The project of grounding necessity in essence often goes together with the model of essence that assimilates the constitutive essence of an object to the definition of it. The paper argues that if the grounding project is to succeed, the definitional model must be questioned. Like any object whatever, a concrete individual is necessarily identical to that individual. It is argued that this necessity can have an essential ground only if the primitive identity property of it or its thisness is (...) essential to it, and the thisness is in its constitutive essence while not in the definition of it. A concrete individual is in essence partly definable but not fully explainable, for the definition of it forms a crucial part of its constitutive essence, but the constitutive essence includes something fundamental beyond definition or explanation. The definitional model must give way to a model of essence that accommodates this. (shrink)

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)

It is common to argue that something x is distinct from something y by pointing out that x and y do not share all their essential properties. I show that arguments of this type are unsound. This unsoundness is rooted in the fact that sentences of the form ‘x is essentially F’ are ambiguous. Under one reading, the sentence says of x that it has a property of a unique and special kind. Interpreted in that way, the sentence is false, (...) for there are no such properties. Under another reading, the sentence says of x that it has a property and adds that this property is essential to x. Interpreted in that way, the sentence may be true but it does not allow to reach the desired conclusion that x is distinct from y. Thus, if someone argues that x is distinct from y by pointing out that x and y differ in essential properties, they face the following dilemma: either one of the argument’s premises implies the existence of the special property and it is false, or none of the premises implies the existence of the special property and the argument is invalid. (shrink)

This essay reassesses the relation between Kant and Kripke on the relation between necessity and the a priori. Kripke famously argues against what he takes to be the traditional view that a statement is necessary only if it is a priori, where, very roughly, what it means for a statement to be necessary is that it is true and could not have been false and what it means for a statement to be a priori is that it is knowable independently (...) of experience. Call such a view the Entailment Thesis. Along with many Kant scholars, Kripke thinks that Kant endorses the Entailment Thesis. Thus Kripke and many others take his arguments against the Entailment Thesis to tell against Kant and to mark an important point of disagreement with him. I will argue that this is a mistake. Kant does not endorse the Entailment Thesis that Kripke and many others attribute to him. He does endorse two quite different theses concerning the relation between necessity and the a priori, as he conceives them. One is a matter of definition and the other is a very substantial philosophical thesis indeed—to establish it is the aim of the entire Critique of Pure Reason. But Kripke’s arguments against the Entailment Thesis tell against neither of Kant’s theses, as they involve crucially different conceptions of necessity and the a priori. This superficial lack of disagreement masks deep disagreements, but these result from divergent views regarding matters such as realism, modal epistemology, and philosophical methodology; views which Kant does a lot, and Kripke very little, to argue for. (shrink)

The Introduction to "Knowledge, Number and Reality. Encounters with the Work of Keith Hossack" provides an overview over Hossack's work and the contributions to the volume.

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 three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for (...) identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part. (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)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

The dissertation is in the format of a collection of several academic texts, composed of a two-part presentation and three papers on the topic of conceivability and the epistemology of modality. The presentation is composed of, first, a general introduction to conceivability theses and objections and, second, a discussion of two cases. Following the presentation, Asger provides three papers. The first paper, Pretense and Conceivability: A reply to Roca-Royes, presents a problem and a dilemma for Roca-Royes’ Non-Standard Dilemma for conceivability-based (...) epistemologies of de re modality in which she concludes that conceivability cannot be the whole story of our de re modal knowledge. The second paper, Conceivability Externalized, proposes an externalist conceivability-based epistemology of possibility inspired by Stalnaker. The third paper, Inconceivability as a Guide to Impossibility, considers inconceivability as an epistemic guide to impossibility, aiming to explore and add support to the underexplored thesis that one can justify beliefs about the impossibility of P on the basis of the inconceivability of P. (shrink)

I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.

Gideon Rosen has recently sketched an argument which aims to establish that the notion of metaphysical modality is systematically ambiguous. His argument contains a crucial sub-argument which has been used to argue for Metaphysical Contingentism, the view that some claims of fundamental metaphysics are metaphysically contingent rather than necessary. In this paper, Rosen’s argument is explicated in detail and it is argued that the most straight-forward reconstruction fails to support its intended conclusion. Two possible ways to save the argument are (...) rebutted and it is furthermore argued that the crucial sub-argument only supports a rather particular variant of Metaphysical Contingentism. (shrink)

We show, that given two fundamental theses of Kripke, no statement of the form ‘‘a=b’ is necessarily true’, is true, if ‘a’ and ‘b’ are distinct rigid designators.

In this paper, I argue that adherents of Patrick Toner’s hylemorphic animalism who also assent to orthodox Christology and a thesis about the necessity of identity must reject a prima facie plausible theological possibility held by Ockham, entertained in one form by St. Thomas Aquinas, and recently held by Richard Cross, Thomas Flint,, and, and Timothy Pawl and concerning which individual concrete human natures an omnipotent God could assume.

