In between impossible worlds

The traditional Lewis-Stalnaker semantics of counterfactuals suffers from the problem of counterpossibles: Many counterpossibles seem non-trivially true or false, but the Lewis-Stalnaker semantics deems all counterpossibles trivially true. Many proposed solutions to this problem center around the use of impossible worlds, where necessary falsehoods can be true. Ersatzists have commonly identified impossible worlds with maximal, inconsistent sets of sentences. However, Jens Christian Bjerring (2013) has recently argued that the extended Lewis-Stalnaker semantics delivers the wrong truth values for some counterpossibles if all impossible worlds are maximal. To remedy this defect, Bjerring considers two alternative world ontologies: one in which impossible worlds correspond to arbitrary (maximal or non-maximal) inconsistent sets of sentences, and another in which impossible worlds correspond to (maximal or non-maximal) sets of sentences that are deductively closed in some non-classical logic. Bjerring raises a worry about the former alternative and therefore prefers the latter. In this paper, I argue that Bjerring’s worry about the former alternative is based on a conflation of two distinct conceptions of what it means for a logic to be true in a world. I also argue that the latter alternative does not allow for impossible worlds to be sufficiently logically ill-behaved. I conclude that this tips the balance in favour of the former world ontology.

Analysis, 1984

Noûs

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.

Worlds, Possible and Impossible (Elsevier), 2024

Introduction 1 Modality 1 Applications of Possible Worlds 2 What are Possible Worlds? 2 Impossible Worlds 3 Conclusion 4 References 4 Key Points • actuality • possibility • analysis of nonemodal claims • analysis of modal claims • impossibility

Review of Analytic Philosophy, 2021

As philosophers have discovered theoretical limits of intensional frameworks for analyzing philosophical phenomena, which have been partly but intimately developed along with the theories about possible worlds, the attention directed to impossible worlds as further theoretical resources has been increasing. This fact naturally provokes the ontological question: what is the nature of impossible worlds? Given the growing importance of the ontology of impossible worlds, I aim to defend the fictionalism about impossible worlds in this paper. First, I divide the positions in the ontology of impossible worlds into six kinds based on whether possible and impossible worlds are concrete, abstract, or fictional. Second, I examine each position and show that the most promising view is that impossible worlds are fictional while possible worlds are either concrete or abstract. Finally, I consider and try to accommodate possible concerns with the fictionalism about impossible worlds.

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where "anything goes'' in modal space, it is easy to model extremely non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that "anything goes''. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents.

2008

I. Formal Theory of the Subject \ II. Great Logic 1: The Transcendental \ III. Great Logic 2: The Object \ IV. Great Logic 3: The Relation \ V. The Four Forms of Change \ VI. Theories of Points \ VII. What is a Body? \ Conclusion \ Appendices \ Bibliography

2010

Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories.

Dialetheism and its Applications, ed. A Reiger and G Young, Springer (Trends in logic), 2020

David Lewis famously dismisses genuine impossible worlds on the basis that a contradiction bound within the scope of his modifier ‘at w’ amounts to a contradiction tout court – an unacceptable consequence. Motivated by the rising demand for impossible worlds in philosophical theorising, this paper examines whether anything coherent can be said about an extension of Lewis’ theory of genuine, concrete possible worlds into genuine, concrete impossible worlds. Lewis’ reasoning reveals two ways to carve out conceptual space for the genuinely impossible. The first is to abandon Lewis’ classical translation schema for negation, on the basis that it begs the question against incomplete and inconsistent worlds. I argue that, whilst this option incurs some loss in the semantics, it preserves the core spirit of Lewis’ metaphysics. The alternative is to bite the bullet, abandon classical logic and embrace true contradictions. The key challenge with this strategy is that the resulting theory seems committed to a particularly strong kind of dialetheism — one that even dialetheists would be reluctant to accept. I motivate such a dialethic account of genuine impossibilia using Lewis’ own methodology and defend it against triviality objections. I close with a few comments on why impossible worlds should not be reduced to set theoretic constructs out of possible worlds.

Philosophy Compass, 2009

dialectica, 2019

Several theorists have been attracted to the idea that in order to account for counterpossibles, i.e. counterfactuals with impossible antecedents, we must appeal to impossible worlds. However, few have attempted to provide a detailed impossible worlds account of counterpossibles. Berit Brogaard and Joe Salerno's 'Remarks on Counterpossibles' is one of the few attempts to fill in this theoretical gap. In this article, I critically examine their account. I prove a number of unanticipated implications of their account that end up implying a counterintuitive result. I then examine a suggested revision and point out a surprising implication of the revision.

2001

RESUMEN El siguiente articulo es, en parte, una respuesta a la propuesta de Steffen Borges publicada en teorema, Vol. XIX/1 (2000), con el título "A Call for a Possible World Argument in Ethics". Quisiera sugerir aquí que la relación entre mundos posibles y deliberación ética no es, de por sí, diferenciada y auxiliar. Al contrario, propongo que la contemplación de mundos posibles es una parte esencial de la teorización ética. El carácter inmediato de la ética en relación con lo posible se evidencia a través del modelo de deliberación moral propuesto por una cierta idea de particularismo moral y, más específicamente, en el trabajo de John McDowell, quien demuestra los aspectos inextricablemente modales de la ética en este respecto.

2019

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play.

The Journal of Philosophy, 1988

An Empire of Thin Air (1988) David Lewis's book, On the Plurality of Worlds, is derived from his 1984 John Locke Lectures, and is the latest word on possible worlds from the discipline's foremost champion of possibilia. It is a serious defense, a priori, of Lewis's notorious doctrines (here called 'modal realism') to the effect that there are tiny purple anthropologists who study human culture unobserved, colossal human-eating monsters 50 feet in height, professional philosophers earning annual salaries in excess of 37 million dollars (pre-inflation), and the like, and that these oddities reside in fabulous alternative universes that are never empirically detected by us (but that are empirically detectable by us). The central idea of Lewis's theory is that whatever might have transpired involving individuals of our universe does indeed transpire in one of these alternative universes, involving counterparts of these individuals (p. 2)-'the principle of plenitude.' Equally critical to Lewis's project is the converse principle that everything that transpires in one of these alternative universes involving our counterparts is something that might have transpired involving ourselves. We may call this 'the principle of moderation.' 1 Together these two principles assert an isomorphism between total ways things might have been with regard to this universe and extant alternative universes, prompting Lewis to identify the former with the latter (p. 86). Lewis thus misleadingly calls his alleged alternative universes 'possible worlds,' and indeed they play a role in Lewis's theory of modal discourse similar in many respects to that of the intensional possible worlds invoked in contemporary philosophical semantics, as conceived of by such writers as Saul Kripke and Robert Stalnaker, that is, maximally specific states or histories. 2 These genuine possible worlds Lewis misleadingly labels 'ersatz worlds.' Like genuine possible worlds, Lewis's alternative universes allegedly 'represent' possible events and states of affairs that might have occurred concerning the individuals of our universe; they are supposed to be entities according to which 1 These principles are not explicitly articulated as I have them. My statement of plenitude is based on a plausible interpretation of Lewis's less explicit formulation. Lewis provides a version of moderation which is closely related to, but much weaker than, the principle formulated here, and which he derives from the trivial modal logical truth that whatever is the case might have been the case (p. 5). This weaker principle, however, is insufficient for Lewis's purposes.

The Philosophy of Penelope Maddy, 2022

The paper compares two theories of the nature of logic: Penelope Maddy's and my own. The two theories share a significant element: they both view logic as grounded not just in the mind (language, concepts, conventions, etc.), but also, and crucially, in the world. But the two theories differ in significant ways as well. Most distinctly, one is an anti-holist, "austere naturalist" theory while the other is a non-naturalist "foundational-holistic" theory. This methodological difference affects their questions, goals, orientations, the scope of their investigations, their logical realism (the way they ground logic in the world), their explanation of the modal force of logic, and their approach to the relation between logic and mathematics. The paper is not polemic. One of its goal is a perspicuous description and analysis of the two theories, explaining their differences as well as commonalities. Another goal is showing that and how (i) a grounding of logic is possible, (ii) logical realism can be arrived at from different perspectives and using different methodologies, and (iii) grounding logic in the world is compatible with a central role for the human mind in logic.