Counterpossibles

In a series of articles, Wes Morriston has launched what can only be considered a full-scale assault on the divine command theory (DCT) of morality. According to Morriston, proponents of this theory are committed to an alarming counterpossible: that if God did command an annual human sacrifice, it would be morally obligatory. Since only a ‘terrible’ deity would do such a ‘terrible’ thing, we should reject DCT. Indeed, if there were such a deity, the world would be a terrible place—certainly far worse than it is. We argue that Morriston’s non-standard method for assessing counterpossibles of this sort is flawed. Not only is the savvy DCT-ist at liberty to reject it, but Morriston’s method badly misfires in the face of theistic activism—a metaphysical platform available to DCT-ists, according to which if God didn’t exist, neither would anything else.

Guy Kahane (2011, 2012) asks an axiological question: what value would (or does) God's existence bestow on the world? Supposing God's existence is a matter of necessity, this axiological question faces a problem because answering it will require assessing the truth-value of counterpossibles. I argue that Kahane, Moser, and Davis and Franks fail in their attempts to render the axiological question substantive. I then offer my own solution by bringing work in cognitive psychology and philosophy of mind to bear on the possibility of assessing counterpossibles. I argue that humans can engage in counterpossible reasoning by 'accepting' or 'supposing' that the antecedent is true and 'screening out' those beliefs that would result in contradiction when combined in inferences with the acceptance or supposition. These screened out propositions are not treated as false, but are ignored. I offer a three-valued logic for counterpossible reasoning. I then conclude by outlining some implications for the axiological question.

It is widely alleged that metaphysical possibility is “absolute” possibility (Kripke [1980], Lewis [1986], Rosen [2006, 16], Stalnaker [2005, 203], Williamson [2016, 460]).  Indeed, this is arguably its metaphysical significance.  Kripke calls metaphysical necessity “necessity in the highest degree” ([1980, 99]).  Williamson calls metaphysical possibility the “maximal objective modality” [2016, 459].  Rosen says that “metaphysical possibility is the [most inclusive] sort of real possibility” ([2006, 16]).  And Stalnaker writes, “we can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense [2003, 203].”  But what exactly does the thesis that metaphysical possibility is absolute amount to?  Is it true?  In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith.  I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it.

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson's objections.

The uploaded document contains my PhD dissertation. The abstract is given below.

ABSTRACT

The two main features of this thesis are (i) an account of contextualized (context indexed) counterfactuals, and (ii) a non-vacuist account of counterpossibles. Experience tells us that the truth of the counterfactual is contingent on what is meant by the antecedent, which in turn rests on what context is assumed to underlie its reading (intended meaning). On most conditional analyses, only the world of evaluation and the antecedent determine which worlds are relevant to determining the truth of a conditional, and consequently what its truth value is. But that results in the underlying context being fixed, when evaluating distinct counterfactuals with the same antecedent on any single occasion, even when the context underlying the evaluation of each counterfactual may vary. Alternative approaches go some of the way toward resolving this inadequacy by appealing to a difference in the consequents associated with counterfactuals with the same antecedent. That is, in addition to the world of evaluation and the antecedent, the consequent contributes to the counterfactual’s evaluation. But these alternative approaches nevertheless give a single, determinate truth value to any single conditional (same antecedent and consequent), despite the possibility that this value may vary with context. My reply to these shortcomings (chapter 4) takes the form of an analysis of a language that makes appropriate explicit access to the intended context available. That is, I give an account of a contextualized counterfactual of the form ‘In context C: If it were the case that … , then it would be the case that …’. Although my proposal is largely based on Lewis’ (1973, 1981) analyses of counterfactuals (the logic VW and its ordering semantics), it does not require that any particular logic of counterfactuals should serve as its basis – rather, it is a general prescription for contextualizing a conditional language. The advantage of working with ordering semantics stems from existing results (which I apply and develop) concerning the properties of ordering frames that facilitate fashioning and implementing a notion of contextual information preservation.

