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Remarks on Counterpossibles
Abstract
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 derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds.
... 8 Defenders of counterlogical vacuism include [18,27,38]. 9 Defenders of counterlogical non-vacuism include [8,10,14,15,37,43,53,58,73]. 10 Counterlogical non-vacuists may accept the impossible worlds semantics as it stands. Since truth at impossible worlds is determined solely by the valuation function , and since there are no constraints on how may assign truth values to formulas at impossible worlds, impossible worlds models can contain worlds that are logically impossible. ...
... 9 Defenders of counterlogical non-vacuism include [8,10,14,15,37,43,53,58,73]. 10 Counterlogical non-vacuists may accept the impossible worlds semantics as it stands. Since truth at impossible worlds is determined solely by the valuation function , and since there are no constraints on how may assign truth values to formulas at impossible worlds, impossible worlds models can contain worlds that are logically impossible. ...
... True, in a world governed by intuitionistic logic, people would use the words 'not' and 'or' in such a way so as not to validate the law of excluded middle. That is, the following counterfactual might be false: (10) If intuitionistic logic were the correct logic, then the sentence 'Either the continuum hypothesis is true or it is not true' would be true. ...
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 (developed by Einheuser (Philosophical Studies, 127(3), 459–482 (2006)) and (Kocurek et al. Philosophers’ Imprint, 20(22), 1–27 (2020)) 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.
... Thus, in a sense, there is a natural way of addressing the problem of hyperinstensionality within the framework of PWS. 3 As many have shown, this Extended Possible Worlds Semantics (EPWS) allows one to overcome some of the limitation of the standard approach. That includes investigations concerning causality (Bernstein 2016;Nolan 2017), imagination (Berto 2017), intentionality (Priest 2005(Priest /2016, logical omniscience (Bjerring 2013;Rantala 1982), fiction (Berto and Badura 2019;Sendłak 2021), metaphysical essence (Brogaard and Salerno 2013), and propositional attitudes (Berto and Jago 2019;Jago 2014). Importantly, many of these involve the so-called unorthodox view on counterfactuals. ...
... As opposite to the standard PWS, which has it that all counterpossibles (i.e. counterfactuals with impossible antecedents) are vacuously true (Lewis 1973;Stalnaker 1968Stalnaker /2019Williamson 2018), advocates of unorthodoxy argue in favor of the non-vacuous truth of some counterpossibles (Berto et al. 2018;Brogaard and Salerno 2013;Kocurek 2021;Nolan 1997;Priest 2009;Sendłak 2019;Yagisawa 1988). This is grounded in the general truth-conditions for counterfactuals: ...
The common view has it that there are two families of approaches towards thelogical structure of impossible worlds–Australasian and North American.According to thefirst, impossible worlds are closed under the relation oflogical consequence of one of the non-classical logics. The North Americanapproach is more liberal, allowing for impossible worlds where no logicholds. After pointing out the questionable consequences of each view, Ipropose a third one. While this new perspective allows for worlds where nological consequence holds, it also imposes some constraints on what worldsare built upon. This renders the proposed view not as restrictive as theAustralasian approach and not as liberal as the North American approach.Due to its intermediary nature, I have named this perspective‘the Pacific’approach.
... Both outcomes seem true because reasoners can construct a consistent simulation of either one of them for such unknown-reality content (we do not have sufficient information about the facts to rule out either outcome). A thorny philosophical issue is whether all impossible conditionals should be considered true with both outcomes, i.e., they are logically vacuous (e.g., Williamson, 2018Williamson, , 2020, or whether some are true with only one, and thus are valid in, say, scientific theorizing (e.g., Berto et al., 2018Berto et al., , 2022Brogaard & Salerno, 2013;Wilson, 2018Wilson, , 2021. Psychological evidence about whether people judge some impossible conditionals to be true with both outcomes can contribute to this current philosophical debate. ...
... The content was adapted from philosophical analyses of counterpossible conditionals (e.g., Berto et al., 2018;Williamson, 2018). All the conjectures were intended to refer to metaphysical impossibilities, rather than logical, mathematical, or epistemic ones (Berto et al., 2018(Berto et al., , 2022Brogaard & Salerno, 2013;Williamson, 2018), although whether some are epistemic rather than metaphysical is debatable. The conditionals were in the subjunctive mood, and the present tense. ...
People can think about hypothetical impossibilities and a curious observation is that some impossible conditionals seem true and others do not. Four experiments test the proposal that people think about impossibilities just as they do possibilities, by attempting to construct a consistent simulation of the impossible conjecture with its suggested outcome, informed by their knowledge of the real world. The results show that participants judge some impossible conditionals true with one outcome, for example, “ if people were made of steel, they would not bruise easily ” and false with the opposite outcome, “if people were made of steel they would bruise easily ”, and others false with either outcome, for example, “ if houses were made of spaghetti, their engines would (not) be noisy ”. However, they can sometimes judge impossible conditionals true with either outcome, for example, “ if Plato were identical to Socrates, he would (not) have a small nose ”, or “if sheep and wolves were alike, they would (not) eat grass” . The results were observed for judgments about what could be true (Experiments 1 and 4), judgments of degrees of truth (Experiment 2), and judgments of what is true (Experiment 3). The results rule out the idea that people evaluate the truth of a hypothetical impossibility by relying on cognitive processes that compare the probability of each conditional to its counterpart with the opposite outcome.
