Modal Conventionalism

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with propositional quantifiers, which (...) are necessary for regimenting some logic talk. Second, it develops an alternative framework based on logical expressivism, which explains logic talk using shifting conventions. When combined with the standard S5π+ semantics for propositional quantifiers, this framework results in a well-behaved system that does not face the problems of the impossible worlds semantics. It can also be naturally extended with hybrid operators to regiment a broader range of logic talk, e.g., claims about what laws hold according to other logics. The resulting system, called hyperlogic, is therefore a better framework for modeling logic talk than previous accounts. (shrink)

Some people might be tempted by modal ontological arguments from the possibility that God exists to the conclusion that God in fact exists. They might also be tempted to support the claim that possibly God exists by appealing to the conceivability of God’s existence. In this chapter, I introduce three constraints on an adequate theory of philosophical conceivability. I then consider and develop both imagination-based accounts of conceivability and conceptual coherence-based accounts of conceivability. Finally, I return to the modal ontological (...) argument and consider whether the premise that possibly God exists can be supported by some conceiving. (shrink)

Traditional conventionalism about modality claims that a proposition is necessarily true iff it is true by convention. In the wake of the widespread repudiation of truth-byconvention, traditional conventionalism has fallen out of favour. However, a family of theories of modality have arisen that, whilst abandoning truth-by-convention, retain the spirit of traditional conventionalism. These ‘neo-conventionalist’ theories surpass their forebears and don’t fall victim to the criticisms inherited through truth-by-convention. However, not all criticisms levelled at traditional conventionalism target truth-by-convention. Any conventional theory (...) of modality must face the contingency problem. This claims that the contingency of our linguistic conventions jeopardises the necessity of the necessities they determine. I present the contingency problem as relevant to both the traditional conventionalist and the neo-conventionalist. I examine a response from Einheuser that builds upon a response from Wright. I show that the Einheuser response does more to accommodate the conventionalist’s modal beliefs, but that it does not fully satisfy some further conditions that ought to be laid upon such a response. I then suggest how the response can be revised so as to satisfy these conditions. The resulting model of conventionalism is compatible with the validity of S4, and suitably in the spirit of conventionalism. (shrink)

Sider offers a new take on a linguistic account of necessity. In this paper, I assess his view’s vulnerability to objections made against more traditional linguistic accounts, especially an argument I call the “indexical problem.” I conclude that the indexical problem has no force against Sider’s approach because the view is able to attribute modal properties directly to propositions, rather than indirectly via analytic sentences that express them. However, Sider also argues that traditional linguistic accounts fail because of two well-known (...) problems, and I argue that the same two problems undermine his own account. (shrink)

This project is an investigation into the prospects for an antirealist theory of essence. Essentialism is the claim that at least some things have some of their properties essentially. Essentialist discourse includes claims such as “Socrates is essentially human”, and “Socrates is accidentally bearded”. Historically, there are two ways of interpreting essentialist discourse. I call these positions ‘modal essentialism’ and ‘neo-Aristotelian essentialism’. According to modal essentialism, for Socrates to be essentially human is for it to be necessary that he be (...) a human if he exists, and for Socrates to accidentally have a beard is for it to be contingent that Socrates has a beard if he exists. According to neo-Aristotelian essentialism, objects have definitions in something like the way words do. For Socrates to be essentially human but accidentally bearded is for it to be part of the definition of Socrates that he is human, but not part of that definition that he is bearded. I argue that both are susceptible to antirealist interpretation. This thesis sets about showing that this is the case. In Chapters One and Two I investigate neo-conventionalist theories of modality, in the hope of using such a position to develop an antirealist modal essentialism. In Chapter Three I discuss the debate between modal and neo-Aristotelian essentialism and conclude that it is by no means settled. In Chapter Four I develop an antirealist neo-Aristotelian essentialism based on the mechanism of one of the neo-conventionalist accounts of modality. In Chapter Five I argue that this account is in a better position to give an essentialist theory of necessity than its realist counterparts. I conclude that, regardless of whether one is a modal or neo-Aristotelian essentialist, antirealist essentialism is a viable theory of essence that is worthy of consideration in contemporary debate. (shrink)

