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.

It is a truth universally acknowledged that a claim of metaphysical modality, in possession of good alethic standing, must be in want of an essentialist foundation. Or at least so say the advocates of the reductive-essence-first view, according to which all modality is to be reductively defined in terms of essence. Here, I contest this bit of current wisdom. In particular, I offer two puzzles—one concerning the essences of non-compossible, complementary entities, and a second involving entities whose essences are modally (...) ‘loaded’—that together strongly call into question the possibility of reducing modality to essence. (shrink)

It is a truth universally acknowledged that a claim of metaphysical modality, in possession of good alethic standing, must be in want of an essentialist foundation. Or at least so say the advocates of thereductive-essence-firstview, according to which all modality is to be reductively defined in terms of essence. Here, I contest this bit of current wisdom. In particular, I offer two puzzles—one concerning the essences of non-compossible, complementary entities, and a second involving entities whose essences are modally ‘loaded’—that together (...) strongly call into question the possibility of reducing modality to essence. (shrink)

The object of this paper is to examine two approaches to giving non-vacuous truth conditions for counterpossibles, counterfactuals with impossible antecedents. I first develop modifications of a Lewis-style sphere semantics with impossible worlds. I argue that this approach sanctions intuitively invalid inferences and is supported by philosophically problematic foundations. I then develop modifications of certain ceteris paribus conditional logics with impossible worlds. Tableaux are given for each of these in an appendix and soundness and completeness results are proved. While certain (...) of the latter systems are shown to have similar problems to logics from the first approach, at least one relatively weak system appears to offer an adequate uniform semantics for counterpossibles and counterfactuals. (shrink)

Classical modalism about essence is the view that essence can be analysed in modal terms. Despite Kit Fine's influential critique, no general refutation of classical modalism has yet been given. In the first part of the paper, I provide such a refutation by showing that the notion of essence cannot be analysed in terms of any sentential operator definable in the language of standard quantified modal logic. As a reaction to Fine's critique, some have defended sophisticated modalism, which attempts to (...) analyse essence in an enriched modal language quantifying over both possible and impossible worlds. In the second part of the paper, I argue that sophisticated modalism falls prey to variations on Fine's counterexamples to classical modalism. I conclude that the most promising approaches to understanding the notion of essence consist in taking essence either as primitive or as analysable via a combination of modal and non-modal notions. (shrink)

An influential theory has it that metaphysical indeterminacy occurs just when reality can be made completely precise in multiple ways. That characterization is formulated by employing the modal apparatus of ersatz possible worlds. As quantum physics taught us, reality cannot be made completely precise. I meet the challenge by providing an alternative theory which preserves the use of ersatz worlds but rejects the precisificational view of metaphysical indeterminacy. The upshot of the proposed theory is that it is metaphysically indeterminate whether (...) p just in case it is neither true nor false that p, and no terms in ‘p’ are semantically defective. In other words, metaphysical indeterminacy arises when the world cannot be adequately described by a complete set of sentences defined in a semantically nondefective language. Moreover, the present theory provides a reductive analysis of metaphysical indeterminacy, unlike its influential predecessor. Finally, I argue that any adequate logic of a language with an indeterminate subject matter is neither compositional nor bivalent. (shrink)

In a recent issue of this journal, Berit Brogaard and Joe Salerno presented a counterfactual theory of essence, designed to get around Kit Fine’s influential objections to the standard modal account of essence. I argue that Brogaard and Salerno’s theory does not avoid Fine’s objections. Then I propose a sequence of variations on their theory, and argue that none of them succeed either.

Jonathan Schaffer argues against a necessary connection between properties and laws. He takes this to be a question of what possible worlds we ought to countenance in our best theories of modality, counterfactuals, etc. In doing so, he unfairly rigs the game in favor of contingentism. I argue that the necessitarian can resist Schaffer’s conclusion while accepting his key premise that our best theories of modality, counterfactuals, etc. require a very wide range of things called ‘possible worlds’. However, the necessitarian (...) can and should insist that, in many cases, these worlds are not metaphysically possible. I will further argue that, having taken such a stance, the necessitarian has additional resources to respond to Schaffer’s other arguments against the view. (shrink)

Nina Emery and Christopher Hill proposed a pragmatic approach toward the debate about counterpossibles—i.e., counterfactuals with impossible antecedents. The core of this approach is to move the burden of the problem from the notion of truth value into the notion of assertion. This is meant to explain our pre-theoretical intuitions about counterpossibles while claiming that each and every counterpossible is vacuously true. The aim of this paper is to indicate a problematic aspect of this view.

