This paper draws attention to a proof of the necessity of identity given by Arthur Prior. In its simplicity, it is comparable to a proof of Quine's, popularised by Kripke, but it is slightly different. Prior's Polish notation is transcribed into a more familiar idiom. Prior's proof is followed by a proof of the necessity of difference, possibly the first such proof in the literature, which is also repeated here and transcribed. The paper concludes with a brief discussion of Prior's (...) views on identity and difference over time. (shrink)

This essay considers Kant’s theory of modality in light of a debate in contemporary modal metaphysics and modal logic concerning the Barcan formulas. The comparison provides a new and fruitful perspective on Kant’s complex and sometimes confusing claims about possibility and necessity. Two central Kantian principles provide the starting point for the comparison: that the possible must be grounded in the actual and that existence is not a real predicate. Both are shown to be intimately connected to the Barcan formulas, (...) and Kant’s views on what he distinguishes as three different kinds of modality are then considered in light of this connection. (shrink)

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

In a recent article forthcoming in *Mind*, Leech (2020) presents a challenge for essentialist accounts of metaphysical modality: why should it be that essences imply corresponding necessities? Leech’s main focus is to argue that one cannot overcome the challenge by utilizing an account of essence in terms of generalized identity due to Correia and Skiles (2019), on pain of circularity. In this reply, we will show how to use identity-based essentialism to bridge ‘epistemic’ and ‘explanatory’ understandings of this alleged essence-to-necessity (...) gap without circularity, Leech’s arguments notwithstanding. We do so by first presenting a novel proof that generalized identities imply corresponding necessities. We then propose several substantive identity-based explanations of how it is, exactly, that essences imply necessities. -/- . (shrink)

Many metaphysicians maintain that there is a close connection between essence and modality; if an object a necessarily bears property F , then it is metaphysically necessary that Fa (or, perhaps, it is metaphysically necessary that Fa if a exists). Recently, Leech (Forthcoming) has argued that this connection lacks an adequate explanation. In particular, she argues that identity doesn't explain the link between essence and modality. In contrast, I argue that identity provides the resources to undermine Leech’s explanatory demand.

An essentialist theory of modality claims that the source of possibility and necessity lies in essence, where essence is then not to be defined in terms of necessity. Hence such theories owe us an account of why it is that the essences of things give rise to necessities in the way required. A new approach to understanding essence in terms of the notion of generalized identity promises to answer this challenge by appeal to the necessity of identity. I explore the (...) prospects for this approach, and argue that it fails. If one favours an account of essence in terms of generalized identity, then one will not, I argue, be able to satisfactorily defend an essentialist theory of modality against the challenge; if one wishes to defend an essentialist theory of modality, and thereby to give an explanation of how necessity arises from essence, one should not understand essence in terms of generalized identity. (shrink)

Some people think that grounding is a type of identity. And some people think that grounding connections hold necessarily. I show that, under plausible assumptions, if grounding is a type of identity, then grounding connections hold necessarily.

The subject of this paper is the epistemology of identity: a general theory of knowledge, evidence and justification for the claim that one thing is identical to another. Although identity figures significantly in our epistemic lives, this is a topic that, to the best of my knowledge, has gone entirely unexplored. Initial attempts to integrate such an epistemology into existing theories of evidence---many of which are tailor-made for contingent propositions---are confounded by the necessity of identity. I defend a restricted form (...) of skepticism according to which the only knowable identity claims are trivial. (shrink)

ABSTRACT An apparent objection against my theory of instantiation as partial identity is that identity is necessary, yet instantiation is often contingent. To rebut the objection, I show how it can make sense that identity is contingent. I begin by showing how it can make sense that identity is temporary. I rely heavily on Andre Gallois’s formal theory of occasional identity, but argue that there is a gap in his explanation of how his formalisms make sense that needs to be (...) filled by appeal to my theory of Aspects. (shrink)

When the necessity of identity (NI) is combined with composition as identity (CAI), the contingency of composition (CC) is at risk. In the extant literature, either NI is seen as the basis for a refutation of CAI or CAI is associated with a theory of modality, such that: either NI is renounced (if counterpart theory is adopted); or CC is renounced (if the theory of modal parts is adopted). In this paper, we investigate the prospects of a new variety of (...) CAI, which aims to preserve both NI and CC. This new variety of CAI (CCAI, contingent composition as identity) is the quite natural product of the attempt to make sense of CAI on the background of a broadly Kripkean view of modality, such that one and the same entity is allowed to exist at more than one possible world. CCAI introduces a world-relative kind of identity, which is different from standard identity, and claims that composition is this kind of world-relative identity. CCAI manages to preserve NI and CC. We compare CCAI with Gibbard’s and Gallois’ doctrines of contingent identity and we show that CCAI can be sensibly interpreted as a form of Weak CAI, that is of the thesis that composition is not standard identity, yet is significantly similar to it. (shrink)

