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)

The full-text of this article is not currently available in ORA, but the original publication is available at springerlink.com . Citation: Williamson, T. . 'The necessary framework of objects', Topoi 19, 201-208. N.B. Tim Williamson is now based at the Faculty of Philosophy, University of Oxford.

Realists claim that, amongst the statements weunderstand, there are some which are true, yetwhose truth potentially transcends the limits ofwhat we can recognize. Dummett and othershave argued that this realist thesis is incompatiblewith an account of understanding in termsof recognitional capacities. But careful analysis revealsthat this contention is mistaken. Thealleged incompatibility presupposes the truth of ametaphysical principle which cannot bevindicated on the basis of an account of understanding.Realists have independent reason toreject this metaphysical principle, as it leads to a collapseof (...) more modest forms of realisminto more contentious ones. According to moderate realism,we neither know that there areactually recognition-transcendent truthsnor do we know taht there are none. Pending apositive case for the metaphysical principle, thisagnosticism is sufficient to warrant therealists' key thesis, viz. that there arepotentially recognition-transcendent truths. Thusrealism, in its more moderate guise, turns outto be the default position. (shrink)

Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight into the (...) modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possible worlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)

Le regain de faveur de la thématique des « mondes possibles » dans la philosophie contemporaine est pour l’essentiel un effet collatéral du développement de la logique modale au long du XXe siècle. C’est en effet initialement pour résoudre le problème soulevé par l’évaluation des systèmes modaux, élaborés entre les années trente et cinquante par des auteurs comme Clarence Lewis, Richard Feys ou Georg von Wright, qu’une sémantique...

The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...) neutralized by the possibility of studying all these alternative logics within an agreed metalogical framework, typically that of first-order logic with set theory. In effect, metalogic is given the role of neutral arbiter. The paper will consider a variety of examples in which deep logical disputes re-emerge at the meta-level. One case is quantified modal logic, where some varieties of actualism require a modal meta-language (as opposed to the usual non-modal language of possible worlds model theory) in order not to make their denial of the Barcan formula self-defeating. Similarly, on some views the intended model theory for second-order logic can only be given in a second-order metalanguage—this may be needed to avoid versions of Russell’s paradox when the first-order quantifiers are read as absolutely unrestricted. It can be shown that the phenomenon of higher-order vagueness eventually forces fuzzy logical treatments of vagueness to use a fuzzy metalanguage, with consequent repercussions for what first-order principles are validated. The difficulty of proving the completeness of first-order intuitionistic logic on its intended interpretation by intuitionistically rather than just classically valid means is a more familiar example. These case studies will be discussed in some detail to reveal a variety of ways in which even metalogic is metaphysically contested, substantial and non-neutral. (shrink)

A fairly simple theory of the semantics of tense is obtained by combining three claims: (i) for any time t, a present-tense sentence `p' is either true or false at t; (ii) for any time t0 earlier than t, the future-tense sentence `It will be the case that p at t' is true at t0 if `p' is true at t, false otherwise; (iii) for any time t0 later than t, the past-tense sentence `It was the case that p at (...) t' is true at t0 if `p' is true at t, false otherwise. This theory, which has been called the theory of timeless truth, is often dismissed on the basis of its alleged incapacity to comply with indeterminism. Here, instead, it will be suggested that there is no reason to be dismissive. Section 1 provides some elucidations about the theory. Sections 2 and 3 explain how a foregone objection to it can be resisted. Sections 4 and 5 show that there is a plausible sense in which (i)-(iii) are compatible with indeterminism. Sections 6 and 7 dispel some misunderstandings that may lead to think that indeterminism is not vindicated in some important sense other than that outlined. (shrink)

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...) to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such (...) as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. ​. (shrink)

Evans distinguishes between superficial necessity and deep necessity in his analysis of the contingent a priori. The distinction between these two notions of necessity is formalized by Davies and Humberstone through the addition of the operator Fixedly to Actuality Modal Logic (AML, S5A), where deep necessity is represented by the combination Fixedly Actually. Wehmeier’s Subjunctive Modal Logic (SML) provides an extension of the expressive capacity of ordinary modal predicate logic alternative to AML. I add Fixedly to SML and show that (...) in the system SML with Fixedly the distinction between deep and superficial necessity disappears. I conclude that the existence of the distinction between deep and superficial necessity, as well as the existence of the contingent a priori, cannot be asserted independently of the choice of background logic. (shrink)