The aim of this paper is to argue in favor of the view that some counterpossibles are false. This is done indirectly by showing that accepting the opposite view, i.e., one that ascribes truth to each and every counterpossible, results in the claim that every necessarily false theory has exactly the same consequences. Accordingly, it is shown that taking every counterpossible to be true not only undermines the value of debates over various alternative theories and their consequences, but also puts (...) into question the very possibility of such debates. In order to explicate this thesis, the close bond between counterpossibles and the so-called story prefix is explored. A number of possible responses to this criticism are also presented, and it is argued that none of them address the main problem. (shrink)

According to the most popular theories, counterfactuals with impossible antecedents are vacuously true. Critiques of this view argue that contrary to this, we tend to consider only some of them true and others to be false. In his recent paper Timothy Williamson has ingeniously explained the motivations for the orthodox view and argued that although there are some heuristic reasons that may suggest the plausibility of the unorthodox view, they are fallible. The most important of Williamson’s arguments is that the (...) unorthodox interpretation is inconsistent with the heuristic assumption that supposedly motivates this very view. The aim of this paper is to consider Williamson’s critique and to support the unorthodox approach towards counterpossibles. In order to do so, we argue in favor of the modified version of the heuristic assumption. (shrink)

As I will use the term, an object is a mereological sum of some things just in case those things compose it simply in virtue of existing. In the first half of this paper, I argue that there are no sums. The key premise for this conclusion relies on a constraint on what, in certain cases, it takes for something to ground, or metaphysically explain, something else. In the second half, I argue that in light of my argument against sums, (...) Universalism, which is perhaps the most widely accepted answer to the Special Composition Question, is false. (shrink)

This critical notice provides an overview of Harry Frankfurt’s On Inequality and assesses whether Frankfurt is right to argue that equality is merely formal and empty. I counter-argue that egalitarianism, properly tweaked and circumscribed, can be defended against Frankfurt’s repudiation. After surveying the main arguments in Frankfurt’s book, I argue that whatever plausibility the ‘doctrine of sufficiency’ defended by Frankfurt may have, it does not strike a fatal blow against egalitarianism. There is nothing in egalitarianism that forbids acceptance of the (...) moral platitude expressed in sufficientarianism's positive thesis,. Nor is there anything in egalitarianism as such that makes it impossible to recognize the banal truth that there are many important things besides equality, and that many dimensions of human affairs are improperly appraised from a relational or comparative point of view. The fact that a relational or comparative point o... (shrink)

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 impossible-antecedent 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 ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of (...) conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID or even CN are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. (shrink)

We explore a ‘Neo-Cartesian’ account of divine ultimacy that raises the concept of God to its ultimate level of abstraction so that we can do away with even the question of his existence. Our starting point is God’s relation to the logical and metaphysical order of reality and the views of Descartes and Leibniz on this topic. While Descartes held the seemingly bizarre view that the eternal truths are freely created by God, Leibniz stands for the mainstream view that the (...) eternal truths are grounded in God’s nature. We argue that the implausibility of Descartes’ doctrine stems mainly from the assumption that there is a non-epistemic notion of absolute necessity that constitutes the ultimate court of appeal for all modal questions and that this assumption is questionable. We also question the assumption that God’s ultimacy merely requires that all reality be grounded in God in the sense of mere explanation, so that it suffices if the necessary truths are grounded in God’s nature but not in God’s will. This will lead us to a reassessment of Descartes’ position. In the final and main part of the paper, we push Descartes’ doctrine of the creation of the eternal truths to its ‘logical’ conclusion with the aim of getting to a novel conception of ‘God.’. (shrink)

According to Michael Almeida, reflections on free will and possibility can be used to show that the existence of an Anselmian God is compatible with the existence of evil. These arguments depend on the assumption that an agent can be free with respect to an action only if it is possible that that agent performs that action. Although this principle enjoys some intuitive support, I argue that Anselmianism undermines these intuitions by introducing impossible options. If Anselmianism is true, I argue, (...) then both God and creatures may be free to do the impossible. (shrink)