... If a counterfactual account is to work, then, it needs to be strengthened. One way of doing so is defended by Berit Brogaard and Joe Salerno (Brogaard and Salerno 2013) in their Counterfactual Account of Essence: ...
... But then CAE is committed to the intuitive falsehood 3 They give two accounts, one that corresponds to the ' ordinary use' of ' essence', which forgoes condition (2) of CAE and is equivalent to AAE, and the other, i.e., CAE, which corresponds to the 'philosophical use' of ' essence'. My interest here is in their philosophical use of ' essence '. 4 According to the Lewis-Stalnaker semantics, a counterfactual conditional 'If A were the case, B would be the case' is true iff in the 'most similar' worlds where A is true, B is also true. 5 See (Brogaard and Salerno 2013) for the details. Their account also depends on a non-standard notion of the a priori according to which neither mathematical nor logical truths are a priori. ...
According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing on lessons from these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus’s defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections.
... Lewis-Stalnaker and also Chellas semantics of conditional logic have it that all counterpossibles are vacuously true (for a discussion on counterpossibles see e.g. [13,50,12,33]). We show that the same holds in LPC + . Lemma 4.5. ...
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For the semantics, we offer relational models that merge the selection-function semantics of conditional logics with the relational semantics of justification logics. As an application, we formalize Nozick's counterfactual conditions in his analysis of knowledge and investigate their connection to Aumann's concepts of knowledge. Additionally, we explore Gettier's counterexamples to the justified true belief analysis, as well as McGinn's counterexamples to Nozick's analysis of knowledge. Furthermore, we introduce a justification logic that includes a relevant counterfactual conditional and we demonstrate the variable-sharing property for this conditional. We also develop a tableau system for this logic and establish its completeness with respect to Routley relational models. Finally, we formalize Nozick's counterfactual conditions using this relevant counterfactual conditional and represent the sheep in the field example of Chisholm within this logic.
... In the context of dispositionalism, this can be justified by assuming that possibilities form a treelike structure, with alternative histories branching off from a common past (cf.Vetter, 2015, 273-277 and Kimpton- Nye, 2021, 354-357). 26 Some philosophers (e.g.Brogaard & Salerno, 2013;Berto & Jago, 2019) deny (I) on the grounds that it renders all counterpossibles (counterfactuals with impossible antecedents) true, even though some of them are (allegedly) false. (For pushback, seeLewis, 1973, 24-26; Williamson, 2010, 81-83; Williamson, 2010, 93-96.) ...
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.
... 360-362). 2 Authors who choose the second horn of the dilemma includeNolan (1997),Kment (2006),Priest (2009), Brogaard & Salerno (2013 andBerto et al. (2018). ...
Counterpossibles are counterfactuals with an impossible antecedent. According to the orthodox view of counterfactuals, all counterpossibles are vacuously true. This is puzzling because some counterpossible statements seem to be false. The paper analyzes two approaches to explaining why certain counterpossibles, though perhaps true, may appear to be false. The first, which appeals to the Gricean mechanism of conversational implicatures, asserts that some counterpossibles appear to be false because their assertion carries with it a false conversational implicature. However, I argue that, under a closer scrutiny, this approach collapses. I therefore turn to a second approach, proposed by Timothy Williamson. It appeals to a heuristic according to which speakers may regard a counterpossible to be false if they have previously accepted its opposite. Since the applicability of Williamson’s solution is limited, I suggest a more general account. Its underlining idea is that a counterpossible is rejected if the speaker cannot find what they regard as a universally true conditional function derivable from the counterpossible by substitutions and syntactic transformations.
... Given the standard Lewis-Stalnaker possible world semantics for counterfactuals, counterpossibles are all vacuously true. Several authors regard this as a problematic result (e.g. , Brogaard & Salerno 2013;Berto et al., 2018), and all the more so because counterpossibles apparently figure so frequently in scientific reasoning, and in particular in model-based reasoning. As a result, the issue of counterpossibles and counterlegals (counterfactuals with antecedents that are impossible given the actual laws of nature) in science has been much discussed in recent years (Dohrn forthcoming;Jenny 2018;McLoone, 2020;Tan 2019;Wilson, 2021). ...
... Definition 2 is standard in the literature. If we interpret 'Necessarily p' as the claim that p is true in every possible world, then 7 Examples of nonvacuists include Zagzebski (1990); Nolan (1997); Brogaard and Salerno (2007); Kment (2014). ...
This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that it is equivalent to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic
... Whether this is the appropriate way to construe impossible worlds when evaluating counterpossibles with mathematically or logically impossible antecedents raises questions about the nature of impossible worlds that are outside the scope of this paper. For discussion and varied proposals concerning the nature of impossible worlds, seeBrogaard and Salerno (2013),Bjerring (2014),Berto and Jago (2018), and Sandgren and Tanaka (2019). We do not take our approach to provide guidance on how to evaluate counterpossibles with mathematically or logically impossible antecedents. ...