Analyses of counterfactuals, such as Lewis’ (1973), that cash out the truth of counterfactuals in terms of the corresponding material conditional’s truth at possible worlds result in all counterpossibles being evaluated as vacuously true. This is because antecedents of counterpossibles are not true at any possible world, by definition. Such vacuist analyses have already been identified and challenged by a number of authors. I join this critical front, and drawing on existing proposals, I develop an impossible world semantics for a non-vacuist account of counterpossibles (chapter 5), by modifying the same system and semantics that serve the basis of the contextualized account offered in chapter 4, i.e. Lewis’ (1986) ordering semantics for the logic VW. I critically evaluate the advantages and disadvantages of key conditions on the ordering of worlds on the extended domain and show that there is a sense in which all of Lewis’ analysis of mere counterfactuals can be preserved, whilst offering an analysis of counterpossibles that meets our intuitions.

The first part of chapter 1 consists of an outline of the usefulness of impossible worlds across philosophical analyses and logic. That outline in conjunction with a critical evaluation of Lewis’ logical arguments in favour of vacuism in chapter 2, and his marvellous mountain argument against impossible worlds in chapter 3, serves to motivate and justify the impossible world semantics for counterpossibles proposed in chapter 5. The second part of chapter 1 discusses the limitations that various conditional logics face when tasked to give an adequate treatment of the influence of context. That introductory discussion in conjunction with an overview of conditional logics and their various semantics in chapter 2 – which includes an in-depth exposition of Stalnaker-Lewis similarity semantics for counterfactuals – serves as the motivation and conceptual basis for the contextualized account of counterfactuals proposed in chapter 4.

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(Perhaps it is worth emphasizing that the most original work is contained in chapter 4, where I give an account of a contextualized (context relativized) counterfactual of the form ‘In context C: If it were the case that … , then it would be the case that …’, based on Lewis’ (1974, 1981) analysis of the counterfactual. Drawing on earlier work by Lewis (1973, 1981) I first give an ordering semantics for counterfactuals, based on the idea of comparative similarity, interpreted as ‘similarity in relevant respects’ or as ‘relevant similarity’, and modelled by total preorderings of possible worlds. Subsequently, building on that analysis I develop model-theoretic methods for a semantic consequence relation of contextualized counterfactuals (contextualized validity), which is given as the culminating item of the chapter.)

A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and I show that Anselm's treatment of counterpossible conditionals concerning the procession of the spirit from the son in Trinitarian theology represent an early foray into default logic. Thus, the mutual estrangement of eastern and western positions on the matter may not lie fundamentally in a change in dogma, but rather in a change in logic. Mathematics Subject Classification. Primary 01A35; Secondary 03B60, 03B80.

Abstract

The two main features of this thesis are (i) an account of contextualized (context indexed) counterfactuals, and (ii) a non-vacuist account of counterpossibles. Experience tells us that the truth of the counterfactual is contingent on what is meant by the antecedent, which in turn rests on what context is assumed to underlie its reading (intended meaning). On most conditional analyses, only the world of evaluation and the antecedent determine which worlds are relevant to determining the truth of a conditional, and consequently what its truth value is. But that results in the underlying context being fixed, when evaluating distinct counterfactuals with the same antecedent on any single occasion, even when the context underlying the evaluation of each counterfactual may vary. Alternative approaches go some of the way toward resolving this inadequacy by appealing to a difference in the consequents associated with counterfactuals with the same antecedent. That is, in addition to the world of evaluation and the antecedent, the consequent contributes to the counterfactual’s evaluation. But these alternative approaches nevertheless give a single, determinate truth value to any single conditional (same antecedent and consequent), despite the possibility that this value may vary with context. My reply to these shortcomings (chapter 4) takes the form of an analysis of a language that makes appropriate explicit access to the intended context available. That is, I give an account of a contextualized counterfactual of the form ‘In context C: If it were the case that … , then it would be the case that …’. Although my proposal is largely based on Lewis’ (1973, 1981) analyses of counterfactuals (the logic VW and its ordering semantics), it does not require that any particular logic of counterfactuals should serve as its basis – rather, it is a general prescription for contextualizing a conditional language. The advantage of working with ordering semantics stems from existing results (which I apply and develop) concerning the properties of ordering frames that facilitate fashioning and implementing a notion of contextual information preservation.