Standard truthmaker theory has generally assumed a realist account of de re modality and essences. But there are reasons to be skeptical about such a view, and for considering antirealist alternatives. Can truthmaker theory survive in the face of such skepticism? I argue that it can, but that only certain antirealist perspectives on de re modality are acceptable for truthmaker theory. In particular, either a quasi-realist or conventionalist account of de re modality is needed to provide the best account of (...) essential and accidental features that can be put to work in truthmaker theory. An important consequence of this approach is that it offers an account of truthmaking that is consistent with a nominalist perspective on properties, and yet fully respects the ontological ambitions driving truthmaker theory. (shrink)

In this paper I examine Crispin Wright's modal anti-realism as based on the availability of a certain attitude of Caution towards judgements of necessity. I think that Wright's account should be attractive in several ways for modal theorists with an anti-realist bend. However, the attitude of Caution to which it appeals has attracted some controversy. Wright himself has later come to doubt whether Caution is ultimately coherent. Here I first address Wright's worries concerning the coherence of Caution and show that (...) they are unfounded. But then I argue that although the attitude of Caution is coherent, it cannot provide a suitable basis for a non-eliminativist account of necessity. I offer two different objections against Caution. I argue that Wright's appeal to Caution, if successful, would show not only that modal judgement is non-objective but also that it is dispensable. Thus, I claim that appeal to Caution would seem to serve more as a threat against a non-eliminativist account of necessity, rather than as a potential adequate basis for it. However, I argue that Wright's appeal to Caution is unsuccessful, for there is no genuine Caution: Caution is a mere verbal attitude. (shrink)

Sider (2011, 2013) proposes a reductive analysis of metaphysical modality—‘(modal) Humeanism’—and goes on to argue that it has interesting epistemological and methodological implications. In particular, Humeanism is supposed to undermine a class of ‘arguments from possibility’, which includes Sider's (1993) own argument against mereological nihilism and Chalmers's (1996) argument against physicalism. I argue that Sider's arguments do not go through, and moreover that we should instead expect Humeanism to be compatible with the practice of arguing from possibility in philosophy.

One type of deflationism about metaphysical modality suggests that it can be analysed strictly in terms of linguistic or conceptual content and that there is nothing particularly metaphysical about modality. Scott Soames is explicitly opposed to this trend. However, a detailed study of Soames’s own account of modality reveals that it has striking similarities with the deflationary account. In this paper I will compare Soames’s account of a posteriori necessities concerning natural kinds with the deflationary one, specifically Alan Sidelle’s account, (...) and suggest that Soames’s account is vulnerable to the deflationist’s critique. Furthermore, I conjecture that both the deflationary account and Soames’s account fail to fully explicate the metaphysical content of a posteriori necessities. Although I will focus on Soames, my argument may have more general implications towards the prospects of providing a meaning-based account of metaphysical modality. (shrink)

This paper looks at what David Kaplan's work on indexicals can teach us about logic and the philosophy of logic, and also what Kaplan's logic (i.e. the Logic of Demonstratives) can teach us about indexicals. The lessons are i) that logical consequence is not necessary truth-preservation, ii) that that the linguistic doctrine of necessary truth (also called conventionalism about modality) fails, and iii) that there is a kind of barrier to entailment between non-context-sensitive and context-sensitive claims.

Some truths are necessary, others could have been false. Why? What is the source of the distinction between the necessary and the contingent? What's so special about the necessary truths that account for their necessity? In this article, we look at some of the most promising accounts of the grounds of necessity: David Lewis' reduction of necessity to truth at all possible worlds; Kit Fine's reduction of necessity to essence; and accounts of necessity that take the distinction between the necessary (...) and the contingent to be a matter of convention. (shrink)

My target in this paper is a view that has sometimes been called the ‘ Linguistic Doctrine of Necessary Truth ’ and sometimes ‘Conventionalism about Necessity’. It is the view that necessity is grounded in the meanings of our expressions—meanings which are sometimes identified with the conventions governing those expressions—and that our knowledge of that necessity is based on our knowledge of those meanings or conventions. In its simplest form the view states that a truth, if it is necessary, is (...) necessary because it is analytic. It is widely recognized that this simple version of the view faces a prima facie problem with the existence of the necessary a posteriori. Assuming that all analytic truths are a priori, if there are necessary a posteriori truths then there are necessary synthetic truths—contradicting the view’s claim that all necessary truths are analytic. Contemporary L-DONTers have things to say about the problem, but in this paper I want to suggest that there is a different, more serious, problem which arises from the phenomenon of indexicality, which L-DONTers have not taken account of. Though there are many versions of the problem, a simple one is this. Consider Kaplan’s celebrated sentence. (shrink)