According to classical theism, the universe depends on God in a way that goes beyond mere (efficient) causation. I have previously argued that this ‘deep dependence’ of the universe on God is best understood as a type of grounding. In a recent paper in this journal, Aaron Segal argues that this doctrine of deep dependence causes problems for creaturely free will: if our choices are grounded in facts about God, and we have no control over these facts, then we do (...) not control our choices and are therefore not free. This amounts to a grounding analogue of the Consequence Argument for the incompatibility of free will and determinism. If successful, it would have application beyond classical theism: similar concerns would apply to any view that takes our choices to be grounded in a deeper reality which is beyond our control. However, I show that the argument is not successful. Segal’s Grounding Consequence Argument is so closely analogous to the Causal Consequence Argument that any response to the one provides a response to the other. As a result, if you don’t think that prior causes (whether deterministic or indeterministic) undermine free will, you shouldn’t think that prior grounds undermine free will. (shrink)

Making sense of our reasoning in disputes about necessary truths requires admitting nonvacuous counterpossibles. One class of these is the counteressentials, which ask us to make contrary to fact suppositions about essences. A popular strategy in accounting for nonvacuous counterpossibles is to extend the standard possible worlds semantics for subjunctive conditionals by the addition of impossible worlds. A conditional A □-> C is then taken to be true if all of the nearest A worlds are C worlds. I argue that (...) a straightforward extension of the standard possible worlds semantics to impossible worlds does not result in a viable account of counteressentials and propose an alternative covering law semantics for counteressentials. (shrink)

Since Kit Fine presented his counter-examples to the standard versions of the modal view, many have been convinced that the standard versions of the modal view are not adequate. However, the scope of Fine's argument has not been fully appreciated. In this paper, I aim to carry Fine’s argument to its logical conclusion and argue that once we embrace the intuition underlying his counter-examples, we have to hold that properties obtained, totally or partially, by application of logical operations are not (...) essential to non-logical entities. I also demonstrate that most of the post-Finean versions of the modal view, which were developed to accommodate Fine’s counter-examples, entail that such properties are essential to the entities, and so fail to capture the notion of essence at issue in Fine's counter-examples. Additionally, I explore the consequence of my argument for Fine’s proposed logic of essence. The logic turns out to be inadequate in its present shape as it represents such properties to be essential to the entities. I conclude by developing a modification to the logic to overcome the shortcoming. (shrink)

According to proponents of the causal exclusion problem, there cannot be a sufficient physical cause and a distinct mental cause of the same piece of behaviour. Increasingly, the causal exclusion problem is circumvented via this compatibilist reasoning: a sufficient physical cause of the behavioural effect necessitates the mental cause of the behavioural effect, so the effect has a sufficient physical cause and a mental cause as well. In this paper, I argue that this compatibilist reply fails to resolve the causal (...) exclusion problem. (shrink)

Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.

In this paper, I discuss how to distinguish between ontological categories and ordinary categories. Using an argument against van Inwagen’s proposed account of what makes a category ontological as a springboard, I argue that if ontological categories are modally robust, then ontological categories need to be understood hyperintensionally. This conclusion opens up a wide range of new ways to define ‘ontological category’, and I close by briefly outlining one such way in order to illustrate the advantages of embracing hyperintensionality in (...) this debate. (Published Open Access). (shrink)

I discuss several problems for Williamson’s counterfactual-theory of modal knowledge and argue that they have a common source, in that the theory neglects to elucidate the proper constraints on modal reasoning. Williamson puts forward an empirical hypothesis that rests on the role of counterfactual reasoning for modal knowledge. But he overlooks central questions of normative modal epistemology. In order for counterfactual reasoning to yield correct beliefs about modality, it needs to be suitably constrained. I argue that what is needed is, (...) specifically, information concerning the nature or essence of things. By integrating this information, essentialist deduction arguably provides a better account of our knowledge of modality. Furthermore, I argue that essences have distinctive causal and explanatory powers—indeed, essences are superexplanatory for how things are. Compared to Williamson’s counterfactual-theory, superexplanatory essentialism clarifies what the proper constraints on modal reasoning are, and why they have such a special status. (shrink)

Counterpossibles are counterfactuals that involve some metaphysical impossibility. Modal normativism is a non-descriptivist account of metaphysical necessity and possibility according to which modal claims, e.g. ‘necessarily, all bachelors are unmarried’, do not function as descriptive claims about the modal nature of reality but function as normative illustrations of constitutive rules and permissions that govern the use of ordinary non-modal vocabulary, e.g. ‘bachelor’. In this paper, I assume modal normativism and develop a novel account of counterpossibles and claims about metaphysical similarity (...) between possible and impossible worlds. I argue that considerations of metaphysical similarity between various impossible worlds and the actual world only require us to tacitly consider how the actual constitutive rules that govern the use of our terms change in order to accommodate the description of some hypothetical impossible scenario. I then argue for my account by raising worries for alternative epistemic and realist accounts of counterpossibles and showing how my account avoids those worries. (shrink)

