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A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including $\mathsf {PA}$ [39], $\mathsf {ZF}$, $\mathsf {Z}_2$, and $\mathsf {KM}$ [6]. In this article we extend Enayat’s investigations to subsystems of these latter two theories. We prove that restricting the Comprehension schema of $\mathsf {Z}_2$ and $\mathsf {KM}$ gives non-tight theories. Specifically, we show that $\mathsf {GB}$ and $\mathsf {ACA}_0$ each admit different bi-interpretable extensions, (...) |
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Many accept David Lewis's (1983) claim that, among the candidate meanings for our predicates, some are more natural than others -- they do better or worse at ``carving nature at its joints''. Call this claim predicate naturalism. Disagreement remains over whether the notion of naturalness extends ``beyond the predicate'' (à la Sider, 2011). Are the candidate meanings of logical vocabulary also more or less natural? Call this claim logical naturalism. -/- One motivation for predicate naturalism comes from its supposed ability (...) |
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The other chapters in this volume discuss the important, but neglected, topic of systematicity in metaphysics. In this chapter I begin by taking a step back and asking: why is systematicity important in metaphysics? Assuming that metaphysics should be systematic, why is this the case? I canvas some answers that emerge naturally within contemporary philosophy and argue that none of them adequately explains why metaphysics should be systematic. I then turn to Kant’s account of systematicity for his explanation. I argue (...) |
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This dialogue explores the question of whether intentionality—the “ofness”, “aboutness”, or “directedness” of mental states—is a relation. We explore three views: the Naive View, on which intentionality is a relation to ordinary, everyday objects, facts, and other such items; the Abstract Contents View, on which intentionality is a relation to mind-independent abstract entities that are our contents; and the Aspect View, on which intentionality is a matter of having intentional states with particular (non-relational) aspects that are our contents. We consider (...) |
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In the Introduction to the Critique of Pure Reason Kant raises a famous question: how is metaphysics possible as a science? Kant posed this question for his predecessors in early modern philosophy. I raise this question anew for the resurgence of metaphysics within analytic philosophy. I begin by dividing the question of the possibility of metaphysics into separate questions about its semantic and epistemic possibility, and translate them into contemporary terms as: (1) Why do terms in metaphysical theories refer? (2) (...) |
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Unger’s Problem of the Many seems to show that the familiar macroscopic world is much stranger than it appears. From plausible theses about the boundaries of or- dinary objects, Unger drew the conclusion that wherever there seems to be just one cat, cloud, table, human, or thinker, really there are many millions; and likewise for any other familiar kind of individual. In Lewis’s hands, this puzzle was subtly altered by an appeal to vagueness or indeterminacy about the the boundaries of (...) |
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Categorial logic, as its name suggests, applies the techniques and machinery of category theory to topics traditionally classified as part of logic. We claim that these tools deserve attention from a greater range of philosophers than just the mathematical logicians. We support this claim with an example. In this paper we show how one particular tool from categorial logic---hyperdoctrines---suggests interesting metaphysics. Hyperdoctrines can provide semantics for quantified languages, but this account of quantification suggests a metaphysical picture quite different from the (...) |
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A major challenge in the philosophy of mathematics is to explain how mathematical language can pick out unique structures and acquire determinate content. In recent work, Button and Walsh have introduced a view they call ‘internalism’, according to which mathematical content is explained by internal categoricity results formulated and proven in second-order logic. In this paper, we critically examine the internalist response to the challenge and discuss the philosophical significance of internal categoricity results. Surprisingly, as we argue, while internalism arguably (...) |
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This chapter contains sections titled: Introduction Hegel's Introduction Sense Certainty Perception Force and Understanding Hegel's Epistemological Analysis in the Phenomenology of Spirit Conclusion References Further Reading. |
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This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine 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, (...) |
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This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine 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, (...) |
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Dasgupta poses a serious challenge to realism about natural properties. He argues that there is no acceptable explanation of why natural properties deserve the value realists assign to them and are consequently absent of value. In response, this paper defines and defends an alternative non-explanatory account of normativity compatible with realism. Unlike Lewis and Sider, who believe it is sufficient to defend realism solely on realist terms, I engage with the challenge on unfriendly grounds by revealing a tu quoque. Dasgupta (...) |
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Kripkenstein’s challenge is usually described as being essentially about the use of a word in new kinds of cases ‒ the old kinds of cases being commonly considered as non-problematic. I show that this way of conceiving the challenge is neither true to Kripke’s intentions nor philosophically defensible: the Kripkean skeptic can question my answering “125” to the question “What is 68 plus 57?” even if that problem is one I have already encountered and answered. I then argue that once (...) |
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According to Sider, a question is metaphysically substantive just in case it has a single most natural answer. Recently, Barnes and Mikkola have argued that, given this notion of substantivity, many of the central questions in the metaphysics of gender are nonsubstantive. Specifically, it is plausible that gender pluralism—the view that there are multiple, equally natural gender kinds—is true, but this view seems incompatible with the substantivity of gender. The goal of this paper is to argue that the notion of (...) |