As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing (...) the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory. (shrink)

In 1901 Russell had envisaged the new analytic philosophy as uniquely systematic, borrowing the methods of science and mathematics. A century later, have Russell’s hopes become reality? David Lewis is often celebrated as a great systematic metaphysician, his influence proof that we live in a heyday of systematic philosophy. But, we argue, this common belief is misguided: Lewis was not a systematic philosopher, and he didn’t want to be. Although some aspects of his philosophy are systematic, mainly his pluriverse of (...) possible worlds and its many applications, that systematicity was due to the influence of his teacher Quine, who really was an heir to Russell. Drawing upon Lewis’s posthumous papers and his correspondence as well as the published record, we show that Lewis’s non- Quinean influences, including G.E. Moore and D.M. Armstrong, led Lewis to an anti- systematic methodology which leaves each philosopher’s views and starting points to his or her own personal conscience. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

There is a certain argument against the principle of the indiscernibility of identicals, or the thesis that whatever is true of a thing is true of anything identical with that thing. In this argument, PInI is used together with the self-evident principle of the necessity of self-identity to reach the conclusion, which is held to be paradoxical and, thus, fatal to PInI. My purpose is to show that the argument in question does not have this consequence. Further, I argue that (...) PInI is a universally valid principle which can be used to prove the necessity of identity. (shrink)

An odd dissensus between confident metaphysicians and neopragmatist antimetaphysicians pervades early twenty-first century analytic philosophy. Each faction is convinced their side has won the day, but both are mistaken about the philosophical legacy of the twentieth century. More historical awareness is needed to overcome the current dissensus. Lewis and his possible-world system are lionised by metaphysicians; Quine’s pragmatist scruples about heavy-duty metaphysics inspire antimetaphysicians. But Lewis developed his system under the influence of his teacher Quine, inheriting from him his empiricism, (...) his physicalism, his metaontology, and, I will show in this paper, also his Humeanism. Using published as well as never-before-seen unpublished sources, I will make apparent that both heavy-duty metaphysicians and neopragmatist antimetaphysicians are wrong about the roles Quine and Lewis played in the development of twentieth-century philosophy. The two are much more alike than is commonly supposed, and Quine much more instrumental to the pedigree of current metaphysics. (shrink)

Suppose that all non-qualitative facts are grounded in qualitative facts. I argue that this view naturally comes with a picture in which trans-world identity is indeterminate. But this in turn leads to either pervasive indeterminacy in the non-qualitative, or else contingency in what facts about modality and possible worlds are determinate.

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This paper outlines a novel solution to the Ship of Theseus puzzle. The solution relies on situations, a philosophical tool used in natural language semantics among other places. The core idea is that what is true is always relative to the situation under consideration. I begin by outlining the problem before briefly introducing situations. I then present the solution: in smaller situations the candidate is identical to Theseus’s ship. But in larger situations containing both candidates these identities are neither true (...) nor false. Finally, I discuss some worries for the view that arise from the nature of identity, and suggest responses. It is concluded that the solution, and the theory that underpins it, are worth further investigation. (shrink)

This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...) is part of. This framework allows us to define the familiar Ockhamist temporal/modal connectives, most notably for past, future, and settledness. The novelty of our framework becomes visible in our discussion of substances in branching histories, i.e., in its first-order part. That discussion shows how the basic idea of tracing an individual thing from case to case via an absolute property is applicable in a branching histories framework. We stress the importance of keeping apart extensionality and moment-definiteness, and give a formal account of how the specification of natural sortals and natural qualities turns out to be a coordination task in BH-CIFOL. We also provide a detailed answer to Lewis’s well-known argument against branching histories, exposing the fallacy in that argument. (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...) classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