Since K. Fine’s influential criticism of modalism, many philosophers have agreed that we cannot understand the concept of essence with that of modality. However, some philosophers have resisted this mainstream position. In this paper, I examine N. Wildman’s claim that, unlike other versions of modalism, his version of modalism, namely Sparse Modalism can save modalism. I will argue first that if we introduce the notion of grounding into this debates, Wildman’s criticisms of other versions are significantly undermined. Next, I will (...) argue that since Sparse Modalism has an implicit commitment to grounding Wildman cannot blame revising other versions modalism with the concept of grounding. From these claims, I will conclude that the prospect of the success of modalism in general is at best dubious. Without the concept of grounding no version of modalism can succeed and with the concept of grounding no version is well motivated. (shrink)

In a recent paper, Pruss proves the validity of the rule beta-2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can (...) be formulated. This new transfer rule is immune to the counter-examples involving the actuality operator and rigidified descriptions. However, we show that counter-examples to this new rule can also be generated, demanding that the Lewisian semantics be generalized for higher dimensions where counter-examples can always be generated. (shrink)

If ontic dependence is the basis of explanation, there cannot be mathematical explanations. Accounting for the explanatory dependency between mathematical properties and empirical phenomena poses i...

This paper deals with generalisations of modally based criteria for determining whether a given property is essential to an individual to the case of generic essences. These criteria usually presuppose extensionally individuated properties. The limitations of their generalisations are demonstrated using the case of the necessarily empty individual property and the necessarily empty individual office. I do not present a novel stance on the discussion of individual essences. The novelty of this paper lies in its claim that none of these (...) criteria can be generalised to generic essences. (shrink)

This paper deals with generalisations of modally based criteria for determining whether a given property is essential to an individual to the case of generic essences. These criteria usually presuppose extensionally individuated properties. The limitations of their generalisations are demonstrated using the case of the necessarily empty individual property and the necessarily empty individual office. I do not present a novel stance on the discussion of individual essences. The novelty of this paper lies in its claim that none of these (...) criteria can be generalised to generic essences. (shrink)

Dispositions (powers, potentialities) have become popular in metaphysics in recent years, and some of their proponents are advertising them as the best metaphysical grounds for modality. This project has a logical as well as an ontological side: dispositionalists offer modal and counterfactual semantics that make no use of possible worlds. I argue that, as a result of their counterfactual semantics, dispositionalists are in fact committed to entities that play the same theoretical role as possible worlds. Roughly, the claim is that (...) certain counterfactuals (ones that concern 'very large' states) force the dispositionalist to posit world-sized states that play the theoretical role of worlds. As a result, dispositionalists can (and perhaps should) make use of the mainstream framework (Kripke frames and the Lewis–Stalnaker counterfactual semantics) even if they ground all modal facts in dispositions. (shrink)

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 (...) with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...) interpretation of the logical connectives. I argue this semantics compares favorably to the more common impossible worlds semantics, which faces difficulties interpreting propositionally quantified logic talk. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, 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 (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...) can be extended to counterpossibles more generally. (shrink)

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal properties in (...) terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)

Amie Thomasson has argued against descriptivism about modality, which starts from the idea that modal statements serve to track features of the world and that these features explain the truth-values of modal claims. Thomasson objects that descriptivists cannot satisfactorily explain how modal features fit into the naturalistic picture of the world and that they cannot account for our apparent capacity to acquire modal knowledge. On Thomasson’s alternative to descriptivism (called ‘normativism’), the function of modal claims is to facilitate communication about (...) certain semantic rules. I argue that it is not obvious that the semantic rules that Thomasson takes to be expressed by modal truths really exist. Moreover, I defend a specific version of descriptivism – essentialism – against Thomasson’s objections. Essential truths play a central role in the best explanations of many facts about the world. That includes the explanations delivered by our best scientific theories once these theories are correctly interpreted philosophically. In this way, essences earn their keep in a naturalistic view of the world. Furthermore, the abductive methods by which we confirm our explanatory theories also support certain theses about essences. This allows essentialists to explain knowledge of essences and modal knowledge. (shrink)