A counterpossible is a counterfactual whose antecedent is impossible. The vacuity thesis says all counterpossibles are true solely because their antecedents are impossible. Recently, some have rejected the vacuity thesis by citing purported non-vacuous counterpossibles in science. One limitation of this work, however, is that it is not grounded in experimental data. Do scientists actually reason non-vacuously about counterpossibles? If so, what is their basis for doing so? We presented biologists (N = 86) with two counterfactual formulations of a well-known model in biology, the antecedents of which contain what many philosophers would characterize as a metaphysical impossibility. Participants consistently judged one counterfactual to be true, the other to be false, and they explained that they formed these judgments based on what they perceived to be the mathematical relationship between the antecedent and consequent. Moreover, we found no relationship between participants’ judgments about the (im)possibility of the antecedent and whether they judged a counterfactual to be true or false. These are the first experimental results on counterpossibles in science with which we are familiar. We present a modal semantics that can capture these judgments, and we deal with a host of potential objections that a defender of the vacuity thesis might make.
... 18 It would also not advance evidentialism to adopt a semantics on which Counterpossible comes out non-vacuously true (cf. Brogaard & Salerno, 2013). The problem for the evidentialist has nothing to do with whether she can find a way to make Counterpossible come out (non-vacuously) true. ...
Evidentialism as an account of epistemic justification is the position that a doxastic attitude, D, towards a proposition, p, is justified for an intentional agent, S, at a time, t, iff having D towards p fits S’s evidence at t, where the fittingness of an attitude on one’s evidence is typically analyzed in terms of evidential support for the propositional contents of the attitude. Evidentialism is a popular and well-defended account of justification. In this paper, I raise a problem for evidentialism on the grounds that there can be epistemic circumstances in which a proposition is manifestly and nonmisleadingly supported by an agent’s total evidence, and yet believing the proposition is not justified for the agent. As I argue, in order for an agent to have justification to believe a proposition, it needs to be the case that the belief as possessed by the agent could exhibit certain epistemic good making features, e.g., the propositional content of the belief as possessed by the agent would be supported by the agent’s evidence. As I demonstrate, the fact that a proposition, p, is supported by an agent’s total evidence at a time, t, doesn’t guarantee that a belief in p as possessed by the agent at t could exhibit any epistemic good making features, including having propositional contents (i.e., p) that would be supported by the agent’s evidence. Thus, the fact that a proposition is supported by an agent’s evidence doesn’t guarantee that the agent has justification to believe the proposition.
... The unorthodox (UNORT) opposition argues in favor of a modified account, according to which some counterpossibles are true and others are false (e.g., Brogaard & Salerno, 2013;Nolan, 1997;Priest, 2009;Yagisawa, 1988). This is meant to be partly motivated by the observation that in some contexts the modal status of the antecedents does not have to play a role when it comes to evaluating counterfactuals. ...
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 (i.e., the sentential operator 'According to fiction F, P') 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.
... An example may be counterpossibles tracking hyperintensional metaphysical relationships (cf. Nolan 1997;Dorr 2008;Brogaard and Salerno 2013;Kment 2014;Bernstein 2016;Wilson 2018). Metaphysical explanations are among the main contexts in which counterpossibles seem useful to nonvacuists. ...
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.
... The standard closeness-based account provided by Lewis trivialises for mathematical counterfactuals [Lewis, 1973;Stalnaker, 1968]. Accordingly, we will adopt an extension of that account that avoids triviality [Beall et al, 2012;Bernstein, 2016;Brogaard and Salerno, 2013;Jago, 2013;Vander Laan, 1997;2004;Lycan, 2001;Mares, 1997;Mares and Fuhrmann, 1995;Nolan, 2001;Priest, 2 See [Reutlinger et al., MS] for a pilot corpus analysis, which turned up a number of examples of counterfactuals and counterpossibles, many of these in the context of explaining the mathematical results in question and many instances from distinguished mathematicians (e.g., Terrence Tao [2016, p. 311]). ...
Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical 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.
Can natural language represent logically impossible circumstances? Can there be logically impossible contents? The received view on semantic content allows for logically impossible contents. Much recent work in the philosophy of language and logic meant to account for hyperintensional phenomena also assumes that the answer to both of these questions is “yes.” I want to argue that this widespread assumption is indefensible. Representing the logically impossible in language, contrary to the dominant view in semantics, is not truly possible. The main argument for this position appeals to a highly plausible and minimal condition for the possession of semantic content. I call this the negative coherence condition . Any candidate's meaningful sentence S possesses semantic content only if the content of S is logically compossible with the content of the meaning‐constituting sentences associated with each of the descriptive constituent terms of S . However, the sentences of L thought to express logically impossible contents that cannot meet the negative coherence condition on semantic content. In an intuitive sense, sentences with logically impossible contents are incoherent with the conditions of their own meaningfulness.