“The confusion of a logical with a real predicate,” according to the Critique of Pure Reason, “is almost beyond correction”. Kant did not assert that existence is no predicate, but that it is only a “logical” one, and not a “real” one. Much the same thing has been said about identity, although Kant himself thought it is real and not logical. We have long lacked a rigorous criterion to distinguish real from logical predicates, and hence have not been able to (...) say why the difference matters. This paper has two objects. First it provides a demarcation between real and logical predicates that confirms Kant's dictum that existence is only “logical.” Secondly it states the theory of a “logical” relation of identity. Perhaps this is not the only identity relation. I show only that once it has been precisely defined in the right setting, there are definite answers to a number of disputed questions about identity. Maybe there are other concepts of identity for which different answers are to be given, but I shall not discuss that disagreeable prospect here. A third application concerns the ontological argument. (shrink)

In this paper, presented at an APA colloquium in Boston on December 28, 1994, it is argued that Ruth Barcan Marcus' 1961 article on Modalities and Intensional Languages originated many of the key ideas of the New Theory of Reference that have often been attributed to Saul Kripke and others. For example, Marcus argued that names are directly referential and are not equivalent to contingent descriptions, that names are rigid designators, and that identity sentences with co-referring names are necessary if (...) true. She also first presented the modal argument that names are directly referential, the epistemic argument that names are directly referential, and the argument that there area posteriori necessities. (shrink)

I compare three sorts of case in which philosophers have argued that we cannot assert the Law of Excluded Middle for statements of identity. Adherents of Smooth Infinitesimal Analysis deny that Excluded Middle holds for statements saying that an infinitesimal is identical with zero. Derek Parfit contended that, in certain sci-fi scenarios, the Law does not hold for some statements of personal identity. He also claimed that it fails for the statement ‘England in 1065 was the same nation as England (...) in 1067’. I argue that none of these cases poses a serious threat to Excluded Middle. My analysis of the last example casts doubt on the principle of the Determinacy of Distinctness. While David Wiggins's ‘conceptualist realism’ provides a metaphysics which can dispense with that principle, it leaves no house-room for infinitesimals. (shrink)

Analytic philosophy in the mid-twentieth century underwent a major change of direction when a prior consensus in favour of extensionalism and descriptivism made way for approaches using direct reference, the necessity of identity, and modal logic. All three were first defended, in the analytic tradition, by one woman, Ruth Barcan Marcus. But analytic philosophers now tend to credit them to Kripke, or Kripke and Carnap. I argue that seeing Barcan Marcus in her historical context – one dominated by extensionalism and (...) descriptivism – allows us to see how revolutionary she was, in her work and influence on others. I focus on her debate with Quine, who found himself retreating to softened, and more viable, versions of his anti-modal arguments as a result. I make the case that Barcan's formal logic was philosophically well-motivated, connected to her views on reference, and well-matched to her overall views on ontology. Her nominalism led her to reject posits which could not be directly observed and named, such as possibilia. She conceived of modal calculi as facilitating counterfactual discourse about actual existents. I conclude that her contributions ought to be recognized as the first of their kind. Barcan Marcus must be awarded a central place in the canon of analytic philosophy. (shrink)

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. (...) This result raises the question: For which normal modal logics L can one axiomatize the quantified propositional modal logic determined by the complete modal algebras for L? (shrink)

Today there appears to be a widespread impression that W. V. Quine's notorious critique of modal logic, based on certain ideas about reference, has been successfully answered. As one writer put it some years ago: “His objections have been dead for a while, even though they have not yet been completely buried.” What is supposed to have killed off the critique? Some would cite the development of a new ‘possible-worlds’ model theory for modal logics in the 1960s; others, the development (...) of new ‘direct’ theories of reference for names in the 1970s.These developments do suggest that Quine's unfriendliness towards any formal logics but the classical and indifference towards theories of reference for any singular terms but variables were unfortunate. (shrink)

On the one hand, philosophers have presented numerous apparent examples of indeterminate individuation, i.e., examples in which two things are neither determinately identical nor determinately distinct. On the other hand, some have argued against even the coherence of the very idea of indeterminate individuation. This paper defends the possibility of indeterminate individuation against Evans’s argument and some other arguments. The Determinacy of Identity—the thesis that identical things are determinately identical—is distinguished from the Determinacy of Distinctness—the thesis that distinct things are (...) determinately distinct. It is argued that while the first thesis holds universally and there is no case of indeterminate identity, there are reasons to think that the second thesis does not hold universally, and that there are cases of indeterminate distinctness. (shrink)