A not-unpopular position in the metaphysics of material objects (Ted Sider's, for instance) combines realism about what objects there are and the conditions of objecthood with conventionalism about de re modality. I argue that this is not a coherent combination of views: one must go fully conventionalist, or fully realist. The central argument displays the difficulty for the modal conventionalist/object realist in specifying the object that satisfies de re modal predicates. I argue that if this is a mind-independent object, contradictions (...) arise when we consider the possibility or actuality of non-equivalent conventions both applying to 'the same object'. (shrink)

The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal (...) logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality. (shrink)

One common objection to Conventionalism about modality is that since it is contingent what our conventions are, the modal facts themselves will thereby be contingent. A standard reply is that Conventionalists can accept this, if they reject the S4 axiom, that what is possibly possible is possible. I first argue that this reply is inadequate, but then continue to argue that it is not needed, because the Conventionalist need not concede that the contingency of our conventions has any bearing on (...) the modal status of necessary truths. It is explained why this does not compromise the Conventionalist claim that necessity – and particularly, essence – is due to conventions. (shrink)

The problem of the source of necessity is the problem of explaining what makes necessary truths necessarily true. Simon Blackburn has presented a dilemma intended to show that any reductive, realist account of the source of necessity is bound to fail. Although Blackburn's dilemma faces serious problems, reflection on the form of explanations of necessities reveals that a revised dilemma succeeds in defeating any reductive account of the source of necessity. The lesson is that necessity is metaphysically primitive and irreducible.

The Donkey Problem (as I am calling it) concerns the relationship between more and less fundamental ontologies. I will claim that the moral to draw from the Donkey Problem is that the less fundamental objects are merely conventional. This conventionalism has consequences for the 3D/4D debate. Four-dimensionalism is motivated by a desire to avoid coinciding objects, but once we accept that the non-fundamental ontology is conventional there is no longer any reason to reject coincidence. I therefore encourage 4Dists to become (...) even more radical—embrace the Donkey Problem’s conventionalism and deflate the debate between 3Dists and 4Dists. (shrink)

In my previous paper "Has the later Wittgenstein accounted for necessity?" I argued against the conventionalist account of necessity proposed by Wittgenstein and his followers. Glock has addressed some of my objections in his paper "Necessity and Language: In Defence of Conventionalism". This brief rejoinder considers Glock's replies to three of those objections. In the course of doing so, I revisit Wittgenstein's explanation of the special status of necessary propositions, the supposedly arbitrary nature of colour-grammatical propositions, and the relation between (...) rules and modality. (shrink)

Despite the otherwise-dominant trends towards physicalism and naturalism in philosophy, it has become increasingly common for metaphysicians to accept the existence either of modal facts and properties, or of Lewisian possible worlds. This paper raises the historical question: why did these heavyweight realist views come into prominence? The answer is that they have arisen in response to the demand to find truthmakers for our modal statements. But this demand presupposes that modal statements are descriptive claims in need of truthmakers. This (...) presupposition was, however, rejected by many earlier analytic philosophers, including the logical positivists, Wittgenstein, Ryle and Sellars, all of whom denied that modal statement were descriptive at all. Yet the non-descriptivist approach has largely fallen out of discussion and out of philosophical consciousness. In this paper I examine why non-descriptivist views first came into and then fell out of favor, and consider what the prospects are for reviving this more deflationary approach to modality. (shrink)

Much has happened in modal logic since 1947. In particular, in regard to the problem of interpreting such logics. In that fateful year Quine published his seminal paper “The Problem of Interpreting Modal Logic” from which this work takes inspiration. Since then a certain kind of model theory – universally referred to as “possible worlds semantics” – has come to dominate both advanced research and introductory textbooks. Many would say that the problem of interpreting modal logic has been resolved. In (...) the work below I argue that some of the 1947 problems raised by Quine have indeed been resolved by the possible worlds model theory. But I also claim – perhaps against common perception, but in line with Quine’s persisting fifty-year-old skepticism – that one problem of Quine’s original paper is still alive: the problem of interpreting modal logic. Surprisingly, Quine’s best ally on these matters turns out to be the very philosopher who engineered the possible worlds model theory: Saul Kripke. (shrink)

