibility. Cambridge University Press.
Theodore Sider (2005). Another Look at Armstrong's Combinatorialism. Noûs 39 (4):679–695.
Phillip Bricker (1983). Worlds and Propositions: The Structure and Ontology of Logical Space. Dissertation, Princeton University
Maxwell J. Cresswell (2006). From Modal Discourse to Possible Worlds. Studia Logica 82 (3):307 - 327.
Achille C. Varzi (1996). Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology. Data and Knowledge Engineering 20:259–286.
Silvio Valentini (2006). Every Countably Presented Formal Topology is Spatial, Classically. Journal of Symbolic Logic 71 (2):491-500.
Nicholas Rescher (1975). A Theory of Possibility: A Constructivistic and Conceptualistic Account of Possible Individuals and Possible Worlds. University of Pittsburgh Press.
Michael Jubien (2009). Possibility. Oxford University Press.
Added to index2012-06-05
Total downloads158 ( #5,553 of 1,139,988 )
Recent downloads (6 months)22 ( #8,738 of 1,139,988 )
How can I increase my downloads?