Since the publication of Kit Fine's “Essence and Modality”, there has been lively debate over how best to think of essence in relation to necessity. The present aim is to draw attention to a definition of essence in terms of modality that has not been given sufficient attention. This neglect is perhaps unsurprising, since it is not a proposal made in response to Fine's 1994 paper and ensuing discussion, but harks back to Ruth Barcan Marcus's earlier work in the 1960s (...) and 1970s on essentialist claims. At the core of Barcan Marcus's account is Minimal Essentialism, of which there are several extensions, in particular, for cases of referential predicates (such as “x is identical to Socrates”), Individuating Essentialism, and Aristotelian Essentialism. I argue that Minimal Essentialism fares favourably against a host of familiar examples. I close with some historical observations, that the distinction between essence and necessity was already commonplace in the early days of quantified modal logic and its philosophy. (shrink)

The literature suggests two main answers to the question of what it is for a material object to be located at a region of spacetime. Both have a number of virtues. However, both suffer from well-known problems. According to one answer, location is a primitive relation with no informative metaphysical analysis. But this makes a number of necessary truths seem mysterious and leaves them unexplained. According to the other answer, to be located at a region is just to be identical (...) to that region. But this is inconsistent with a number of independently plausible theses about material objects and their locations. In this paper, I explore a new theory of location and argue that it has the virtues of these familiar theories but not their vices. I then explore some further connections the new theory has with some contemporary issues in metaphysics. (shrink)

Core principles of mereology have been questioned by appealing to time travel scenarios. This paper questions the methodology of employing time travel scenarios to argue against mereology. We show some time travel scenarios are structurally equivalent to more standard ones not involving time travel; and that the three main theories about persistence through time can each solve both the time travel scenario as well as the structurally similar classical scenario. Time travel scenarios that are not similar to more standard arguments (...) are instead problematic because they are open to different, incompatible interpretations. We conclude that compared to the classical arguments against mereological principles, time travel scenarios do not add anything new. (shrink)

Efforts to include women in the canon have long been beset by reactionary gatekeeping, typified by the charge “That's not philosophy.” That charge doesn't apply to early and mid‐analytic female philosophers—Welby, Ladd‐Franklin, Bryant, Jones, de Laguna, Stebbing, Ambrose, MacDonald—with job titles like lecturer in logic and professor of philosophy and publications in Mind, the Journal of Philosophy, and Proceedings of the Aristotelian Society. It's hopeless to dismiss their work as “not philosophy.” But comparable reactionary gatekeeping affects them, this paper argues, (...) typified by the labels “bad philosophy” and “derivative philosophy.” Virtue and vice epistemology help explain why these women have been neglected and why their own approaches are epistemically virtuous. Their contemporaries and historians are deficient in scholarly virtues in labelling these women's work “bad” or derived from male mentors with no or specious justification. Their disparaged qualities—intellectual humility, modesty, critical self‐reflection, disclosing biases—are often epistemic virtues. (shrink)

The so-called New Theory of Reference (Marcus, Kripke etc.) is inspired by the insight that in modal and intensional contexts quantifiers presuppose nondescriptive unanalyzable identity criteria which do not reduce to any descriptive conditions. From this valid insight the New Theorists fallaciously move to the idea that free singular terms can exhibit a built-in direct reference and that there is even a special class of singular terms (proper names) necessarily exhibiting direct reference. This fallacious move has been encouraged by a (...) mistaken belief in the substitutional interpretation of quantifiers, by the myth of thede re reference, and a mistaken assimilation of direct reference to ostensive (perspectival) identification. Thede dicto vs.de re contrast does not involve direct reference, being merely a matter of rule-ordering (scope).The New Theorists' thesis of the necessity of identities of directly referred-to individuals is a consequence of an unmotivated and arbitrary restriction they tacitly impose on the identification of individuals. (shrink)

I present a novel argument against the non-contingency of identity. I first argue that the necessity of distinctness is intimately connected with numerous paradoxes of recombination. In particular, I argue that those who reject the necessity of distinctness have natural solutions to various paradoxes of recombination which have plagued the metaphysics of modality. Moreover, I argue that adding the necessity of distinctness to modest, paradox-free assumptions is sufficient to reinstate the paradoxes. Given that identity is non-contingent only if distinctness is (...) necessary, I suggest this constitutes new evidence against the non-contingency of identity. (shrink)