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In “Models and Reality” (1980), Putnam sketched a version of his internal realism as it might arise in the philosophy of mathematics. Here, I will develop that sketch. By combining Putnam’s model-theoretic arguments with Dummett’s reflections on Gödelian incompleteness, we arrive at (what I call) the Skolem-Gödel Antinomy. In brief: our mathematical concepts are perfectly precise; however, these perfectly precise mathematical concepts are manifested and acquired via a formal theory, which is understood in terms of a computable system of proof, (...) |
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Pancomputationalism is the view that everything is a computer. This, if true, poses some difficulties to the computational theory of cognition. In particular, the strongest version of it suggested by John Searle seems enough to trivialize computational cognitivists’ core idea on which our cognitive system is a computing system. The aim of this paper is to argue against Searle’s pancomputationalism. To achieve this, I will draw a line between realized computers and unrealized computers. Through this distinction, I expect that it (...) |
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The Russellian argument against the possibility of absolutely unrestricted quantification can be answered by the partisan of that quantification in an apparently easy way, namely, arguing that the objects used in the argument do not exist because they are defined in a viciously circular fashion. We show that taking this contention along as a premise and relying on an extremely intuitive Principle of Determinacy, it is possible to devise a reductio of the possibility of absolutely unrestricted quantification. Therefore, there are (...) |
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We can use radically different reference‐schemes to generate the same truth‐conditions for the sentences of a language. In this paper, we do three things. (1) Distinguish two arguments that deploy this observation to derive different conclusions. The first argues that reference is radically indeterminate: there is no fact of the matter what ordinary terms refer to. This threat is taken seriously and most contemporary metasemantic theories come with resources intended to rebut it. The second argues for radical parochialism about reference: (...) |
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The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which the green-hypothesis (...) |
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This dissertation is about human knowledge of reality. In particular, it argues that scientific knowledge is bounded by historically available instruments and theories; nevertheless, the use of several independent instruments and theories can provide access to the persistent potentialities of reality. The replicability of scientific observations and experiments allows us to obtain explorable evidence of robust entities and properties. The dissertation includes seven chapters. It also studies three cases – namely, Higgs bosons and hypothetical Ϝ-particles (section 2.4), the Ptolemaic and (...) |
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In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...) |
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In this paper, we offer a novel defense of descriptivism about reference. Our argument is based on principles about the relevance of speaker intentions to reference that are shared by many opponents of descriptivism, including Saul Kripke. We first show that two such principles that are plausibly endorsed by Kripke and other prominent externalists in fact entail descriptivism. The first principle states that when certain kinds of speaker intentions are present, they suffice to determine and explain reference. According to the (...) |
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On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order PA and Zermelo’s quasi-categoricity (...) |
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It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we can’t (...) |
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یکی از چالشهای حوزۀ زبان دینی به امکانِ جمع میان فرض تعالی و فرض ارجاع متعارف دینی برمیگردد. فرض تعالی مدعی است که ساحت الهی/مطلق به طور کامل از ساحت بشری/ممکن منفک است. فرض ارجاع متعارف دینی نیز مدعی است که میتوان به ساحت الهی/مطلق به شکل متعینی ارجاع داد. تردید در امکان جمعِ میان این دو از آنجا میآید که گویا مدعایی در ذهن هست که «اگر ساحتِ الهی/مطلق، به طور کامل از ساحتِ بشری/ممکن منفک باشد، آنگاه نمیتوان به (...) |
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This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for (...) |
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In this paper, I argue that Amie Thomasson’s Easy Ontology rests on a vicious circularity that is highly damaging. Easy Ontology invokes the idea of application conditions that give rise to analytic entailments. Such entailments can be used to answer ontological questions easily. I argue that the application conditions for basic terms are only circularly specifiable showing that Thomasson misses her self-set goal of preventing such a circularity. Using this circularity, I go on to show that Easy Ontology as a (...) |
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Few if any distinctions are more easily recognisable and assented to than that between _objects_, that is, things which are some ways, and that which they are, that is, _ways for objects to be_ (‘ways of being’ for short). In this paper I present an argument designed to show that this distinction is indeterminate in the sense that the truth-conditions of predicational sentences leave open what should count as an object and a way of being. The bulk of the argument (...) |
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This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. -/- In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical (...) |
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What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) |
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In this paper, I argue from a metasemantic principle to the existence of analytic sentences. According to the metasemantic principle, an external feature is relevant to determining which concept one expresses with an expression only if one is disposed to treat this feature as relevant. This entails that if one isn’t disposed to treat external features as relevant to determining which concept one expresses, and one still expresses a given concept, then something other than external features must determine that one (...) |
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The book is devoted to the contemporary stage of quantum mechanics – quantum information, and especially to its philosophical interpretation and comprehension: the first one of a series monographs about the philosophy of quantum information. The second will consider Be l l ’ s inequalities, their modified variants and similar to them relations. The beginning of quantum information was in the thirties of the last century. Its speed development has started over the last two decades. The main phenomenon is entanglement. (...) |