Necessitism is the view that necessarily everything is necessarily something; contingentism is the negation of necessitism. The dispute between them is reminiscent of, but clearer than, the more familiar one between possibilism and actualism. A mapping often used to ‘translate’ actualist discourse into possibilist discourse is adapted to map every sentence of a first-order modal language to a sentence the contingentist (but not the necessitist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables (...) the necessitist to extract a ‘cash value’ from what the contingentist says. Similarly, a mapping often used to ‘translate’ possibilist discourse into actualist discourse is adapted to map every sentence of the language to a sentence the necessitist (but not the contingentist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables the contingentist to extract a ‘cash value’ from what the necessitist says. Neither mapping is a translation in the usual sense, since necessitists and contingentists use the same language with the same meanings. The former mapping is extended to a second-order modal language under a plural interpretation of the second-order variables. It is proved that the latter mapping cannot be. Thus although the necessitist can extract a ‘cash value’ from what the contingentist says in the second-order language, the contingentist cannot extract a ‘cash value’ from some of what the necessitist says, even when it raises significant questions. This poses contingentism a serious challenge. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)

In this critical review I discuss the main themes of the papers in Kit Fine's Modality and Tense: Philosophical Papers. These themes are that modal operators are intelligible in their own right and that actualist quantifiers are to be taken as basic with respect to possibilist quantifiers. I also discuss a previously unpublished paper of Fine's on modality and existence.

The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of (...) discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia. Building on recent work by Christopher Menzel (Synthese 85 (1990)), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension. I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adequate, and yet is at the same time more ontologically frugal, it is certainly to be preferred. (shrink)

The word 'actually' often refers to what is in fact the case, but it also often points to what would have been the case in a possible situation that is being envisaged. To capture such nuances, the formal languages discussed in the paper add subscripts to modal operators; in the model theory the subscripts allow an actuality operator to turn the evaluation of a formula to a world introduced by a preceding possibility or necessity operator having the same subscript. The (...) paper covers both propositional and predicate logic and proves the completeness of axiomatizations that extend standard modal systems beginning with K. (shrink)

I define 'skim semantics' to be a Davidson-style truth-conditional semantics combined with a variety of deflationism about truth. The expressive role of truth in truth-conditional semantics precludes at least some kinds of skim semantics; thus I reject the idea that the challenge to skim semantics derives solely from Davidson's explanatory ambitions, and in particular from the 'truth doctrine', the view that the concept of truth plays a central explanatory role in Davidsonian theories of meaning for a language. The fate of (...) skim semantics is not determined by the fate of the truth doctrine, so rejecting the truth doctrine does not in itself open the way to skim semantics. I establish my thesis by showing that some recently proposed versions of skim semantics fail because of truth's expressive role. I also discuss the conditions that might permit skim semantics. (shrink)

It seems to be an obvious truth that There could be something that doesn't actually exist.That is, it seems to be obiously true that ◊∃×).It is sufficient for the truth of that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do and suchlike statements involve a commitment to possibilia, (...) to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which and its ilk commit us? These simple little questions are at the tip of an iceberg. (shrink)

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as (...) multiple indexing or quantification over times. (shrink)

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are (...) adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis' counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics. (shrink)

To give a good account of deductive inference, we need to recognise two new relations, one in the realm of contents, the other in the psychological realm of mental action. When these new relations are properly coordinated, they can supply an account of what it is for a thinker to be making a deductive inference. The account endorses the condition that in deductive reasoning, a thinker must take the premises to support the conclusion. The account is distinguished from the positions (...) of Broome, Ryle, and Wright. (shrink)

The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.

If we wish to formulate an axiomatic truth-theory interpreting a modal language and treat the symbol of necessity as a sentential operator and not as a quantifier over possible worlds, there arise various problems. These are due partly to the fact that words could have meant something other than what they actually mean and partly to certain principles of modal metaphysics. One of those principles is existentialism about propositions: a proposition that is expressed in a sentence containing a non-empty name (...) could not exist if the referent of the name did not exist. The paper explains how the problems arise. It also explains how we can avoid them using substitutional quantification in the metalanguage. The truth-theory we can construct in that way is compositional and homophonic, and its theorems interpreting the various sentences of the modal language are derived in a straightforward way. The paper develops one such theory for a propositional modal language and one for a first-order modal language. The first-order case involves a number of intricacies that are discussed. (shrink)

This paper develops some modal metatheory for quantified modal logic. In such a theory, the logic of a first-order modal object-language is made sensitive to the modal facts, stated in the metalanguage. This is radically different from possible worlds semantics, which reduces questions of validity to questions of nonmodal set theory. We consider theories which characterize a notion of truth under a second-order interpretation, where an operator for metaphysical necessity is treated homophonically. The form they take is crucially influenced by (...) whether the Barcan formulas are part of the metalogic. The main result is that, with the Barcan formulas, formulating a modal metatheory is easy; principles of classical semantics transfer over smoothly with natural adaptations to the modal setting. Without the Barcan formulas, it seems to be much harder. Several options are considered, but each involves commitments plausibly in tension with the underlying philosophical motivations for rejecting them. (shrink)