Substantive counterlegal discourse poses a problem for those according to whom the laws of nature are metaphysically necessary. I discern two types of necessitarianism about laws: dispositional essentialism and modal necessitarianism. I argue that Toby Handfield’s response to the problem of counterlegals cannot help the modal necessitarian, according to whom all possible worlds are identical with respect to the laws. I thus propose a fictionalist treatment of counterlegals. Fictions are not limited by metaphysical possibility; hence, fictionalism affords the modal necessitarian (...) the means to account for the apparent substance of counterlegals even granting the metaphysical necessity of the laws. (shrink)

Wright (In Gendler and Hawthorne (Eds.), Conceivability and possibility, 2002) rejects some dominant responses to Kripke’s modal argument against the mind-body identity theory, and instead he proposes a new response that draws on a certain understanding of counterpossibles. This paper offers some defensive remarks on behalf of Lewis’ objection to that argument, and it argues that Wright’s proposal fails to fully accommodate the conceivability intuitions, and that it is dialectically ineffective.

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well (...) as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources. (shrink)

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 (...) essences; and that we can gain knowledge of them. We can know about which properties are, and which properties are not, essential to a given entity. This knowledge of essence offers a route to knowledge of the ways those entities must be or could be. (shrink)

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 (...) essences; and that we can gain knowledge of them. We can know about which properties are, and which properties are not, essential to a given entity. This knowledge of essence offers a route to knowledge of the ways those entities must be or could be. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne, who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening, which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close (...) by discussing the dispensability of counterfactual conditionals within the language of mathematics. (shrink)

Since our capacities and methods of cognizing reality merely seem to tell us how things are but only within close limits how they could or must be, our claims to knowledge of mere possibilities and necessities raise the suspicion of exceptionalism: the capacities and methods used in developing these claims seem special compared to those involved in cognizing reality. One may be sceptical especially with regard to them, and there are doubts that they can be naturalistically explained. To avoid exceptionalism, (...) Timothy Williamson has proposed to reduce the epistemology of modality to the epistemology of everyday counterfactuals. There are doubts that the proposal succeeds. One objection is that the counterfactual-based epistemology fails to account for metaphysical necessities like the necessity of origin. For the account to cover such necessities, constitutive facts like the origin of a living being would have to form implicit constraints built into the capacity for everyday counterfactual reasoning. But is counterfactual reasoning indeed so constrained? I answer this question in the affirmative, presenting an epistemology of counterfactuals for modal epistemology to build on. The constraints gradually emerge by a broadly abductive process, starting from within everyday counterfactual reasoning. The process does not presuppose any independent knowledge of the constitutive status of certain facts. (shrink)

It has been suggested that intuitions supporting the nonvacuity of counterpossibles can be explained by distinguishing an epistemic and a metaphysical reading of counterfactuals. Such an explanation must answer why we tend to neglect the distinction of the two readings. By way of an answer, I offer a generalized pattern for explaining nonvacuity intuitions by a stand-and-fall relationship to certain indicative conditionals. Then, I present reasons for doubting the proposal: nonvacuists can use the epistemic reading to turn the table against (...) vacuists, telling apart significant from spurious intuitions. Moreover, our intuitions tend to survive even if we clear-headedly intend a metaphysical reading. -/- . (shrink)

While recent history has seen significant debate concerning the nature and extension of essence, comparatively little attention has been paid to the epistemology of essence. This is strange, as, plausibly, what answers we give to the metaphysical questions about essence will (or should) be partially constrained by our essence epistemology. Here, I aim to go some way towards filling this lacuna. In particular, I here argue that there is no plausible epistemic story available for non-modal accounts of essence. In particular, (...) existing accounts of essence epistemology cannot explain how we are able to know that something is genuinely essential, rather than merely necessary. One consequence is that modal accounts of essence – which only needs to supply an epistemology for a non-hyperintensional notion – look that much more plausible. (shrink)

The distinction between essential versus accidental properties has been characterized in various ways, but it is currently most commonly understood in modal terms: an essential property of an object is a property that it must have, while an accidental property of an object is one that it happens to have but that it could lack. Let’s call this the basic modal characterization, where a modal characterization of a notion is one that explains the notion in terms of necessity/possibility. In the (...) characterization just given of the distinction between essential and accidental properties, the use of the word “must” reflects the fact that necessity is invoked, while the use of the word “could” reflects that possibility is invoked. The notions of necessity and possibility are interdefinable: to say that something is necessary is to say that its negation is not possible; to say that something is possible is to say that its negation is not necessary; to say that an object must have a certain property is to say that it could not lack it; and to say that an object could have a certain property is to say that it is not the case that it must lack it. (shrink)