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The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) |
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Semantic realism can be characterised as the idea that scientific theories are truth-bearers, and that they are true or false in virtue of the world. This notion is often assumed, but rarely discussed in the literature. I examine how it fares in the context of the semantic view of theories and in connection with the literature on scientific representation. Making sense of semantic realism requires specifying the conditions of application of theoretical models, even for models that are not actually used, (...) |
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Putnam’s most famous contribution to mathematical logic was his role in investigating Hilbert’s Tenth Problem; Putnam is the ‘P’ in the MRDP Theorem. This volume, though, focusses mostly on Putnam’s work on the philosophy of logic and mathematics. It is a somewhat bumpy ride. Of the twelve papers, two scarcely mention Putnam. Three others focus primarily on Putnam’s ‘Mathematics without foundations’ (1967), but with no interplay between them. The remaining seven papers apparently tackle unrelated themes. Some of this disjointedness would (...) |
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The Tarskian notion of truth-in-a-model is the paradigm formal capture of our pre-theoretical notion of truth for semantic purposes. But what exactly makes Tarski’s construction so well suited for semantics is seldom discussed. In my Semantics, Metasemantics, Aboutness (OUP 2017) I articulate a certain requirement on the successful formal modeling of truth for semantics – “locality-per-reference” – against a background discussion of metasemantics and its relation to truth-conditional semantics. It is a requirement on any formal capture of sentential truth vis-à-vis (...) |
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Many think that expressivists have a special problem with negation. I disagree. For if there is a problem with negation, I argue, it is a problem shared by those who accept some plausible claims about the nature of intentionality. Whether there is any special problem for expressivists turns, I will argue, on whether facts about what truth-conditions beliefs have can explain facts about basic inferential relations among those beliefs. And I will suggest that the answer to this last question is, (...) |
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This paper discusses the relevance of supertask computation for the determinacy of arithmetic. Recent work in the philosophy of physics has made plausible the possibility of supertask computers, capable of running through infinitely many individual computations in a finite time. A natural thought is that, if supertask computers are possible, this implies that arithmetical truth is determinate. In this paper we argue, via a careful analysis of putative arguments from supertask computations to determinacy, that this natural thought is mistaken: supertasks (...) |
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Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper is (...) |
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The metaphysics of representation poses questions such as: in virtue of what does a sentence, picture, or mental state represent that the world is a certain way? In the first instance, I have focused on the semantic properties of language: for example, what is it for a name such as ‘London’ to refer to something? Interpretationism concerning what it is for linguistic expressions to have meaning, says that constitutively, semantic facts are fixed by best semantic theory. As here developed, it (...) |
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This paper examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, the philosophical (...) |
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The topic of this paper is the general thesis that the death of the human organism is what constitutes the death of a person. All admit that when the death of a human organism occurs, in some form or another, this normally does result in the death of a person. But, some maintain, organismic death is not the same thing as personal death. Why? Because, they maintain, despite the fact that persons are associated with a human organism (‘their organism’), they (...) |
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The concept of moral wrongness, many think, has a distinctive kind of referential stability, brought out by moral twin earth cases. This article offers a new account of the source of this stability, deriving it from a metaphysics of content: “substantive” radical interpretation, and first-order normative assumptions. This story is distinguished from extant “reference magnetic” explanations of the phenomenon, and objections and replies are considered. |
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I argue in this dissertation that natural properties play a central role in David Lewis' modal realism. To argue in favor of this thesis I present: a bottom-up explanation of a top-down possible world metaphysics; a new definition of natural properties and natural fusion, a new mereological operation. To achieve these aims, in the first chapter, I contextualize the discussion, in the second I resume the discussion about universals in contemporary philosophy and argue that, considering the distinct formulations of the (...) |
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In this paper, I review the objections against the claim that brains are computers, or, to be precise, information-processing mechanisms. By showing that practically all the popular objections are either based on uncharitable interpretation of the claim, or simply wrong, I argue that the claim is likely to be true, relevant to contemporary cognitive (neuro)science, and non-trivial. |
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It's currently fashionable to take Putnamian model theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. But I will argue that (under certain mild assumptions) merely securing determinate reference to physical possibility suffices to rule out nonstandard models of our talk of numbers. So anyone who accepts realist reference to physical possibility should not reject reference to the standard model of the natural numbers on Putnamian model theoretic grounds. |
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In the introduction to his Realism, mathematics and modality, and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to platonism in the philosophy of mathematics. Justin Clarke-Doane Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge. |
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