In this paper, I examine Ruth Barcan Marcus's early formal work on modal systems and the deduction theorem, both for the material and the strict conditional. Marcus proved that the deduction theorem for the material conditional does not hold for system S2 but holds for S4. This last result is at odds with the recent claim that without proper restrictions the deduction theorem fails also for S4. I explain where the contrast stems from. For the strict conditional, Marcus proved the (...) deduction theorem for S4 though restricted to arguments with necessary premises. I discuss Marcus's result and analyze her philosophical position on the significance of the deduction theorem for modal systems designed to express the notion of deducibility. (shrink)

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS and show (...) that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal. (shrink)

In a growing number of papers, one encounters arguments to the effect that certain philosophical views are objectionable because they would imply that there are necessary truths for whose necessity there is no explanation. That is, they imply that there are propositions p such that (a) it is necessary that p, but (b) there is no explanation why it is necessary that p. For short, they imply that there are “brute necessities.” Therefore, the arguments conclude, the views in question should (...) be rejected in favor of rival views under which the necessities would be explained. This style of argument raises a number of important and difficult questions. Do necessary truths really require explanation? Are they not paradigms of truths that either need no explanation or automatically have one, being in some sense self‐explanatory? If some necessary truths do require or admit of explanation, what types of explanation, are available? Are some necessary truths explained by other necessary truths? Are some necessary truths self‐explanatory? Are all necessary truths either self‐explanatory or explained by others? Or are there some necessary truths that are truly brute? This article surveys several representative arguments from brute necessity as well as a variety of answers to the questions above, noting their bearing on arguments from bruteness. (shrink)

This paper provides an overview of the history of the notion of essence in 20th century analytic philosophy, focusing on views held by influential analytic philosophers who discussed, or relied on essence or cognate notions in their works. It in particular covers Russell and Moore’s different approaches to essence before and after breaking with British idealism, the (pre- and post-)logical positivists’ critique of metaphysics and rejection of essence (Wittgenstein, Carnap, Schlick, Stebbing), the tendency to loosen the notion of logical necessity (...) to accommodate certain metaphysical truths in Wittgenstein and others, Quine’s logical rehabilitation of metaphysics and criticism of de re modality, the modal view of essence promoted by the development of quantified modal logic (C. I. Lewis, Barcan Marcus, Kripke) and direct reference theory (Barcan Marcus, Kripke, Putnam), and the emergence of the notion of metaphysical necessity (Kneale, Kripke), and finally Fine’s re-establishment of a Neo-Aristotelian, hyperintensional notion of essence in contemporary metaphysics. (shrink)

Although Kripke’s œuvre has had a major impact on analytic philosophy and nearly every aspect of his studies has been thoroughly examined, this does not hold for his schmidentity argument, which, so far, has been widely neglected. To the extent to which it has been treated at all, it has been for the most part radically misunderstood. I hold that this argument, in its correctly reconstructed form, has general relevance for a treatment of Frege’s Puzzle and points towards a fundamental (...) methodological restriction for philosophy of language and especially for semantics, as far as informativity and the general topic of cognitive significance are concerned. To show this, I will briefly set out the context of the schmidentity argument and, in Sects. 2 and 4, sketch a reconstruction thereof, including some criticisms of the argument, and an excursion about Kit Fine’s semantic relationism, which stands in stark contrast to this paper’s central claim. Moreover, I will draw a genuinely new and probably quite unexpected conclusion from all the above, to finally give a glimpse at a bigger picture of where this conclusion should lead our thinking about a theoretical treatment of informativity and a linguistic expression’s cognitive value. (shrink)

According to anti-individualism, the basic building blocks of the world are not individuals. The anti-individualist argues that standard, individual-entailing claims–for instance, that Theia is a cat–are mistaken in presupposing that there are individuals, but that such claims correspond to statements in a feature-placing language devoid of these presuppositions. Instead, the world is entirely made up of non-individualistic features–structurally akin to familiar examples such as it's raining or it's snowing–that are arranged in particular ways. Since features do not carve out individual (...) differences, however, this seems to entail that there is a class of statements in an individualistic language–statements expressing mere differences in which object is which–the members of which all correspond to the same anti-individualist description. That is, anti-individualism seems to entail anti-haecceitism, according to which all differences in ways the world could be supervene on qualitative differences. In this paper, I argue that, on the contrary, the anti-individualist has the resources to accommodate non-qualitative differences among ways the world could be. Moreover, haecceitistic anti-individualism does justice to the motivations for rejecting individuals while nevertheless accommodating intuitions that certain kinds of scenarios are metaphysically distinct. (shrink)

Standard arguments for essentialism with respect to natural kinds such as gold, star, water or tiger enlist essentialist principles or essentialist intuitions. I argue that we need neither. All it takes to establish essentialism for the kinds in question are insights from science and semantics. Semantics establishes that natural kind predicates such as “is gold” or “is a star” are paradigm terms whose application conditions are relationally determined, object involving, and actuality dependent. Science assures us that a posteriori hypotheses such (...) as “∀x” are deeply explanatory, as well as true. Taken together, these results establish essentialism for kinds such as gold, star, water or tiger. I consider this a deflationary result. When it comes to natural kind essentialism, there is no need for substantial metaphysics, be it essentialist or otherwise. (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.

U radu se nudi opis konteksta unutar kojeg je formuliran poznati dokaz za nužnost identiteta. Iznosi se formalni prikaz ovog dokaza kako ga je formulirao poznati filozof i logičar Saul Kripke. Također se razmatra gledište filozofa Allana Gibbarda koji nasuprot Kripkeu brani tvrdnju da neki iskazi identiteta mogu biti kontingentni. Osnovni cilj rada je upoznati domaćeg čitatelja s formalnim aspektom rasprave o nužnosti identiteta te dati kratki pregled konteksta unutar kojeg su formulirani argumenti za nužnost identiteta. In the paper, we (...) offer an overview of the context within which the well-known proof of the necessity of identity is formulated. A formal account of this proof is presented as formulated by the renowned philosopher and logician Saul Kripke. Furthermore, we discuss the account of the philosopher Allan Gibbard, who defends the claim that some statements of identity can be contingent. The main goal of the paper is to acquaint the readers who understand the Croatian language with the formal aspect of the discussion on the necessity of identity and to give a brief overview of the context within which the arguments for the necessity of identity are formulated. (shrink)