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)

The grounding relation is routinely characterized by means of logical postulates. The aim of this paper is twofold. First, I show that a subset of those postulates is incompatible with a minimal characterization of metaphysical modality. Then I consider a number of ways for reconciling ground with modality. The simplest and most elegant solution consists in adopting serious actualism, which is best captured within a first-order modal language with predicate abstraction governed by negative free logic. I also explore a number (...) of alternative strategies by revising the ground-theoretic postulates, while keeping the modal ones fixed. As I argue, each of those strategies is either unviable, highly contentious, or insufficiently motivated. (shrink)

Aspects of kripke's recent work in philosophy are considered in connection with the formal approach he set forth over a decade ago regarding semantics for modal logic. An ambiguity is pointed out concerning kripke's intuitive test for rigid designators and it is argued that, Relative to an appropriate framework for considering actual and possible physical objects, Certain proper names fail to be rigid designators.

In this paper certain aspects of rigidity are studied through Hintikka’s work in modal semantics. The paper surveys Hintikka’s extraordinary struggles with rigidity from the late 50’s to this millennium. I argue that Hintikka’s many ambivalent remarks concerning rigidity become more comprehensible if, first, three different variants of rigidity are distinguished and, second, Hintikka’s largely implicit doctrine of semantic neo-Kantianism is made explicit.

In his published work and even more in conversations, Tarski emphasized what he thought were important philosophical aspects of his work. The English translation of his more philosophical papers [56m] was dedicated to his teacher Tadeusz Kotarbinski, and in informal discussions of philosophy he often referred to the influence of Kotarbinski. Also, the influence of Leiniewski, his dissertation adviser, is evident in his early papers. Moreover, some of his important papers of the 1930s were initially given to philosophical audiences. For (...) example, the famous monograph on the concepotf truth ([33”], [35b]) was first given as twol ectures to the Logic Section of the Philosophical Society in Warsaw in 1930. Second, his paper [33], which introduced the concepts of co-consistency and co-completeness as well as the rule of infinite induction: was first given at the Second Conference of the Polish Philosophical Society in Warsaw in 1927. Also [35c] was based upon an address given in 1934 to the conference for the Unity of Science in Prague; C361 and [36a] summarize an address given at the International Congress of Scientific Philosophy in Paris in 1935. The article [44a] was published in a philosophical journal and widely reprinted in philosophical texts. This list is of course not exhaustiveb ut only representative of Tarski’s philosophical interactions as reflected in lectures given to philosophical audiences, which were later embodied in substantial papers. After 1945 almost all of Tarski’s publications and presentations are mathematical in character with one or two minor exceptions. This division, occurring about 1945, does not, however, indicate al oss of interest in philosophical questionbsu t is a result of Tarski’s moving to the Department of Mathematics at Berkeley. There he assumed an important role in the development of logic within mathematics in the United States. (shrink)

I discuss Stalnaker’s views on modality. In particular, his views on actualism, anti-essentialism, counterpart theory, and the Barcan formulas.

Counterpart theory is often advertised by its track record at solving metaphysical puzzles. Here I focus on puzzles of occasional identity, wherein distinct individuals at one world or time appear to be identical at another world or time. To solve these puzzles, the usual interpretation rules of counterpart theory must be extended beyond the simple language of quantified modal logic. I present a more comprehensive semantics that allows talking about specific times and worlds, that takes into account the multiplicity and (...) sortal-dependence of counterpart relations, and that does not require names to denote actual or present individuals. In addition, the semantics I defend does not identify ordinary individuals with world-bound or time-bound stages and thereby avoids the most controversial aspect of counterpart theory. Humphrey’s counterpart at other worlds or times is none other than Humphrey himself. (shrink)

This paper is a criticism of Plantinga’s analysis of a version of the ontological argument. He thinks it is obvious that his version is valid and that the only question of interest is whether a key premise is true. The paper lays out two relevant semantical accounts of modal logic. It contends that Plantinga needs to show that one is preferable to the other.