Analyses of counterfactuals, such as Lewis’ (1973), that cash out the truth of counterfactuals in terms of the corresponding material conditional’s truth at possible worlds result in all counterpossibles being evaluated as vacuously true. This is because antecedents of counterpossibles are not true at any possible world, by definition. Such vacuist analyses have already been identified and challenged by a number of authors. I join this critical front, and drawing on existing proposals, I develop an impossible world semantics for a non-vacuist account of counterpossibles (chapter 5), by modifying the same system and semantics that serve the basis of the contextualized account offered in chapter 4, i.e. Lewis’ (1986) ordering semantics for the logic VW. I critically evaluate the advantages and disadvantages of key conditions on the ordering of worlds on the extended domain and show that there is a sense in which all of Lewis’ analysis of mere counterfactuals can be preserved, whilst offering an analysis of counterpossibles that meets our intuitions.
The first part of chapter 1 consists of an outline of the usefulness of impossible worlds across philosophical analyses and logic. That outline in conjunction with a critical evaluation of Lewis’ logical arguments in favour of vacuism in chapter 2, and his marvellous mountain argument against impossible worlds in chapter 3, serves to motivate and justify the impossible world semantics for counterpossibles proposed in chapter 5. The second part of chapter 1 discusses the limitations that various conditional logics face when tasked to give an adequate treatment of the influence of context. That introductory discussion in conjunction with an overview of conditional logics and their various semantics in chapter 2 – which includes an in-depth exposition of Stalnaker-Lewis similarity semantics for counterfactuals – serves as the motivation and conceptual basis for the contextualized account of counterfactuals proposed in chapter 4.

(Perhaps it is worth emphasizing that the most original work is contained in chapter 4, where I give an account of a contextualized (context relativized) counterfactual of the form ‘In context C: If it were the case that … , then it would be the case that …’, based on Lewis’ (1974, 1981) analysis of the counterfactual. Drawing on earlier work by Lewis (1973, 1981) I first give an ordering semantics for counterfactuals, based on the idea of comparative similarity, interpreted as ‘similarity in relevant respects’ or as ‘relevant similarity’, and modelled by total preorderings of possible worlds. Subsequently, building on that analysis I develop model-theoretic methods for a semantic consequence relation of contextualized counterfactuals (contextualized validity), which is given as the culminating item of the chapter.)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic.

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counter-factuals, which would treat them as uniformly true. What's more, I argue that these counterpossibles don't just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models.

The aim of this paper is to show why the theories of impossible worlds do not fully solve the problem of counterpossibles, but merely shift it. Moreover, by making a distinction between two types of languages, we will show that some expectations about proper theory of counterfactuals might be too great.

The aim of this paper is to point out the limitations of Hybrid Modal Realism as a general theory of modalities, i.e. one that gives an analysis of possibilities as well as impossibilities. To do so we will firstly sketch the goals that theories of impossible worlds should achieve. Secondly we will briefly present the two most popular accounts of impossibilities - Extended Modal Realism and Extended Ersatzism. We will focus on the aspects of both theories which became the motivation for a hybrid view. In the last part of this paper we will analyze Francesco Berto's Hybrid Modal Realism and present reasons why this account is an insufficient tool for analyzing impossibilities.

The subject of this paper is a world-semantic analysis of counterpossibles, i.e., counterfactuals with impossible antecedents. We focus on the notion of similarity between worlds, which determines truth value of counterfactuals. There are two commonly accepted assumptions about this notion. According to the first one, every possible world is more similar to the actual world than any impossible world. According to the second one, the trivial world (the world where everything is true) is the most dissimilar to the actual world. Considering the notion of similarity we argue for a negative thesis and a positive thesis. The negative thesis is that both of these assumptions are false, and as such should not be taken as a " guide " to our understanding of similarity. The positive thesis is an alternative interpretation of the notion of similarity. The interpretation is based on an analogy of the inference to the best explanation and on the assumption that similarity is a ternary relation satisfied by the actual world, a non actual world and a given factor of similarity. Similarity understood in this manner is a notion which requires an indication of a rule which supports the truth of the antecedent and explains its connection with the consequent.

