Two Kinds of Logical Impossibility

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic

Logicism, Possibilism, and the Logic of Kantian Actualism

In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stang’s account of Kant’s doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stang’s interpretation of Kant’s view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: ‘could there be non-actual possibilia?’ (p.35). Kant’s view, according to Stang, is that there could not, and that the very notion of non-actual or ‘mere’ possibilia is incoherent. In §5 I take a close look at Stang’s master argument that Kant’s Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stang’s reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia

Automated Reasoning over Deontic Action Logics with Finite Vocabularies

In this paper we investigate further the tableaux system for a deontic action logic we presented in previous work. This tableaux system uses atoms (of a given boolean algebra of action terms) as labels of formulae, this allows us to embrace parallel execution of actions and action complement, two action operators that may present difficulties in their treatment. One of the restrictions of this logic is that it uses vocabularies with a finite number of actions. In this article we prove that this restriction does not affect the coherence of the deduction system; in other words, we prove that the system is complete with respect to language extension. We also study the computational complexity of this extended deductive framework and we prove that the complexity of this system is in PSPACE, which is an improvement with respect to related systems.Comment: In Proceedings LAFM 2013, arXiv:1401.056

The Ontological Ground of the Alethic Modality

This paper is concerned with the wholly metaphysical question of whether necessity and possibility rest on nonmodal foundations—whether the truth conditions for modal statements are, in the final analysis, nonmodal. It is argued that Lewis’s modal realism is either arbitrary and stipulative or else it is circular. Even if there were Lewisean possible worlds, they could not provide the grounds for modality. D. M. Armstrong’s combinatorial approach to possibility suffers from similar defects. Since more traditional reductions to cognitive or linguistic facts suffer similar fates, the conclusion that the alethic modality is primitive and incapable of reduction is offered

Impossibility and Impossible Worlds

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible worlds face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face

Essentialism and Absolute Necessity

Bob Hale has argued that logical necessity is absolute necessity. Furthermore, he presents a challenge to the essentialist who tries to evade the consequences of his argument. Here I examine the direct argument he presents for his thesis. I argue that it presents no problem for the essentialist because (1) it begs the question and (2) it relies upon premises that are not entailed by essentialism. I then proceed to show how the essentialist can meet Hale’s challenge

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

Necessity, a Leibnizian Thesis, and a Dialogical Semantics

In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed