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Williamson on Counterpossibles
Journal of Philosophical Logic 47 (4):693713 (2018)
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Several themes of David Lewis's theory of counterfactuals, especially their sensitivity to context, pave the way for a viable theory of nontrivial counterpossibles. If Lewis was successful in defending his account against the early objections, a semantics of counterpossibles can be defended from similar objections in the same way. The resulting theory will be extended to address 'might' counterfactuals and questions about the relative "nearness" of impossible worlds. 

Timothy Williamson devotes significant effort in his "The Philosophy of Philosophy" to arguing against skepticism about judgment. One might think that the recent "experimental philosophy" challenge to the philosophical practice of appealing to intuitions as evidence is a possible target of those arguments. However, this is not so. The structure of that challenge is radically dissimilar from that of traditional skeptical arguments, and the aims of the challenge are entirely congruent with the spirit of methodological improvement that Williamson himself exemplifies (...) 

Some of the most eminent and enduring philosophical questions concern matters of priority: what is prior to what? What 'grounds' what? Is, for instance, matter prior to mind? Recently, a vivid debate has arisen about how such questions have to be understood. Can the relevant notion or notions of priority be spelled out? And how do they relate to other metaphysical notions, such as modality, truthmaking or essence? This volume of new essays, by leading figures in contemporary metaphysics, is the (...) 

The second volume in the _Blackwell Brown Lectures in Philosophy_, this volume offers an original and provocative take on the nature and methodology of philosophy. Based on public lectures at Brown University, given by the preeminent philosopher, Timothy Williamson Rejects the ideology of the 'linguistic turn', the most distinctive trend of 20th century philosophy Explains the method of philosophy as a development from nonphilosophical ways of thinking Suggests new ways of understanding what contemporary and past philosophers are doing. 



It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. / An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) 

Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation. 

Kit Fine (1994. “Essence and Modality”, Philosophical Perspectives 8: 116) argues that the standard modal account of essence as de re modality is ‘fundamentally misguided’ (p. 3). We agree with his critique and suggest an alternative counterfactual analysis of essence. As a corollary, our counterfactual account lends support to nonvacuism the thesis that counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are not always vacuously true. 

A number of philosophers have recently become receptive to the idea that, in addition to scientific or causal explanation, there may be a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some sort of causal mechanism, but through some constitutive form of determination. I myself have long been sympathetic to this idea of constitutive determination or ‘ontological ground’; and it is the aim of the present paper to help put the idea on a firmer (...) 

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality. 





Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossible worlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossible worlds and argues that commitment to them can and should be had without great metaphysical or logical cost. The paper then provides an (...) 



This book contends that insufficient attention has been paid to the syntax of conditionals, as investigated by linguists. 





where F is a contradiction (I use his numbering). Tim says about these equivalences: (1) “modulo the implicit recognition of this equivalence, the epistemology of metaphysically modal thinking is a special case of the epistemology of counterfactual thinking. Whoever has what it takes to understand the counterfactual conditional and the elementary logical auxiliaries ~ and F has what it takes to understand possibility and necessity operators.” (158) (2) The idea that we evaluate metaphysically modal claims “by some quite different means (...) 

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be nontrivially true and nontrivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...) 

Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification (...) 

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (ii) causal (...) 

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and socalled impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) 

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, manyvalued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and (...) 







This paper outlines a nonreductive counterfactual account of grounding along interventionist lines, and uses the account to argue that taking grounding seriously requires ascribing nontrivial truthconditions to a range of counterpossible counterfactuals. This result allows for a diagnosis of a route to scepticism about grounding, as deriving at least in part from scepticism about nontrivial counterpossible truth and falsity. 

In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the RoutleyMeyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a nontrivial treatment. 



This paper discusses two distinct strategies that have been adopted to provide finegrained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on finenessofgrain issues: just how finely should propositions be individuated? Here, I compare the two strategies with an (...) 

In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twentyfirst century is seeing a hypterintensional revolution. Theoretical tools in common use carve more finely (...) 

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) 

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to noncausal cases, involving extramathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extramathematical explanation. We address some objections to our approach. 



The paper provides an explanation of our knowledge of metaphysical modality, or modal knowledge, from our ability to evaluate counterfactual conditionals. The latter ability lends itself to an evolutionary explanation since it enables us to learn from mistakes. Different logical principles linking counterfactuals to metaphysical modality can be employed to extend this explanation to the epistemology of modality. While the epistemological use of some of these principles is either philosophically implausible or empirically inadequate, the equivalence of ‘Necessarily p’ with ‘For (...) 

Counterpossibles are counterfactuals with necessarily false antecedents. The problem of counterpossibles is easiest to state within the "nearest possible world" framework for counterfactuals: on this approach, a counterfactual is true when the consequent is true in the "nearest" possible world where the antecedent is true. Since counterpossibles have necessarily false antecedents, there is no possible world where the antecedent is true. On the approach favored by Lewis, Stalnaker, Williamson, and others, counterpossibles are all trivially true. I introduce several arguments against (...) 



The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be nontrivially true and nontrivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...) 





I. NonTrivial Counterpossibles On Lewis’ account, a subjunctive of the form ‘if it were the case that p, it would be the case that q’ (represented as ‘p → q’) is to be given the following rough metalinguistic truthconditions1. 

Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to nonempty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition. 

￼Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, when one (...) 

A theory of ersatz impossible worlds is developed to deal with the problem of counterpossible conditionals. Using only tools standardly in the toolbox of possible worlds theorists, it is shown that we can construct a model for counterpossibles. This model is a natural extension of Lewis's semantics for counterfactuals, but instead of using classical logic as its base, it uses the logic LP. 

In this paper I will argue that Professor Goodman was correct in thinking that there is a problem concerning counterfactual conditionals, but that it is somewhat different from the problem he thought it to be, and is one that is even more basic. I will also try to show that this problem is distinct from Hume's "problem" of induction, and that additional assumptions have to be made for counterfactual induction beyond those required for other kinds of induction. 





In recent work Timothy Williamson argues that the epistemology of metaphysical modality is a special case of the epistemology of counterfactuals. I argue that Williamson has not provided an adequate argument for this controversial claim, and that it is not obvious how what he says should be supplemented in order to derive such an argument. But I suggest that an important moral of his discussion survives this point. The moral is that experience could play an epistemic role which is more (...) 

A significant reorientation is currently under way in analytic metaphysics, away from an almost exclusive focus on questions of existence and towards a greater concentration on questions concerning the dependence of one type of phenomenon on another. Surprisingly, despite the central role dependence has played in philosophy since its inception, interest in a systematic study of this concept has only recently surged among contemporary metaphysicians. In this paper, I focus on a promising account of ontological dependence in terms of a (...) 