Scientific anti-realists who appeal to the pessimistic induction (PI) claim that the theoretical terms of past scientific theories often fail to refer to anything. But on standard views in philosophy of language, such reference failures prima facie lead to certain sentences being neither true nor false. Thus, if these standard views are correct, then the conclusion of the PI should be that significant chunks of current theories are truth-valueless. But that is semantic anti-realism about scientific discourse—a position most philosophers of (...) science, anti-realists included, consider anathema today. Therefore, proponents of the PI confront a dilemma: either accept semantic anti-realism or reject common semantic views. I examine strategies (with particular emphasis on supervaluations) for the PI proponent to either lessen the sting of this argument, or learn to live with it. 1 Introduction2 Designation Failure 2.1 Designation failure leads to truth-valueless sentences2.1.1 Direct reference theory2.1.2 Fregeanism2.1.3 Accounts of reference-fixing: why ‘phlogiston’ fails to designate 2.2 Objection: sentences exhibiting designation failure are false not truth-valueless 2.3 Avoiding truth-valuelessness via controversial semantic positions3 What to do? Closing the Gaps4 Conclusion. (shrink)

A number of important philosophical problems are problems in the overlap of logic and ontology. Both logic and ontology are diverse fields within philosophy, and partly because of this there is not one single philosophical problem about the relation between logic and ontology. In this survey article we will first discuss what different philosophical projects are carried out under the headings of "logic" and "ontology" and then we will look at several areas where logic and ontology overlap.

This paper outlines a defense of hybrid contingentism: that it is contingent which individuals there are, but not contingent what properties there are. Critics pursue two main lines of complaint. First, that the hybrid contingentist’s treatment of haecceitistic properties is metaphysically mysterious, and second, that hybrid contingentism involves an unjustified asymmetry in the associated modal logic. I suggest that these complaints may be too quick, at least in the setting of higher-order metaphysics. It is not at all obvious whether and (...) to what extent we should expect particular "symmetries" across the orders, and so whether (as Williamson (2013) argues) “the default preference is for a uniform metaphysics, on which being is contingent at all orders or none.”. (shrink)

Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that the domain of interpretation is not empty, every name denotes exactly one object in the domain and the quantifiers have existential import. Free logics usually reject the claim that names need to denote in, and of the systems considered in this paper, the positive free logic concedes that (...) some atomic formulas containing non-denoting names are true, while negative free logic rejects even the latter claim. Inclusive logics, which reject, are likewise considered. These logics have complex and varied axiomatizations and semantics, and the goal of this paper is to present an orderly examination of the various systems and their mutual relations. This is done by first offering a formalization, using sequent calculi which possess all the desired structural properties of a good proof system, including admissibility of contraction and cut, while streamlining free logics in a way no other approach has. We then present a simple and unified system of abstract semantics, which allows for a straightforward demonstration of the meta-theoretical properties, and offers insights into the relationship between different logics. The final part of this paper is dedicated to extending the system with modalities by using a labeled sequent calculus, and here we are again able to map out the different approaches and their mutual relations using the same framework. (shrink)

Confused terms appear to signify more than one entity. Carnap maintained that any putative name that is associated with more than one object in a relevant universe of discourse fails to be a genuine name. Although many philosophers have agreed with Carnap, they have not always agreed among themselves about the truth-values of atomic sentences containing such terms. Some hold that such atomic sentences are always false, and others claim they are always truth-valueless. Field maintained that confused terms can still (...) refer, albeit partially, and offered a supervaluational account of their semantic properties on which some atomic sentences with confused terms can be true. After outlining many of the most important theoretical considerations for and against various semantic theories for such terms, we report the results of a study designed to investigate which of these accounts best accords with the truth-value judgments of ordinary language users about sentences containing these terms. We found that naïve participants view confused names as capable of successfully referring to one or more objects. Thus, semantic theories that judge them to involve total reference failure do not comport well with patterns of ordinary usage. (shrink)

In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain - outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent (...) statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails. (shrink)