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

I explore options for a plenitudinarian solution to the Paradox of Flexible Origin Essentialism, taking as my unlikely starting point the views of Sarah-Jane Leslie, who holds that if plenitudinarianism is true, then there is in fact no paradox to be solved, only the illusion of one. The first three sections are expository: Sect. 1 on plenitudinarianism, Sect. 2 on the paradox, and Sect. 3 on Leslie’s views about how plenitudinarianism bears on the paradox. In Sect. 4, I reject the (...) contention that there is no paradox and critically explore three options for a plenitudinarian solution. In Sect. 5, I argue that the plenitudinarian ought to endorse a fourth option. In Sect. 6, I consider an objection. I endorse neither plenitudinarianism nor its denial; the main aim of the paper is to argue that for one who does endorse plenitudinarianism, the best solution to the Paradox of Flexible Origin Essentialism is clear. (shrink)

On its usual interpretation, the Barcan Formula—◊∃_xB_ → ∃_x_◊_B_—says that, if there could have been something that is such and such a way, then there is something that could have been that way. It is traditionally held that contingentist actualists should—indeed, must—reject the Barcan Formula. I argue that contingentist actualists should—indeed, must—endorse the Barcan Formula, at least assuming a standard, Tarskian conception of truth and truth preservation. I end by proposing a logic for contingentist actualists that validates the Barcan Formula. (...) This logic has the surprising feature of also validating the Converse Barcan Formula, □∀_xB_ → ∀_x_□_B_, while still invalidating related formulas—such as □∀_x_□∃_y x_ = _y_ (NNE)—that contingentist actualists should reject. It does this by employing models with fixed domains but assignments to the identity predicate that vary across worlds. (shrink)

In a short exchange published in 2000, Richard Rorty and Robert Brandom differed over the status of “facts” in a world containing no speakers and, hence, no speech acts. While Brandom wanted to retain the meaningfulness of talk of “facts” or “truths” about things—in this case truths about photons —in a world in which there could be no claimings about such things, Rorty denied the existence of any such “worldly items” as “facts.” In this essay the difference between Rorty and (...) Brandom on this issue is used to explore their differing attitudes to modality. Brandom appeals to a Kantian approach of modal realism to support counterfactual claims. However, I argue that when his approach to modality is examined in the context of current debates over possible world semantics, his own “incompatibilist” semantics itself seems incompatible with a Kantian approach to modality. In turn, I suggest that this difference between Brandom and Rorty in their attitudes to modality reveals a difference in their respective attitudes to pragmatism’s relation to philosophy in general. (shrink)

In the 1930s, C. I. Lewis, who was responsible for the revival of modal logic in the era of modern symbolic logic, characterized ‘intensional’ approaches to logic as typical of post-Leibnizian ‘continental philosophy’, in contrast to the ‘extensionalist’ approaches dominant in the British tradition. Indeed Lewis’s own work in this area had been inspired by the logic of his teacher, the American ‘Absolute Idealist’, Josiah Royce. Hegel’s ‘Subjective Logic’ in Book III of hisScience of Logic, can, I suggest, be considered (...) as an intensional modal logic, and this paper explores parallels between it and a later variety of modal logic—tenselogic, as developed by Arthur Prior in the 1950s and 60s. Like Lewis, Prior too had been influenced in this area by a teacher with strong Hegelian leanings—John N. Findlay. Treated as anintensional logic, Hegel’s subjective logic can be used as a framework for addressing issues ofintentionality—the mind’s capacity to be intentionally directed to objects. In this way, I suggest that the structures of his subjective logic can clarify what is at issue in the ‘Psychology’ section of theEncyclopaediaPhilosophy of Subjective Spirit. (shrink)

Here, I suggest a hitherto relatively unexplored way beyond the opposed Aristotelian realist and Kantian idealist approaches that divide recent interpretations of the categories or “thought determinations” of Hegel’s Logic, by locating his idealism within the terrain of recent debates in modal metaphysics. In particular, I return to the outlook of the first philosopher to attempt to bring Hegel into the analytic conversation, John Niemeyer Findlay, and consider Hegel’s idealism as instantiating the metaphysical position that, following the work of Findlay’s (...) former student, Arthur Prior, has come to be called “modal actualism”. (shrink)