This paper examines the potential for abstracting propositions – an as yet untested way of defending the realist thesis that propositions as abstract entities exist. I motivate why we should want to abstract propositions and make clear, by basing an account on the neo-Fregean programme in arithmetic, what ontological and epistemological advantages a realist can gain from this. I then raise a series of problems for the abstraction that ultimately have serious repercussions for realism about propositions in general. I first (...) identify problems about the number of entities able to be abstracted using these techniques. I then focus on how issues of language relativity result in problems akin to the Caesar problem in arithmetic by exposing circularity and modal concern over the status of the criterion of identity for propositions. (shrink)

In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that abstract mathematical objects exist. I wish to defend a particular objection to such arguments that has become increasingly popular recently. It is called instrumental nominalism. I consider the recent versions of this view and conclude that it has yet to be given an adequate formulation. I provide such a formulation and show that it can be used to answer the indispensability arguments. -/- There (...) are two main indispensability arguments in the literature, though one has received nearly all of the attention. They correspond to two ways in which we use mathematics in science and in everyday life. We use mathematical language to help us describe non-mathematical reality; and we use mathematical reasoning to help us perform inferences concerning non-mathematical reality using only a feasible amount of cognitive power. The former use is the starting point of the Quine-Putnam indispensability argument ([Quine, 1980a], [Quine, 1980b], [Quine, 1981a], [Quine, 1981b], [Putnam, 1979a], [Putnam, 1979b]); the latter provides the basis for Ketland’s more recent argument ([Ketland, 2005]). I begin by considering the Quine-Putnam argument and introduce instrumental nominalism to defuse it. Then I show that Ketland’s argument can be defused in a similar way. (shrink)

In the paper (Braüner, 2001) we gave a minimal condition for the existence of a homophonic theory of truth for a modal or tense logic. In the present paper we generalise this result to arbitrary modal logics and we also show that a modal logic permits the existence of a homophonic theory of truth if and only if it permits the definition of a socalled master modality. Moreover, we explore a connection between the master modality and hybrid logic: We show (...) that if attention is restricted to bidirectional frames, then the expressive power of the master modality is exactly what is needed to translate the bounded fragment of first-order logic into hybrid logic in a truth preserving way. We believe that this throws new light on Arthur Prior's fourth grade tense logic. (shrink)

We investigate and compare two major approaches to enhancing the expressive capacities of modal languages, namely the addition of subjunctive markers on the one hand, and the addition of scope-bearing actuality operators, on the other. It turns out that the subjunctive marker approach is not only every bit as versatile as the actuality operator approach, but that it in fact outperforms its rival in the context of cross-world predication.

Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...) of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion. (shrink)

In this paper, I explore Rosen’s ‘transcendental’ objection to constructive empiricism—the argument that in order to be a constructive empiricist, one must be ontologically committed to just the sort of abstract, mathematical objects constructive empiricism seems committed to denying. In particular, I assess Bueno’s ‘partial structures’ response to Rosen, and argue that such a strategy cannot succeed, on the grounds that it cannot provide an adequate metalogic for our scientific discourse. I conclude by arguing that this result provides some interesting (...) consequences in general for anti-realist programmes in the philosophy of science.Keywords: Constructive empiricism; Mathematical fictionalism; Partial structures; Modality. (shrink)

Modal primitivists hold that some modal truths are primitively true. They thus seem to face a special epistemological problem: how can primitive modal truths be known? The epistemological objection has not been adequately developed in the literature. I undertake to develop the objection, and then to argue that the best formulation of the epistemological objection targets all realists about modality, rather than the primitivist alone. Furthermore, the moves available to reductionists in response to the objection are also available to primitivists. (...) I conclude by suggesting that extant theories of the epistemology of modality are not sensitive to the question of primitivism versus reductionism. (shrink)

§1. Introduction. By means of what semantic features is a proper name tied to its bearer? This is a puzzling question indeed: proper names — like “Aristotle” or “Paris” — are syntactically simple, and it therefore does not seem possible to reduce their meanings, by means of a principle of compositionality, to the meanings of more basic, and hence perhaps more tractable, linguistic elements.

For the sentences of languages that contain operators that express the concepts of definiteness and indefiniteness, there is an unavoidable tension between a truth-theoretic semantics that delivers truth conditions for those sentences that capture their propositional contents and any model-theoretic semantics that has a story to tell about how indetifiniteness in a constituent affects the semantic value of sentences which imbed it. But semantic theories of both kinds play essential roles, so the tension needs to be resolved. I argue that (...) it is the truth theory which correctly characterises the notion of truth, per se. When we take into account the considerations required to bring model theory into harmony with truth theory, those considerations undermine the arguments standardly used to motivate supervaluational model theories designed to validate classical logic. But those considerations also show that celebration would be premature for advocates of the most frequently encountered rival approach - many-valued model theory. (shrink)