At present, there is an almost universal consensus that the linguistic doctrine of logical necessity is grotesque. This paper explores avenues for rehabilitating a limited version of the doctrine, according to which the special status of analytic statements like 'All vixens are female' is to be explained by reference to language. Far from being grotesque, this appeal to language has a respectable philosophical pedigree and chimes with common sense, as Quine came to realize. The problem lies in developing it in (...) a way that avoids the powerful objections facing previous versions of the linguistic doctrine. I argue tentatively that this can be done by reconciling Wittgenstein's claim that such statements have a normative role with Carnap's concession that they are true. (shrink)

Logic begins but does not end with the study of truth and falsity. Within truth there are the modes of truth, ways of being true: necessary truth and contingent truth. When a proposition is true, we may ask whether it could have been false. If so, then it is contingently true. If not, then it is necessarily true; it must be true; it could not have been false. Falsity has modes as well: a false proposition that could not have been (...) true is impossible or necessarily false; one that could have been true is merely contingently false. The proposition that some humans are over seven feet tall is contingently true; the proposition that all humans over seven feet tall are over six feet tall is necessarily true; the proposition that some humans are over seven feet tall and under six feet tall is impossible, and the proposition that some humans are over nine feet tall is contingently false. Of these four modes of truth, let us focus on necessity, plus a fifth: possibility. A proposition is possible if it is or could have been true; hence propositions that are either necessarily true, contingently true, or contingently false are possible. Notions that are similar to the modes of truth in being concerned with what might have been are called modal. Dispositions are modal notions, for example the disposition of fragility. Relatedly, there are counterfactual conditionals, for example “if this glass were dropped, it would break.” And the notion of supervenience is modal.1 But let us focus here on necessity and possibility. Modal words are notoriously ambiguous (or at least context-sensitive2). I may reply to an invitation to give a talk in England by saying “I can’t come; I have to give a talk in California the day before”. This use of “can’t” is perfectly appropriate. But it would be equally appropriate for me to say that I could cancel my talk in California (although that would be rude) and give the talk in England instead. What I cannot do is give both talks.. (shrink)

Kant's claim that modality is a 'category' provides an approach to modality to be contrasted with Lewis's reductive analysis. Lewis's position is unsatisfactory, since it depends on an inherently modal conception of a world. This suggests that modality is 'primitive'; and the Kantian position is a prima facie plausible position of this kind, which is filled out by considering the relationship between modality and inference. This provides a context for comparing the Kantian position with Wright's non-cognitivist 'conventionalism'. Wright's position is (...) vulnerable to the type of argument used against ethical non-cognitivism, and the Kantian position is further confirmed by Blackburn's acknowledgment that modality is 'antinaturalistic to its core'. The position is further elaborated to show that it can accommodate the famous Kripkean categories of the empirically necessary and the contingent a priori, and finally defended against the criticisms used by Quine against Carnap. (shrink)

Modality and Anti-Metaphysics critically examines the most prominent approaches to modality among analytic philosophers in the twentieth century, including essentialism. Defending both the project of metaphysics and the essentialist position that metaphysical modality is conceptually and ontologically primitive, Stephen McLeod argues that the logical positivists did not succeed in banishing metaphysical modality from their own theoretical apparatus and he offers an original defence of metaphysics against their advocacy of its elimination. -/- Seeking to assuage the sceptical worries which underlie modal (...) anti-realism, McLeod provides an original contribution to essentialist epistemology, engaging with current debates about modality and suggesting that standard essentialist approaches to some issues in the philosophies of logic and language require revision. -/- This book offers valuable insights to professional philosophers, postgraduates and advanced undergraduates interested in metaphysics, philosophy of logic or the history of twentieth-century analytic philosophy. (shrink)