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion of semantics into syntax. The charge is shown to be mistaken. It is argued on inferentialist grounds that labelled deductive systems are as syntactically (...) pure as any formal system in which the rules define the meanings of the logical constants. (shrink)

One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics using non-normal worlds (...) of different kinds. (shrink)

David Lewis’s counterpart-theoretic semantics for quantified modal logic is motivated originally by worries about identifying objects across possible worlds; the counterpart relation is grounded more cautiously on comparative similarity. The possibility of contingent identity is an unsought -- and in some eyes, unwelcome -- consequence of this approach. In this paper I motivate a Kripkean counterpart theory by way of defending the prior, pre-theoretical, coherence of contingent directness. Contingent identity follows for free. The theory is Kripkean in that the counterpart (...) relation is in a sense stipulated rather than grounded on similarity, and is such that no object has more than one counterpart at a world. This avoids a number of objections Fara and Williamson have recently levelled against counterpart theory generally; their other objections are addressed by enriching the theory with special quantifiers and actuality operators. (shrink)

Standard approaches to possible-world semantics allow us to define necessity and logical truth, but analyticity is considerably more difficult to account for. The source of this difficulty lies in the received model-theoretical conception of a language interpretation. In intuitive terms, analyticity amounts to truth in virtue of meaning alone, i.e. solely in virtue of the interpretation of linguistic expressions. In other words, an analytic sentence should remain true under all variations of ‘extralinguistic reality’ as long as the interpretation is kept (...) constant. However, the received conception of an interpretation as a mapping from language to a model frame hinders keeping the interpretation constant while varying other components of the model. To make room for analyticity, the concept of an interpretation should therefore be revised. The latter should be made richer in content than it has usually been assumed. As a by-product, this revision also gives us a one-dimensional analogue of the influential two-dimensional account of a priori. We are thus able to map out the network of formal connections between the notions of analyticity, apriority, logical truth and necessity. (shrink)

This essay argues that relativist semantics provide fruitful frameworks for the study of the relationships between meaning and truth-conditions, and consequently for the analysis of the logical properties of expressions. After a discussion of the role of intensionality and indexicality within classic double-indexed semantics, I explain that the non-relativistic identification of the parameters needed for the definition of truth and for the interpretation of indexicals is grounded on considerations that are irrelevant for the assessment of the relationships between meaning and (...) truth. (shrink)

A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs (EGs). The contribution of the gamma part of EGs to the study of modalities is examined. Some ramifications of Peirce’s remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce’s unpublished manuscript on modality from 1901.

A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs. The contribution of the GAMMA part of EGs to the study of modalities is examined. Some ramifications of Peirce's remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce's unpublished manuscript on modality from 1901.

According to the zombie conceivability argument, phenomenal zombies are conceivable, and hence possible, and hence physicalism is false. Critics of the conceivability argument have responded by denying either that zombies are conceivable or that they are possible. Much of the controversy hinges on how to establish and understand what is conceivable, what is possible, and the link between the two—matters that are at least as obscure and controversial as whether consciousness is physical. Because of this, the debate over physicalism is (...) unlikely to be resolved by thinking about zombies—or at least, zombies as discussed by philosophers to date.



In this paper, I explore an alternative strategy against the zombie conceivability argument. I accept the possibility of zombies and ask whether that possibility is accessible (in the sense of ‘accessible’ used in possible world semantics) to our world. It turns out that the question of whether zombie worlds are accessible to our world is equivalent to the question of whether physicalism is true. By assuming that zombie worlds are accessible to our world, supporters of the zombie conceivability argument beg the question against physicalists. I will then consider what happens if a supporter of the zombie conceivability argument should insist that zombie worlds are accessible to our world. I will argue that the same ingredients used in the zombie conceivability argument—whatever they might be—can be used to construct an argument to the opposite conclusion. If that is correct, we reach a stalemate between physicalism and property dualism: while the possibility of some zombies entails property dualism, the possibility of other creatures entails physicalism. Since these two possibilities are inconsistent, one of them is not genuine. To resolve this stalemate, we need more than thought experiments. (shrink)

