Citations of:
Williamson on Counterpossibles
Journal of Philosophical Logic 47 (4):693713 (2018)
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The moving spotlight account (MS) is a view that combines an eternalist ontology and an Atheoretic metaphysics. The intuition underlying MS is that the present time is somehow privileged and experientially vivid, as if it were illuminated by a moving spotlight. According to MStheorists, a key reason to prefer MS to Btheoretic eternalism is that our experience of time supports it. We argue that this is false. To this end, we formulate a new family of positions in the philosophy of (...) 

The epistemology of modality has focused on metaphysical modality and, more recently, counterfactual conditionals. Knowledge of kinds of modality that are not metaphysical has so far gone largely unexplored. Yet other theoretically interesting kinds of modality, such as nomic, practical, and ‘easy’ possibility, are no less puzzling epistemologically. Could Clinton easily have won the 2016 presidential election—was it an easy possibility? Given that she didn’t in fact win the election, how, if at all, can we know whether she easily could (...) 

Proves Completeness for the Evidential Conditional. 

The aim of my paper is to compare three alternative formal reconstructions of van Inwagen’s famous argument for incompatibilism. In the first part of my paper, I examine van Inwagen’s own reconstruction within a propositional modal logic. I point out that, due to the expressive limitations of his propositional modal logic, van Inwagen is unable to argue directly (that is, within his formal framework) for incompatibilism. In the second part of my paper, I suggest to reconstruct van Inwagen’s argument within (...) 

Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossibleantecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘modelimplied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of (...) 

I compare two prominent approaches to knowledge of metaphysical modality, the more traditional approach via conceiving viz. imagining a scenario and a more recent approach via counterfactual reasoning. In particular, Timothy Williamson has claimed that the proper context for a modal exercise of imagination is a counterfactual supposition. I critically assess this claim, arguing that a purely conceivability/imaginabilitybased approach has a key advantage compared to a counterfactualbased one. It can take on board Williamson’s insights about the structure of modal imagination (...) 

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intramathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intramathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines. 

A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and (...) 

Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the nonexplanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...) 

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern noncontingent matters. I try to show that their arguments (...) 

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role. 

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem nontrivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) 

I know that I could have been where you are right now and that you could have been where I am right now, but that neither of us could have been turnips or natural numbers. This knowledge of metaphysical modality stands in need of explanation. I will offer an account based on our knowledge of the natures, or essencess, of things. I will argue that essences need not be viewed as metaphysically bizarre entities; that we can conceptualise and refer to (...) 

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals (...) 

