Worlds and Propositions Set Free (original) (raw)
Related papers
The Russell-Kaplan paradox and other modal paradoxes: A new solution
Nordic Journal of Philosophical Logic, 1999
The most successful semantics for modal logic in the narrow sense, the logic of possibility, necessity, impossibility and contingency, has been possible worlds semantics. And though various kinds of algebraic semantics (as in Bealer 1982) are emerging as noteworthy rivals to ...
On Propositions as Sets of Possible Worlds
Hoffmann has recently argued that propositions cannot be sets of possible worlds. I show that this is not the case if 'proposition' is understood in the correct way and that Hoffmann's arguments rest on premises that should be rejected.
Impossible Worlds and Propositions - The Philosophical Quarterly
The Philosophical Quarterly, 2010
Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian worlds, and impossibilities are represented as set-theoretic constructions out of them. This hybrid account (1) distinguishes many intuitively distinct impossible propositions; (2) identifies impossible propositions with extensional constructions; (3) avoids resorting to primitive modality, at least so far as Lewisian modal realism does.
This paper will presumably appear in the Routledge Handbook of Propositions, ed. Chris Tillman. It sets out various resolutions of various propositional paradoxes short of the ramified theory of types.
Cantor Paradoxes, Possible Worlds and Set Theory
Mathematics, 2019
In this paper, we illustrate the paradox concerning maximally consistent sets of propositions, which is contrary to set theory. It has been shown that Cantor paradoxes do not offer particular advantages for any modal theories. The paradox is therefore not a specific difficulty for modal concepts, and it also neither grants advantages nor disadvantages for any modal theory. The underlying problem is quite general, and affects anyone who intends to use the notion of "world" in its ontology.
Erkenntnis, 1979
May I always speak of the extension of a conceptspeak of a class? And if not how are the exceptional cases recognized ?
Paradoxical Aspects of the Russellian Conception of Existence
Foundations of Science, 2021
In this paper, the authors try to clarify the relations between Meinong's and Russell's thoughts on the ontological ideas of existence. The Meinongian theory on non-existent objects does not in itself violate the principle of non-contradiction, since the problem that this hypothesis offers to the theory of definite descriptions is not so much a logical problem as an ontological problem. To demonstrate this we will establish what we believe are the two main theses basic to the theory of descriptions: the epistemological thesis and logical thesis.
Analysis, 2012
argues that the definition of possible worlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord's argument depends on the Powerset axiom and that the axiom can be reasonably denied. counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim's argument and to present a sound alternative argument for his conclusion -basically the argument Russell gave to establish a well--known paradox in
Logic of paradoxes in classical set theories
2013
According to Cantor (Mathematische Annalen 21:545-586, 1883; Cantor's letter to Dedekind, 1899) a set is any multitude which can be thought of as one ("jedes Viele, welches sich als Eines denken läßt") without contradiction-a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root-lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do exist. However we do not understand this logical truth so well as we understand, for example, the logical truth ∀x x = x. In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29-53, 1906) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued ∈-language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theorythe cumulative cardinal theory of sets. The theory is based on the idea of cardinality