Saul Kripke’s work on the semantics of non-normal modal logics introduced the idea of non-normal worlds, worlds where certain connectives behave differently from the way in which they behave in the worlds of normal modal logics. Such worlds may be thought of as impossible worlds, though Kripke did not, himself, talk of them in this way. Since Kripke’s invention, the notion of an impossible world has undergone much fruitful development and application. Impossible worlds may be of different kinds—or maybe different degrees of impossibility; and these worlds have found application in many areas where hyperintensionality appears to play a significant role: intentional mental states, counterfactuals, meaning, property theory, to name but a few areas. But what, exactly, is an impossible world? How is it best to characterise the notion? To date, the notion is used more by example than by definition. In this paper I will investigate the question, and propose a general characterisation, suitable for all standard purposes and tastes.
The subject of this chapter is the most popular analysis of counterfactuals, i.e., possible worlds semantics. The chapter begins with a general characterization of this semantics, along with the key question of the philosophy of modality (Sect. 3.1). This aims to provide a basis for the analysis of counterfactuals in terms of possible worlds. In virtue of the standard (so-called ‘orthodox’) approach, every counterpossible is vacuously true. This motivates introducing a modification that results in extending the domain of worlds to include impossible worlds. Section 3.2 provides the details of the modified view, i.e., the semantics and metaphysics of impossible worlds. It also shows how the extension of the domain of worlds affects the analysis of one of the key notions of possible worlds semantics for counterfactuals, i.e., the notion of similarity between worlds. Since some advocates of orthodoxy have argued that the problem of counterpossibles should be shifted from the semantic question of truth-value to the pragmatic question of assertability, Sect. 3.3 examines these arguments and provides arguments against a pragmatic-oriented approach to counterpossibles.
Critics of Divine Command Theory (DCT) argue that DCT implies the following counterpossible is true: If God commanded us to perform a terrible act, then the terrible act would be morally obligatory. However, our intuitions tell us that such a counterpossible is false. Therefore, DCT fails. This is the counterpossible terrible commands objection. In this paper, I argue that the counterpossible terrible commands objection fails. I start by considering a standard response by DCT proponents that appeals to vacuism—the view that all counterpossibles are vacuously true. I argue that DCT proponents should pursue a different response instead. I then go on to provide a new response to the counterpossible terrible commands objection: I argue that we lack reason to think that the counterpossible in question is false by examining the underlying intuitions.
Timothy Williamson contends that our primary cognitive heuristic for prospectively assessing conditionals, i.e., the suppositional procedure, is provably inconsistent. Our diagnosis is that stipulations about the nature of suppositional rejection are the likely source of these results. We show that on at least one alternative, and quite natural, understanding of the suppositional attitudes, the inconsistency results are blocked. The upshot is an increase in the reliability of our suppositional heuristics across a wider range of contexts. One interesting consequence of the increased reliability is a proportional decrease in the plausibility of an error-theory that Williamson employs against widespread intuitions about the truth values of counterpossible conditionals.
Hypothetical thinking is an extraordinary human ability that allows people to think beyond the facts of a situation to imagine alternative possibilities. I first consider how people understand factual conditionals, such as, ‘if there was an apple in the fruit bowl there was a banana’, then how they understand counterfactual conditionals, such as, ‘if Pearl had studied harder she would have passed the exam’, and then how they understand counterpossible conditionals, that is, conditionals about impossibilities, such as, ‘ if people were made of steel they would not bruise easily’. I discuss the theory that people understand conditionals by envisaging models of possibilities, and consider experimental evidence that corroborates its predictions for factual, counterfactual, and impossible conditionals.
The practice of scientific modelling often resorts to hypothetical, false, idealised, targetless, partial, generalised, and other types of modelling that appear to have at least partially non-actual targets. In this paper, I will argue that we can avoid a commitment to non-actual targets by sketching a framework where models are understood as having networks of possibilities as their targets. This raises a further question: what are the truthmakers for the modal claims that we can derive from models? I propose that we can find truthmakers for the modal claims derived from models in actuality, even in the case of supposedly non-actual targets. I then put this framework to use by examining a case study concerning the modelling of superheavy elements.
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.
This Element defends mathematical anti-realism against an underappreciated problem with that view-a problem having to do with modal truthmaking. Part I develops mathematical anti-realism, it defends that view against a number of well-known objections, and it raises a less widely discussed objection to anti-realism-an objection based on the fact that (a) mathematical anti-realists need to commit to the truth of certain kinds of modal claims, and (b) it's not clear that the truth of these modal claims is compatible with mathematical anti-realism. Part II considers various strategies that anti-realists might pursue in trying to solve this modal-truth problem with their view, it argues that there's only one viable view that anti-realists can endorse in order to solve the modal-truth problem, and it argues that the view in question-which is here called modal nothingism-is true.
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.