I argue that metaphysicians of mind have not done justice to the notion of accessibility between possible worlds. Once accessibility is given its due, physicalism must be reformulated and conceivability arguments must be reevaluated. To reach these conclusions, I explore a novel way of assessing the zombie conceivability argument. I accept that zombies are possible and ask whether that possibility is accessible from our world in the sense of ‘accessible’ used in possible world semantics. It turns out that the question (...) whether zombie worlds are accessible from our world is equivalent to the question whether physicalism is true at our world. By assuming that zombie worlds are accessible from our world, proponents of the zombie conceivability argument beg the question against physicalism. In other words, it is a mistake to assume that the metaphysical possibility of zombies entails that physicalism is false at our world. I will then consider what happens if a proponent of the zombie conceivability argument should insist that zombie worlds are accessible from our world. I will argue that the same ingredients used in the zombie conceivability argument—whatever exactly they might be—can be used to construct an argument to the opposite conclusion. At that point, we reach a stalemate between physicalism and property dualism: while the possibility of zombies entails property dualism, the possibility of other creatures entails physicalism. Since these two possibilities are mutually inconsistent, either one of them is not genuine or one of them is inaccessible from the actual world. To resolve this stalemate, we need more than traditional conceivability arguments. (shrink)

A series of recent studies have explored the impact of people's judgments regarding physical law, morality, and probability. Surprisingly, such studies indicate that these three apparently unrelated types of judgments often have precisely the same impact. We argue that these findings provide evidence for a more general hypothesis about the kind of cognition people use to think about possibilities. Specifically, we suggest that this aspect of people's cognition is best understood using an idea developed within work in the formal semantics (...) tradition, namely the notion of modality. On the view we propose, people may have separate representations for physical, moral and probabilistic considerations, but they also integrate these various considerations into a unified representation of modality. (shrink)

A frequent criticism of Richard Vallee’s “pluri-propositionalism” is that it multiplies propositions beyond necessity. I argue that this criticism, recently voiced by Robert Stanton and Arthur Sullivan, is based in misconceptions about propositions are and how they help us classify utterances and the mental states and events that lead to them, relying for the most part on extended discussions of examples.

Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory (...) and similar tools of the analysis of language should be understood as capturing the semantically relevant, especially inferential, structure of language. From this vantage point, the reader gains a new light on many of the traditional concepts and problems of logic and philosophy of language, such as meaning, reference, truth and the nature of formal logic. (shrink)

L.E.J. Brouwer famously took the subject’s intuition of time to be foundational and from there ventured to build up mathematics. Despite being largely critical of formal methods, Brouwer valued axiomatic systems for their use in both communication and memory. Through the Dutch Mathematical Society, Gerrit Mannoury posed a challenge in 1927 to provide an axiomatization of intuitionistic arithmetic. Arend Heyting’s 1928 axiomatization was chosen as the winner and has since enjoyed the status of being the de facto formalization of intuitionistic (...) arithmetic. We argue that axiomatizations of intuitionistic arithmetic ought to make explicit the role of the subject’s activity in the intuitionistic arithmetical process. While Heyting Arithmetic is useful when we want to contrast constructed objects with platonistic ones, Heyting Arithmetic omits the contribution of the subject and thus falls short as a response to Mannoury’s challenge. We offer our own solution, Doxastic Heyting Arithmetic, or $${\textsf{DHA}}$$, which we contend axiomatizes Brouwerian intuitionistic arithmetic. (shrink)