The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds (...) of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9), and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification. (shrink)

In Popper's Logik der Forschung, a theoretical system is a set of sentences that describe a particular sub-area of science, in particular of empirical science. The goal of axiomatizing a theoretical system is to specify a small number of "axioms" describing all presuppositions of the sub-area under consideration, so that all other sentences of this system can be derived from them by means of logical or mathematical transformations. The paper discusses two philosophical interpretations of these proper axioms. First, proper axioms (...) stipulate the use of the signs for the basic concepts of the system. Consequently, the proper axioms turn out to be analytic relative to a class of interpretations of the underlying logic. Hence, they cannot be falsified by refuting their logical consequences because these consequences are analytic as well. Secondly, proper axioms are synthetic, falsifiable and uncertain sentences. Hence, they are not immunized against falsification by refuting their logical consequences. (shrink)

The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional expressions. (...) The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism.

The logic of singular terms that refer to nothing, such as ‘Santa Claus,’ has been studied extensively under the heading of free logic. The present essay examines expressions whose reference is defective in a different way: they signify more than one entity. The bulk of the effort aims to develop an acceptable formal semantics based upon an intuitive idea introduced informally by Hartry Field and discussed by Joseph Camp; the basic strategy is to use supervaluations. This idea, as it stands, (...) encounters difficulties, but with suitable refinements it can be salvaged. Two other options for a formal semantics of multiply signifying terms are also presented, and I discuss the relative merits of the three semantics briefly. Finally, possible modifications to the standard logical regimentation of the notion of existence are considered. (shrink)

The practice of thought experimentation plays a central role in contemporary philosophical methodology. Many philosophers rely on thought experimentation as their primary and even sole procedure for testing theories about the natures of properties and relations. This test procedure involves entertaining hypothetical cases in imaginative thought and then undergoing intuitions about the distribution of properties and relations in them. A theory’s comporting with an intuition is treated as evidence in favour of it; but a clash is treated as evidence against (...) the theory and may even be regarded as falsifying it. -/- The epistemic power of thought experimentation is mysterious. How can experiments carried out within the mind enable us to discover truths about the natures of properties and relations like knowledge, causation, personal identity, reference, meaning, consciousness, beauty, justice, morality, and free will? This epistemological challenge is urgent, but a model of philosophical thought experimentation would seem to be a necessary propaedeutic to any serious discussion of it. An adequate model would make the relevant test procedure explicit, thereby assisting in the identification of points of potential epistemic vulnerability. -/- In this monograph I advance the propaedeutical model-building work already done by Timothy Williamson, Anna-Sara Malmgren, and Jonathan Ichikawa and Benjamin Jarvis. Following the lead of these philosophers, I focus on a single Gettier-style thought experiment and the problem of identifying the real content of the Gettier intuition. My first contribution is to establish the inadequacy of all of the existing models. Each of them, I argue, fails to solve the content problem. It emerges from my discussion, however, that Ichikawa and Jarvis’s truth in fiction approach holds out the prospect of a solution. -/- My second contribution is to develop and defend a new way of implementing the general idea behind the truth in fiction approach. The model I put forward does a better overall job of modelling Gettier-style thought experiments than any of the existing models. It has none of the defects which render those models inadequate and Iam unable to find any major defects peculiar to it. This should make us feel confident that my model is adequate. Moreover, since the Gettier-style thought experiment I focus on is paradigmatic, we should also feel confident that my model will generalise naturally to other philosophical thought experiments. (shrink)