This Element examines the contemporary literature on essence in connection with the traditional question whether essence lies within or without our world. Section 1 understands this question in terms of a certain distinction, the distinction between active and latent facts. Section 2 steps back to investigate the connections between essence and other philosophical concepts. Section 3 brings the results of this investigation to bear on the traditional question, sketching an argument from the premise that essentialist facts are explained by the origins of things to the conclusion that such facts are active.
Counterfactuals abound in science, especially when reasoning about and with models. This often requires entertaining counterfactual conditionals with nomologically or metaphysically impossible antecedents, namely, counternomics or counterpossibles. In this paper I defend the make-believe view of scientific counterfactuals , a naturalised fiction-based account of counterfactuals in science which provides a means to evaluate their meanings independently of the possibility of the states of affairs their antecedents describe, and under which they have non-trivial truth-values. Fiction is here understood as imagination (in contrast with its most typical association with falsity), characterised as a propositional attitude of pretense or ‘make-believe’ (Walton 1990). The application of this theory to scientific counterfactuals makes their evaluation a game of make-believe: a counterfactual is (fictionally) true iff its antecedent and the rules of the game prescribe the imagining of its consequent (Kimpton-Nye 2020). The result is a practice-based account of counterfactuals and counterfactual reasoning in science which incorporates insights from theoretical and experimental analytic philosophy as well as cognitive science. This way, the make-believe view of scientific counterfactuals shows that the evaluation of scientific counterfactuals is none other than a question of scientific representation in disguise.
This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched with hyperintensional operators such as counterfactual conditionals and belief operators.
Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators.
Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis’s response was to cite “coincidences”: Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis’s response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim’s failure, one that Lewis would not have liked. The explanation is an obvious one but controversial, so it is defended against all the objections that can be mustered.
In his theory of natural laws David Lewis rejects the authenticity of impossible worlds on the grounds that the contradiction contained within his modifier "in (the world) w" is tantamount to a contradiction in the whole theory, which seems unacceptable. At the same time, in philosophical discourse very often researchers use counterfactual situations and thought experiments with impossible events and objects. There is a need to apply the theory of worlds to genuine, concrete, but impossible worlds. One way to do this is to reject Lewis's classical negation on the grounds that it leads to problems of completeness and inconsistency inside the worlds. The proposed extension for impossibility is compatible with Lewis's extensional metaphysics, although it leads to some loss for description completeness in semantics.
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.
A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.
Sentences about logic are often used to show that certain embedding expressions (attitude verbs, conditionals, etc.) 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.
As part of his geometrical method, Spinoza uses inferences involving impossibilities: what would follow if some impossibility were true. This paper examines a puzzle surrounding his use of such ‘counterpossible’ inferences. The puzzle consists of Spinoza's apparent acceptance of the following three claims: that counterpossible inferences can produce knowledge; that inference‐making produces knowledge only on the basis of a transition between ideas; and that counterpossible inferences are unthinkable. I argue for a solution to this puzzle, which interprets Spinoza's geometrical method as a form of syntactical manipulation.
A Benacerraf–Field challenge is an argument intended to show that common realist theories of a given domain are untenable: such theories make it impossible to explain how we’ve arrived at the truth in that domain, and insofar as a theory makes our reliability in a domain inexplicable, we must either reject that theory or give up the relevant beliefs. But there’s no consensus about what would count here as a satisfactory explanation of our reliability. It’s sometimes suggested that giving such an explanation would involve showing that our beliefs meet some modal condition, but realists have claimed that this sort of modal interpretation of the challenge deprives it of any force: since the facts in question are metaphysically necessary and so obtain in all possible worlds, it’s trivially easy, even given realism, to show that our beliefs have the relevant modal features. Here I show that this claim is mistaken—what motivates a modal interpretation of the challenge in the first place also motivates an understanding of the relevant features in terms of epistemic possibilities rather than metaphysical possibilities, and there are indeed epistemically possible worlds where the facts in question don’t obtain.
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 non-explanatory 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 a counterfactual is explanatory when it is an instance of a generalized counterfactual scheme.
According to sparse modalism, the notion of essence can be analysed in terms of necessity and naturalness. In this paper, I develop and defend a version of sparse modalism that is equipped with a non-standard, relativized conception of naturalness. According to this conception, properties and relations can be natural to different degrees relative to different kinds of things, and relations can be natural to different degrees relative to different slots. I argue that this relativized version of sparse modalism can accommodate various cases that the standard, non-relativized version can’t. The alternative version can accommodate cases where a relation is essential to a relatum but merely necessary to another, cases where a property is essential to an object but merely necessary to another, and cases where a less-than-perfectly natural property is essential to an object.
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 insurmountable metaphysical and epistemic difficulties, and the proposed amendments to the counterfactual theory of explanation invariably violate core commitments of the theory. Instead, mathematical explanations are either abstract mechanistic constitutive explanations or reconceptualizations of the explanandum phenomenon in which mathematics as such does not have an explanatory role. Explanation-like reasoning within mathematics, distinction between explanatory and nonexplanatory proofs, and comparative judgments of mathematical depth can be fully accounted for by a concept of formal understanding.