Simple mass nouns are words like ‘water’, ‘furniture’ and ‘gold’. We can form complex mass noun phrases such as ‘dirty water’, ‘leaded gold’ and ‘green grass’. I do not propose to discuss the problems in giving a characterization of the words that are mass versus those that are not. For the purposes of this paper I shall make the following decrees: (a) nothing that is not a noun or noun phrase can be mass, (b) no abstract noun phrases are considered (...) mass, (c) words like ‘thing’, ‘entity’ and ‘object’ are not mass, (d) I shall not consider such words as ‘stuff’, ‘substance or ‘matter’, (e) measures on mass nouns (like ‘gallon of gasoline’, ‘blade of grass’, etc.) are not considered, (f) plurals of count terms are not considered mass. Within these limitations, we can say generally that mass noun phrases are those phrases that ‘much’ can be prefexed to, by ‘many’ cannot be prefexed to, without an0maly.l Semantically, such phrases usually have the property of collectiveness- they are true of any sum of things of which they are true ; and of divisiveness - they are true of any part (down to a certain limit) of things of which they are true. All of this, however, is only ‘generally speaking’ - I shall mostly use only the simple examples given above and ignore the problems in giving a complete characterization of mass nouns. In the paper I want to discuss some problems involved in casting English sentences containing mass nouns into some artificial language; but in order to do this we should have some anchoring framework on which to justify or reject a given proposal. The problem of finding an adequate language can be viewed as a case of translation (from English to the artificial language), where the translation relation must meet certain requirements. I shall suggest five such requirements; others could be added. (shrink)

This paper attacks the modal ontological argument, as advocated by Plantinga among others. Whereas other criticisms in the literature reject one of its premises, the present line is that the argument is invalid. This becomes apparent once we run the argument assuming fictionalism about possible worlds. Broadly speaking, the problem is that if one defines “x” as something that exists, it does not follow that there is anything satisfying the definition. Yet unlike non-modal ontological arguments, the modal argument commits this (...) “existential fallacy” not in relation to the definition of ‘God’. Rather, it occurs in relation to the modal facts quantified over within a Kripkean modal logic. In brief, we can describe the modal facts by whichever logic we prefer—yet it does not follow that there are genuine modal facts, as opposed to mere facts-according-to-the-fiction. A broader consequence of the discussion is that the existential fallacy is an issue for many projects in “armchair metaphysics.”. (shrink)

Summary This paper is intended to discuss the problems occurring in the relation between the notion of truth and the question of self-reference. To do this, we shall review Tarski's (T) convention and its related terminology. We shall clarify the relation between truth and extension in order to lead into the question of semantic paradoxes appearing in the theoretical models concerned with truth. Subsequently, we shall review the logical system which develops in the reformulation of the modal proposal of the (...) (T) convention. In closing, we shall critically examine Kripke's interpretation from the proposals made by Tarski. (shrink)

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like (...) FOL + K)in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics [40].We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness result for the entire family of classical first order modal systems in terms of them, circumventing some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of either neighborhood or relational frames). We argue that the semantical program that thus arises offers the first complete semantic unification of the family of classical first order modal logics. (shrink)

Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. It considers (...) often neglected issues, such as the need for a more general account of thede dicto-de re distinction, and quasi-indicators. Extended deductive capacities require a subdivision of Konolige''s notion of belief into two distinct technical notions,potential anddispositional belief. The former has to do with what an artificial agent could in principle come to actively believe, given enough time and its specific logical competence; the latter with what an agent can be assumed to believe with respect to a specific goal to be fulfilled. (shrink)

Many philosophers have claimed possible worlds semantics is incoherent because of insoluble problems involved in the notion of identifying a single individual in different worlds. One frequent approach to trans-world identification has been to assume that all the possible worlds, complete with their populations, are described by means of qualities alone prior to our considering the question of identification of the same individual in each world in which it exists. If we interpret possible worlds semantics in this way, trans-world identification (...) could only be accomplished on the basis of some properties the individual has uniquely in every world in which it exists. This becomes problematic since the individual doesn't have the same properties in every world. In ‘Naming and Necessity’ and ‘Identity and Necessity’ Saul Kripke rejects such an account of both possible worlds and trans-world identification, developing an alternative interpretation of the new semantics. His approach involves a distinction between referring expressions which designate different individuals in different worlds according to the distribution of properties within each world and referring expressions which designate the same individual in every world. (shrink)

Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional identity (...) than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation. (shrink)