Possible worlds present a formidable challenge for the lover of desert landscapes. One cannot ignore their usefulness; they provide, as David Lewis puts it, “a philosophers’ paradise”.1 But to enter paradise possibilia must be fit into a believable ontology. Some follow Lewis and accept worlds at face value, but most prefer some other choice from the current menu. Part of Chihara’s book is a critical discussion of some of these menu options: Lewis’s modal realism, Alvin Plantinga’s abstract modal realism, Graeme (...) Forbes’s anti-realism and Gideon Rosen’s modal fictionalism. These discussions are very detailed and conversant with the literature. The discussions of Forbes and of paradox within Plantinga’s system are particularly enlightening. The rest of the book is devoted to Chihara’s positive project: developing an account of the status of model theory for non-modal logic, and then applying it to the modal case. The prize is an understanding of possible worlds semantics that requires no commitment to possible worlds at all What does the relativized notion of truth in an interpretation studied in model theory have to do with plain old truth? Chihara’s answer involves “connecting theorems” that relate truth-in to truth. A “natural-language proto-interpretation of the sentential calculus” is a function that assigns meanings of declarative sentences of English to sentence letters. Where I is an NLPI of SC and φ is a sentence letter, Chihara uses ‘[φ/I ]’ to refer to “φ with the meaning it has been assigned by I ” ; where φ is not atomic, he says. (shrink)

During a short-lived renaissance of medieval Nominalism lasting from approximately 1480 to 1530, many Renaissance Nominalist logicians devoted a great deal of attention to the task of developing an account of the truth and falsity of modal propositions. A modal proposition is any proposition containing one or more occurrences of the four modal terms: possible, necessary, impossible, and contingent. The Nominalist account follows the general procedure outlined in William of Ockham's Summa totius logicae, the goal of which is to translate (...) modal propositions into one or more non-modal propositions, each proposition the subject of a "metalinguistic" modal predicate. For example, the modal proposition 'George possibly is running' would be translated to: " thinspace'George is running' is possible." ;Renaissance Nominalists follow the practice of medieval logicians in distinguishing two types of modal propositions: the "composed" and the "divided". They differ from the medievals in how they define these. Composed modal propositions contain a "second intention" modal term; divided modal propositions contain "syncategorematic" modal terms. Second intention modes appear in either the subject or predicate positions in propositions, and refer to presently existing sentence tokens. Syncategorematic modes do not alone refer to anything, and extend or "ampliate" the reference of other terms in the proposition from presently existing actual entities to non-actual possible beings. ;Determining the truth value of a composed modal proposition was considered an easy task since the non-modal proposition into which the modal proposition is translated preserves the logical form of the original. However, the truth value of a divided modal propositions depends upon the modality belonging to the atomic propositions implied by it. ;A theory of modal truth is not complete unless it develops an account of the metaphysical nature of modality as the basis for ascribing truth values to modal propositions. The Nominalist logicians of the time offer only fragments of such a theory. Some suggested that modalities only exist in the mind; others believed that modalities are real, extramental relations holding between individuals. Such remarks were never fully reconciled with other modal notions found in these texts, particularly notions defined in terms of God's potencies. (shrink)

Conventionalism about logical necessity has, since Quine, been criticised for falling into a vicious regress. The conventionalist model involves a base class of directly stipulated necessary truths, and all other logical necessities are taken to follow from this base. The essentialist model described by Hale is constructed in a broadly similar fashion: there is a class of those necessities which hold directly in virtue of the natures of things, and other necessities are from this class derivative. Hale expresses a concern (...) that the similarity of the two models might leave the essentialist position prey to a similar regress, but argues that such a situation will not arise. This should prompt a question: if the models are similar, could the solution not be also? In other words, can the conventionalist follow the essentialist to escape regress? This paper will offer a negative answer to this question. We will assume that Hale’s attempt to avert disaster for the essentialist was successful, but argue that the route taken by Hale is not open to the conventionalist, and that in attempting to take it the conventionalist fails to avoid regress. The paper will end with an attempt to generalise what we have seen to the conclusion that conventionalism about logical necessity cannot ever avoid regress. Keywords Modality, essentialism, conventionalism, regress, Hale. (shrink)

An account of modality is produced which takes as its foundation the idea that modal concepts are parasitic upon our background theoretical commitments. This position is distinguished from the majority of philosophies of modality, which are either primitivist or reductionist. It is in this sense that our account is less burdened by metaphysics. The primary purpose of the document is to demonstrate that our approach is a coherent one. It supports this claim in three stages. First, we identify the historical (...) lineage of our position and elucidate the main desiderata which must be met if the project is to succeed. Second, we provide a series of logical systems which are designed to meet our requirements. A raft of technical challenges beset this part of the project and this is where the bulk of the result in this thesis are located. Finally, we use the precise formalisation as a means to get a better understanding of what is at stake in the project and to understand the resultant position's relationship with other leading, contemporary philosophies of modality. (shrink)