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 (2018), 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 (the inference from ‘If A were true, then C would be true’ to ‘If A and B were true, then C would be true’), 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.
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.
Modal knowledge accounts that are based on standards possible-worlds semantics face well-known problems when it comes to knowledge of necessities. Beliefs in necessities are trivially sensitive and safe and, therefore, trivially constitute knowledge according to these accounts. In this paper, I will first argue that existing solutions to this necessity problem, which accept standard possible-worlds semantics, are unsatisfactory. In order to solve the necessity problem, I will utilize an unorthodox account of counterfactuals, as proposed by Nolan (Notre Dame J Formal Logic 38:535–572, 1997), on which we also consider impossible worlds. Nolan’s account for counterpossibles delivers the intuitively correct result for sensitivity i.e. S’s belief is sensitive in intuitive cases of knowledge of necessities and insensitive in intuitive cases of knowledge failure. However, we acquire the same plausible result for safety only if we reject his strangeness of impossibility condition and accept the modal closeness of impossible worlds. In this case, the necessity problem can be analogously solved for sensitivity and safety. For some, such non-moderate accounts might come at too high a cost. In this respect, sensitivity is better off than safety when it comes to knowing necessities.
We argue that explanations appealing to logical impossibilities are genuine explanations. Our defense is based on a certain picture of impossibility. Namely, that there are impossibilities and that the impossibilities have structure. Assuming this broad picture of impossibility we defend the genuineness of explanations that appeal to logical impossibilities against three objections. First, that such explanations are at odds with the perceived conceptual connection between explanation and counterfactual dependence. Second, that there are no genuinely contrastive why-questions that involve logical impossibilities and, third, that explanations appealing to logical impossibilities rule nothing out.
In a recent paper, Pruss (Can J Philos 43:430–437, 2013) 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.
The objection of horrible commands claims that divine command metaethics is doomed to failure because it is committed to the extremely counterintuitive assumption that torture of innocents, rape, and murder would be morally obligatory if God commanded these acts. Morriston, Wielenberg, and Sinnott-Armstrong have argued that formulating this objection in terms of counterpossibles is particularly forceful because it cannot be simply evaded by insisting on God's necessary perfect moral goodness. I show that divine command metaethics can be defended even against this counterpossible version of the objection of horrible commands because we can explain the truth-value intuitions about the disputed counterpossibles as the result of conversational implicatures. Furthermore, I show that this pragmatics-based defence of divine command metaethics has several advantages over Pruss's reductio counterargument against the counterpossible version of the objection of horrible commands.
I defend the notion of essence and argue that rather than understanding essence in terms of modality we should understand modality in terms of essence.
This paper is, in part, a straightforward exercise in philosophical analysis: I will try to define metaphysical necessity. But I will combine this aim with another: I want to know which cognitive practices of ordinary life gave rise to the concept of necessity, and what role the notion plays in these practices. Let me describe this goal in more detail, before giving an overview of my strategy.
On the received view, counterfactuals are analysed using the concept of closeness between possible worlds: the counterfactual
‘If it had been the case that p, then it would have been the case that q’ is true at a world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity
between them. The question I consider in the paper is which weights attach to different respects of similarity. I start by
considering Lewis's answer to the question and argue against it by presenting several counterexamples. I use the same examples
to motivate a general principle about closeness: if a fact obtains in both of two worlds, then this similarity is relevant
to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and
some ideas of Lewis's to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry
of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present
version of the account and therefore necessitate further work on the details.
According to two-dimensional semantics, the meaning of an expression involves two different “dimensions”: one dimension involves reference and truth-conditions of a familiar sort, while the other dimension involves the way that reference and truth-conditions depend on the external world (for example, reference and truth-conditions might be held to depend on which individuals and substances are present in the world, or on which linguistic conventions are in place). A number of different two-dimensional frameworks have been developed, and these have been applied to a number of fundamental problems in philosophy: the nature of communication, the relation between the necessary and the a priori, the role of context in assertion, Frege’s distinction between sense and reference, the contents of thought, and the mind-body problem. Manuel Garcia-Carpintero and Josep Macia present a selection of new essays by an outstanding international team, shedding fresh light both on foundational issues regarding two-dimensional semantics and on its specific applications. The volume will be the starting-point for future work on this approach to issues in philosophy of language, epistemology, and metaphysics.
David Lewis’s untimely death on 14 October 2001 deprived the philosophical community of one of the outstanding philosophers of the 20th century. As many obituaries remarked, Lewis has an undeniable place in the history of analytical philosophy. His work defines much of the current agenda in metaphysics, philosophical logic, and the philosophy of mind and language. This volume, an expanded edition of a special issue of the Australasian Journal of Philosophy, covers many of the topics for which Lewis was well known, including possible worlds, counterpart theory, vagueness, knowledge, probability, essence, fiction, laws, conditionals, desire and belief, and truth. Many of the papers are by very established philosophers; others are by younger scholars including many he taught. The volume also includes Lewis’s Jack Smart Lecture at the Australian National University, “How Many Lives has Schrödinger’s Cat?,” published here for the first time. Lewisian Themes will be an invaluable resource for anyone studying Lewis’s work, and a major contribution to the many topics that he mastered.