ABSTRACT Analytic philosophy in the mid-twentieth century underwent a major change of direction when a prior consensus in favour of extensionalism and descriptivism made way for approaches using direct reference, the necessity of identity, and modal logic. All three were first defended, in the analytic tradition, by one woman, Ruth Barcan Marcus. But analytic philosophers now tend to credit them to Kripke, or Kripke and Carnap. I argue that seeing Barcan Marcus in her historical context – one dominated by extensionalism (...) and descriptivism – allows us to see how revolutionary she was, in her work and influence on others. I focus on her debate with Quine, who found himself retreating to softened, and more viable, versions of his anti-modal arguments as a result. I make the case that Barcan's formal logic was philosophically well-motivated, connected to her views on reference, and well-matched to her overall views on ontology. Her nominalism led her to reject posits which could not be directly observed and named, such as possibilia. She conceived of modal calculi as facilitating counterfactual discourse about actual existents. I conclude that her contributions ought to be recognized as the first of their kind. Barcan Marcus must be awarded a central place in the canon of analytic philosophy. (shrink)

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates (...) and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

The aim of this paper is to relate the debate about the status of S4 and S5 as modal logics for metaphysical modality to the debate about the identity of propositions. The necessary truth of the characteristic axioms of S4 and S5 (when interpreted in terms of metaphysical modality) is derived from a view about the identity of propositions, the view that necessarily equivalent propositions are identical.

Ten philosophical sonnets.Export citation.

In his paper “Has Austin Refuted the Sense-Datum Theory?” A. J. Ayer contends that the argument from illusion calls attention to perspectival distortion, perceptual misidentification and elusive perceptual belief only in order to establish the possibility of perceptual error. Pointing to our occasional perceptual failures reminds us that perceptual error is always logically possible—that any particular perceptual belief to the effect that one is perceiving a physical surface could be mistaken. This in turn is thought by Ayer to show that (...) the ordinary belief that we perceive physical surfaces requires qualification—along lines urged by sense-datum philosophers—to the effect that even in those situations properly described for non-philosophical purposes as perceptions of physical surfaces it cannot be physical surfaces that are literally present to one's senses. Ayer believes that this can be established, for any given case, by the possibility of perceptual error alone. (shrink)

This essay examines an argument of perennial importance against naive Leibnizian absolute identity theory, originating with Ruth Barcan in 1947 (Barcan, R. 1947. ?The identity of individuals in a strict functional 3 calculus of second order?, Journal of Symbolic Logic, 12, 12?15), and developed by Arthur Prior in 1962 (Prior, A.N. 1962. Formal Logic. Oxford: The Clarendon Press), presented here in the form offered by Nicholas Griffin in his 1977 book, Relative Identity (Griffin, N. 1977. Relative Identity. Oxford: The Clarendon (...) Press). The objection considers the property of being necessarily identical to a specific object a as a counterexample to Leibnizian identity conditions, and more particularly to the indiscernibility of identicals, when it is only contingently true that a=b. The inquiry eliminates necessity and reference to a specifically designated object as responsible for the counterexample, leaving only identity. The requirements for an exact reinterpretation of Leibniz's Law in light of counterexamples involving converse intentional properties and the family of properties suggested by the property of being necessarily identical to a where a=b (or an equivalent definite descriptor variation) is only logically contingently true, are formalized in a more powerful, counterexample-resistant version of Leibniz's Law that does not succumb to relative identity as a necessary alternative motivated by desperation over the failure of the absolute identity principle. (shrink)

One well-known objection to supersubstantivalism is that it is inconsistent with the contingency of location. This paper presents a new objection to supersubstantivalism: it is inconsistent with the vagueness of location. Though contingency and vagueness are formally similar, there are important philosophical differences between the two. As a result, the objection from vague location will be structurally different than the objection from contingent location. The paper explores these differences and then defends the argument that supersubstantivalism is inconsistent with the plausible (...) thesis that it is vague where I am located. (shrink)

There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...) showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (Necinc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO-f which does not validate (Necinc). An Appendix discusses (Necinc) in relation to counterpart theory. Of course, it would be a mistake to think that the rules for "multiple pointing" follow automatically from the rules for pointing proper. Max Black—The Elusiveness of Sets In some influential articles during the 1980s George Boolos proposed an interpretation of monadic second-order logic in terms of plural quantification [4, 5]. One objection to this proposal, pressed by Williamson [22, 456-7], focuses on the modal behaviour of plural variables, arguing that the proposed interpretation yields the wrong results in respect of the modal status of atomic predications. In the present paper I will present this objection and argue against it. In the course of developing the argument, I will have cause to consider the under-investigated question of how a logic for plurals should be extended to incorporate modal operators. (shrink)