The concept of essence re-gained respectability when it received a possible-worlds analysis: an object has a property essentially just in case there is no possible world where it both exists and lacks that property. After Kit Fine offered several counterexamples to the possible-worlds analysis, it fell out of favor. Berit Brogaard and Joe Salerno recently offered an impossible-worlds analysis of essence intended to accommodate Fine’s examples. In this paper I consider their theory and a series of variations, and argues that each one is inconsistent with one of Fine’s examples.

Hyperintensionality – the failure of substitutivity salva veritate of intensionally equivalent expressions – is one of the most debated topics in recent philosophy of language. Being a phenomenon that affects a wide variety of different sentential contexts, a question concerning its source arises: is hyperintensionality something that can originate from actual features of the world, or it is simply some kind of representational phenomenon, which entirely depends on our conceptual faculties and preferred semantics? After a brief general introduction to the topic from the semantic standpoint, in the present work I defend a view developed by Daniel Nolan, according to which hyperintensionality can be a worldly, non-representational phenomenon. I first reconstruct Nolan’s view and argument for worldly hyperintensionality, understood through the comparison with de re intensional modality. Then, I address the main criticism that has been raised against it, developing three objections. Evidence for worldly hyperintensionality is thereby presented, by focusing on a paradigmatic trigger: counterpossible conditionals. I provide two jointly sufficient criteria for a counterpossible to be a genuine instance of worldly hyperintensionality, then illustrate three case studies from scientific practices that all rely on counterpossible reasoning: reducibility in relative computability theory; scientific explanation of certain substances’ essential properties; and emergent molecular structure in chemistry. Each of them is evaluated by checking if it satisfies the criteria for worldly hyperintensionality, leading to the detection of patterns of counterpossible dependence occurring in at least some specific instances of the case studies discussed. Finally, I suggest a possible realist reading of such dependence relation, locating its relata in the world, independently from our representations.

The subject of this paper is the notion of similarity between the actual and impossible worlds. Many believe that this notion is governed by two rules. According to the first rule, every non-trivial world is more similar to the actual world than the trivial world is. The second rule states that every possible world is more similar to the actual world than any impossible world is. The aim of this paper is to challenge both of these rules. We argue that acceptance of the first rule leads to the claim that the rule ex contradictione sequitur quodlibet is invalid in classical logic. The second rule does not recognize the fact that objects might be similar to one another due to various features.

To solve the problem of counterpossibles, many philosophers have been arguing that one needs to invoke impossible worlds. This extension of the ontology of modality should save the analysis of counterfactuals from being insensitive to the problem of counterpossibles. Since theories of impossible worlds are extensions of original accounts of modalities, it is worth stressing that proper analyses of counterpossibles should not weaken the latter.In this paper I argue that these theories of impossible wolrds, which are  based on D. Lewis' modal realism - Extended Modal Realism and Hybrid Modal Realism - might be consider as either an unattractive for modal realists or insufficient for analyzing counterpossibles.

Counterpossibles, counterfactuals conditional with impossible antecedents, are notoriously contested; while the standard view makes them trivially true, some authors argue that they can be non-trivially true. In this paper, I examine the use of counterfactuals in the context of games, and argue that there is a case to be made for their non-triviality in a restricted sense. In particular, I examine the case of retro problems in chess, where it can happen that one is tasked with evaluating counterfactuals about illegal positions. If we understand illegality as a type of restricted impossibility, those counterfactuals are non-trivial counterpossibles. I suggest that their non-triviality stems from their role in practices of rule coordination and revision, and suggest that this model could be generalized to counterpossibles in different domains. I then compare the approach to the accounts of Vetter (2016) and Locke (2019).

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.