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 pre-eminent 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 non-philosophical ways of thinking Suggests new ways of understanding what contemporary and past philosophers are doing.
I hope that some people see some connection between the two topics in the title. If not, anyway, such connections will be developed in the course of these talks. Furthermore, because of the use of tools involving reference and necessity in analytic philosophy today, our views on these topics really have wide-ranging implications for other problems in philosophy that traditionally might be thought far-removed, like arguments over the mind-body problem or the so-called ‘identity thesis’. Materialism, in this form, often now gets involved in very intricate ways in questions about what is necessary or contingent in identity of properties — questions like that. So, it is really very important to philosophers who may want to work in many domains to get clear about these concepts. Maybe I will say something about the mind-body problem in the course of these talks. I want to talk also at some point (I don’t know if I can get it in) about substances and natural kinds.
Why is two-dimensional semantics important? One can think of it as the most recent act in a drama involving three of the central concepts of philosophy: meaning, reason, and modality. First, Kant linked reason and modality, by suggesting that what is necessary is knowable a priori, and vice versa. Second, Frege linked reason and meaning, by proposing an aspect of meaning (sense) that is constitutively tied to cognitive significance. Third, Carnap linked meaning and modality, by proposing an aspect of meaning (intension) that is constitutively tied to possibility and necessity. Carnap's proposal was intended as something of a vindication of Frege's. Frege's notion of sense is somewhat obscure, but Carnap's notion of intension is more clearly defined. And given the Kantian connection between reason and modality, it follows that intensions have many of the properties of Fregean senses. In effect, Carnap's link between meaning and modality, in conjunction with Kant's link between modality and reason, could be seen as building a Fregean link between meaning and reason. The result was a golden triangle of constitutive connections between meaning, reason, and modality. Some years later, Kripke severed the Kantian link between apriority and necessity, thus severing the link between reason and modality. Carnap's link between meaning and modality was left intact, but it no longer grounded a Fregean link between mean-ing and reason. In this way the golden triangle was broken: meaning and modality were dissociated from reason. Two-dimensional semantics promises to restore the golden triangle. While acknow-ledging the aspects of meaning and modality that derive from Kripke, it promises to explicate further aspects of meaning and modality that are more closely tied to the An abridged version of this paper appeared under the title 'Epistemic Two-Dimensional Semantics' in a special issue of Philsophical Studies in 2004. Portions of this paper have been presented at the conferences on Two-Dimensionalism in Barcelona and ANU, at the Pacific Division meeting of the APA, and at UC Berkeley and the University of North Carolina. I am grateful to the audiences on those occasions for comments. I am especially grateful to Manuel Garcia-Carpintero and Daniel Stoljar for detailed comments on the paper.
In any plausible semantics for conditionals, the semantics for indicatives and subjunctives will resemble each other closely.
This means that if we are to keep the possible‐worlds semantics for subjunctives suggested by Lewis, we need to find a possible‐worlds
semantics for indicatives. One reason for thinking that this will be impossible is the behaviour of rigid designators in indicatives.
An indicative like ‘If the stuff in the rivers, lakes and oceans really is H3O, then water is H3O’ is non‐vacuously true, even though its consequent is true in no possible worlds, and hence not in the nearest possible
world where the antecedent is true. I solve this difficulty by providing a semantics for conditionals within the framework
of two‐dimensional modal logic. In doing so, I show that we can have a reasonably unified semantics for indicative and subjunctive
conditionals.
A collection of 13 papers by David Lewis, written on a variety of topics including causation, counterfactuals and indicative conditionals, the direction of time, subjective and objective probability, explanation, perception, free will, and rational decision. The conclusions reached include the claim that time travel is possible, that counterfactual dependence is asymmetrical, that events are properties of spatiotemporal regions, that the Prisoners’ Dilemma is a Newcomb problem, and that causation can be analyzed in terms of counterfactual dependence between events. These papers can be seen as a “prolonged campaign” for a philosophical position Lewis calls “Humean supervenience,” according to which “all there is to the world is a vast mosaic of local matters of particular fact,” with all global features of the world thus supervening on the spatiotemporal arrangement of local qualities.
Is conceptual analysis required for reductive explanation? If there is no a priori entailment from microphysical truths to phenomenal truths, does reductive explanation of the phenomenal fail? We say yes (Chalmers 1996; Jackson 1994, 1998). Ned Block and Robert Stalnaker say no (Block and Stalnaker 1999).
When I say ‘Hesperus is Phosphorus’, I seem to express a proposition. And when I say ‘Joan believes that Hesperus is Phosphorus’, I seem to ascribe to Joan an attitude to the same proposition. But what are propositions? And what is involved in ascribing propositional attitudes? Frege held distinctive views on both of these questions. He held that when one says ‘Hesperus
The assumption that the future is open makes well known problems for traditional semantics. According to a commonly held intuition,
today's occurrence of the sentence ‘There will be a sea battle tomorrow’, while truth‐valueless today, will have a determinate
truth‐value by tomorrow night. Yet given traditional semantics, sentences that are truth‐valueless now cannot later ‘become’
true. Relativistic semantics has been claimed to do a better job of accommodating intuitions about future contingents than
non‐relativistic semantics does. However, intuitions about future contingents cannot by themselves give good reasons for shifting
to a new paradigm, for despite the initial appearances, standard non‐relativistic semantics (plus an account of truth‐value
gaps) can accommodate both intuitions about future contingents.