This paper examines to what extent Davidsonian truth-theoretic semantics can give an adequate account for empty names in natural languages. It argues that the prospect is dim because of a tension between metaphysical austerity, non-vacuousness of theorems and empirical adequacy. Sainsbury (2005) proposed a Davidsonian account of empty names called ‘Reference Without Referents’ (RWR), which explicates reference in terms of reference-condition rather than referent, thus avoiding the issue of existence. This is an inspiring account. However, it meets several difficulties. First, (...) there is no non-vacuous, interpretive truth-condition available for any T-sentence containing an empty name, because by stipulation there is no way to compose a true atomic sentence using an empty name in RWR. The absence of an interpretive truth-condition implies the absence of an interpretive reference-condition. It also entails empirical inadequacy to support an interpretation because the related propositional attitude can never be truly satisfied. These considerations cast doubt on whether truth is the proper vehicle to articulate meaning. This paper suggests that we can alleviating the problem by employing truth-conditions varying across contexts of utterance, rather than just contexts of evaluation. The result is a two-dimensional model-theoretic approach to empty names. It involves a new function coined counterfactual reference and the account is compatible with both descriptivism and Millianism. (shrink)

This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about (...) mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle of indefinite extensibility; section 2 develops and clarifies the metasemantics of quantifier variance; section 3 solves section 1's puzzle of indefinite extensibility by applying section 2's account of quantifier meanings; and section 4 compares the theory developed in section 3 to several other theories in the literature. (shrink)

The structuralist conception of metaphysics holds that it aims to uncover the ultimate structure of reality and explain how the world's richness and variety are accounted for by that ultimate structure. On this conception, metaphysicians produce fundamental theories, the primitive, undefined expressions of which are supposed to 'carve reality at its joints', as it were. On this conception, ontological questions are understood as questions about what there is, where the existential quantifier 'there is' has a fundamental, joint-carving interpretation. Structuralist orthodoxy (...) holds that there is exactly one fundamental, joint-carving interpretation that an existential quantifier could have. This orthodox assumption could go wrong--either by there being too few fundamental-quantifier interpretations, or by there being too many. In this dissertation I examine the implications of these non-orthodox options. Someone who thinks there are too many fundamental-quantifier interpretations might think this means standard ontological debates are in some sense defective of 'merely verbal', or she might think instead that the different quantifiers show that there are different 'ways' or 'modes' of being. I argue that the first option runs into problems with a certain sort of realism about logic, but that there is no general problem with the second option, despite its longstanding bad philosophical reputation. I also argue that realism about logic gives us reason to think the dispute between someone who thinks there are many 'modes of being' in this sense and someone who thinks there is just one is not itself verbal. Finally, I turn to the case in which there are no fundamental quantifiers, arguing that it brings with it a host of theoretical problems we could avoid with quantifiers. (shrink)

Ontological pluralism is the doctrine that there are different ways or modes of being. In contemporary guise, it is the doctrine that a logically perspicuous description of reality will use multiple quantifiers which cannot be thought of as ranging over a single domain. Although thought defeated for some time, recent defenses have shown a number of arguments against the view unsound. However, another worry looms: that despite looking like an attractive alternative, ontological pluralism is really no different than its counterpart, (...) ontological monism. In this paper, after explaining the worry in detail, I argue that considerations dealing with the nature of the logic ontological pluralists ought to endorse, coupled with an attractive philosophical thesis about the relationship between logic and metaphysics, show this worry to be unfounded. (shrink)

A‐theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A‐theorists. It is commonly thought that A‐theories can only be formally expressed in a tense logic: a logic with operators like P and F . And it seems natural to think that we live in a world where objects come to exist (...) and cease to exist as time passes. Indeed, this is typically a key component of the most prominent kind of A‐theory, presentism. But the temporary existence assumption cannot be upheld in any tense logic with a standard quantification theory. I will explain the problem and outline the philosophical and logical considerations that generate it. I will then consider two possible solutions to the problem – one that targets our logic of quantification and one that targets our assumptions about change. I survey the costs of each solution. (shrink)

This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.

This article presents a sequent calculus for a negative free logic with identity, called N . The main theorem (in part 1) is the admissibility of the Cut-rule. The second part of this essay is devoted to proofs of soundness, compactness and completeness of N relative to a standard semantics for negative free logic.

In section III of Pryor 2006a, I argued against the view that the mere fact that a thought- type is hyper-reliable directly gives one justification to believe a thought of that type. A close alternative says that our merely appreciating that the thought-type is hyper-reliable directly gives us that justification.