Etude de la conception standard de la these des conditionnels contrefactuels developpee par L. Zagzebski qui se presente comme une implication logique du theisme classique tel qu'il est defendu par R. Swinburne. Examinant la definition des contre-possibles par D. Lewis et la demonstration de leur verite triviale par Zagzebski, l'A. montre que les contributions d'A. Freddoso et T. Morris consistent a rejeter la verite triviale de la conception standard et a etablir la verite non-triviale des contre-possibles a partir de leur assymetrie essentielle
1. COUNTERFACTUALS AND FACTUAL BACKGROUND Consider the counterfactual conditional 'If I were to look in my pocket for a penny, I would find one'. Is it true? That depends on the factual background against which it is evaluated. Perhaps I have a penny in my pocket. Its presence is then part of the factual background. So among the possible worlds where I look for a penny, those where there is no penny may be ignored as gratuitously unlike the actual world. (So may those where there is only a hidden penny; in fact my pocket is uncluttered and affords no hiding place. So may those where I'm unable to find a penny that's there and unbidden.) Factual background carries over into the hypothetical situation, so long as there is nothing to keep it out. So in this case the counterfactual is true. But perhaps I have no penny. In that case, the absence of a penny is part of the factual background that carries over into the hypothetical situation, so the counterfactual is false. Any formal analysis giving truth conditions for counterfactuals must somehow take account of the impact of factual background. Two very natural devices to serve that purpose are orderings of worlds and sets of premises. Ordering semantics for counterfactuals is presented, in various versions, in Stalnaker [8], Lewis [5], and Pollock [7]. (In this paper, I shall not discuss Pollock's other writings on counterfactuals.) Premise semantics is presented in Kraker [3] and [4]. (The formally parallel theory of Veltman [l 11 is not meant as truthconditional semantics, and hence falls outside the scope of this discussion.) I shall show that premise semantics is equivalent to the most general version - roughly, Pollock's version - of ordering semantics. I should like to postpone consideration of the complications and disputes that arise because the possible worlds are infinite in number. Let us therefore pretend, until further notice, that there are only finitely many worlds. That pretence will permit simple and intuitive formulations of the theories under consideration.
We present an analysis of counterfactuals in terms of stories and combine it with an account similar to Walton’s account of
truth in fiction to yield truth conditions for counterfactuals. We discuss unusual features of this account, and compare it
to other main approaches. In particular, we argue that our analysis succeeds in accounting for counterpossibles and counterfactuals
with true antecedents while the other two main approaches fail, and we give reasons for thinking that it is important to have
an adequate account of these two areas.
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.
This presentation of a system of propositional logic is a foundational paper for systems of illocutionary logic. The language contains the illocutionary force operators ' ' for assertion and ' ' for supposition. Sentences occurring in proofs of the deductive system must be prefixed with one of these operators, and rules of take account of the forces of the sentences. Two kinds of semantic conditions are investigated; familiar truth conditions and commitment conditions. Accepting a statement A or rejecting A commits a person to accepting some statements (the symbol ' + ' marks this value), to rejecting some statements ( ), and will leave the person uncommitted with respect to others ( n ). Commitment valuations assign the values to sentences of ; such a valuation is conceived as reflecting the beliefs/knowledge of a particular person. This paper explores the relations between truth conditions and commitment conditions, and between semantic concepts defined in terms of these conditions.
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 account of reasoning with impossible worlds, by treating such reasoning as reasoning employing counterpossible conditionals, and provides a semantics for the proposed treatment.
Some recently-proposed counterexamples to the traditional definition of essential property do not require a separate logic of essence. Instead, the examples can be analysed in terms of the logic and theory of abstract objects. This theory distinguishes between abstract and ordinary objects, and provides a general analysis of the essential properties of both kinds of object. The claim ‘ x has F necessarily’ becomes ambiguous in the case of abstract objects, and in the case of ordinary objects there are various ways to make the definition of ‘ F is essential to x ’ more fine-grained. Consequently, the traditional definition of essential property for abstract objects in terms of modal notions is not correct, and for ordinary objects the relationship between essential properties and modality, once properly understood, addresses the counterexample.
Indicatives and subjunctives
- B Weatherson
Weatherson, B. (2001). Indicatives and subjunctives. Philosophical Quarterly, 51, 200–216.
Comments on Delia Graff Fara’s coincidence by another name. Arizona Ontology Conference
- B Brogaard
Most counterfactuals are false
- A Hájek
On the plurality of worlds
- D Lewis
- D. Lewis
The tyranny of the subjunctive
- D Chalmers