Scientific realism holds that the terms in our scientific theories refer and that we should believe in their existence. This presupposes a certain understanding of quantification, namely that it is ontologically committing, which I challenge in this paper. I argue that the ontological loading of the quantifiers is smuggled in through restricting the domains of quantification, without which it is clear to see that quantifiers are ontologically neutral. Once we remove domain restrictions, domains of quantification can include (...) non-existent things, as they do in scientific theorizing. Scientific realism would therefore require redefining without presupposing a view of ontologically committing quantification. (shrink)

This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A (...) unique feature of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, discussing French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu), and pointing to formal semantic literature involving quantification in around thirty languages. -- -/- 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics of quantifier words. (shrink)

Nihilism is the thesis that no composite objects exist. Some ontologists have advocated abandoning nihilism in favor of deep nihilism, the thesis that composites do not existO, where to existO is to be in the domain of the most fundamental quantifier. By shifting from an existential to an existentialO thesis, the deep nihilist seems to secure all the benefits of a composite-free ontology without running afoul of ordinary belief in the existence of composites. I argue that, while there are (...) well-known reasons for accepting nihilism, there appears to be no reason at all to accept deep nihilism. In particular, deep nihilism draws no support either from the usual arguments for nihilism or from considerations of parsimony. (shrink)

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a (...) variable fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional (...) contexts.) One rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

This article reconstructs Kant's view on the existential import of categorical sentences. Kant is widely taken to have held that affirmative sentences (the A and I sentences of the traditional square of opposition) have existential import, whereas negative sentences (E and O) lack existential import. The article challenges this standard interpretation. It is argued that Kant ascribes existential import only to some affirmative synthetic sentences. However, the reasons for this do not fall within the remit of (...) Kant's formal logic. Unlike traditional logic and modern standard quantification theory, Kant's formal logic is free from existential commitments. (shrink)

‘Quantified pure existentials’ are sentences (e.g., ‘Some things do not exist’) which meet these conditions: (i) the verb EXIST is contained in, and is, apart from quantificational BE, the only full (as against auxiliary) verb in the sentence; (ii) no (other) logical predicate features in the sentence; (iii) no name or other sub-sentential referring expression features in the sentence; (iv) the sentence contains a quantifier that is not an occurrence of EXIST. Colin McGinn and Rod Girle have alleged that standard (...) first-order logic cannot adequately deal with some such existentials. The article defends the view that it can. (shrink)

There is a significant difference between the words `is' and `exists' that has either been overlooked or under-appreciated by many philosophers. This difference comes in sentences that express existential quantification using `is', `exists', or their cognates, such as, "There are cookies in the jar," or, "There exists a strange species of fish that nobody has studied yet." Phrases such as `there are' and `there exists' are existential quantifier expressions, since they're used to express existential quantification. (...) The orthodox view of these expressions is that they are, in the words of David K. Lewis, "entirely synonymous and interchangeable". This dissertation presents and argues for an anti-orthodox view of meaning of `there is' and `there exists'. The root of the difference in meaning between the two expressions is that `there is' turns out to be context-sensitive, on the model of demonstratives like `this' or `that', while `there exists' is invariant in its meaning. These views are motivated through the introduction of a notion called `ontological robustness', which helps us evaluate the level of ontological commitment in our assertions. The anti-orthodox view is defended over orthodoxy through holistic arguments that compare the virtues of each theory, including such metrics as how they fare in accounting for our stubborn desire to talk about and quantify over nonexistent objects. (shrink)

"The main aim of the paper is to compare two types of abstractionistic accounts of fictional objects, and to analyze their consequences for interpretation of existential quantification. According to a proponent of general abstractionistic theory, fictional objects have abstract nature in a way similar to contracts, marriages, and the likes. This view is an alternative to strongly realistic accounts of fictional objects, defended by Terence Parsons or David Lewis. Within abstractionistic theories, as in all philosophical areas, one can (...) find divergences of opinions. The main differences between two of them – Peter van Inwagen's and Edward Zalta's – are connected with the interpretation of existential quantification. According to van Inwagen, “being” is the same as “existence” and its sense is captured by the existential quantifier. Edward Zalta's theory is much closer to the Meinongian Theory of Objects. He argues for the need of distinguishing between “being” and “existence” and for invoking nonexistent objects. Because of that he suggests an alternative interpretation of quantification. Admittedly, there is one abstractionistic source for both theories, but their ontological consequences are different - van Inwagen is a staunch opponent of nonexistent objects, and Zalta describes his own theory as "Meinongian".". (shrink)

This essay proposes a new theory of agentive modals: ability modals and their duals, compulsion modals. After criticizing existing approaches—the existential quantificational analysis, the universal quantificational analysis, and the conditional analysis—it presents a new account that builds on both the existential and conditional analyses. On this account, the act conditional analysis, a sentence like ‘John can swim across the river’ says that there is some practically available action that is such that if John tries to do it, he (...) swims across the river. The essay argues that the act conditional analysis avoids the problems faced by existing accounts of agentive modality and shows how the act conditional analysis can be extended to an account of generic agentive modal claims. The upshot is a new vantage point on the role of agentive modal ascriptions in practical discourse: ability ascriptions serve as a kind of hypothetical guarantee, and compulsion ascriptions as a kind of nonhypothetical guarantee. (shrink)

This is the published version of a talk on meta-ontology in a conference of a multidisciplinary research project on "logic and sensibility". It argues against univocalism about "existence" and for a variety of perspectivism.

Data involving epistemic modals suggest that some classically valid argument forms, such as _reductio_, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a _de re–de dicto_ collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms (...) that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic. (shrink)

The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am (...) looking for an explanation of this phenomenon. It is argued that the standard induction scheme plays a key role. (shrink)

In this paper I sketch some arguments that underlie Hegel's chapter on judgment, and I attempt to place them within a broad tradition in the history of logic. Focusing on his analysis of simple predicative assertions or ‘positive judgments’, I first argue that Hegel supplies an instructive alternative to the classical technique of existential quantification. The main advantage of his theory lies in his treatment of the ontological implications of judgments, implications that are inadequately captured by quantification. (...) The second concern of this paper is the manner in which Hegel makes logic not only dependent on ontology generally, but also variant in regard to domains of objects. In other words, he offers a domain-specific logical theory, according to which the form of judgment or inference is specific to the subject of judgment. My third concern lies with the metaphilosophical consequences of this theory, and this includes some more familiar Hegelian themes. It is well known that Hegel frequently questioned the adequacy of the sentential form for expressing higher order truths. My reading of his theory of predication explains and contextualizes this tendency by demystifying notions like the so-called speculative proposition. (shrink)

The notion of computability is developed through the study of the behavior of a set of languages interpreted over the natural numbers which contain their own fully defined satisfaction predicate and whose only other vocabulary is limited to "0", individual variables, the successor function, the identity relation and operators for disjunction, conjunction, and existential quantification.

Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the (...) earlier period where Russell still made a distinction between existence and being/subsistence. But even the later Russell, including that of the Logical Atomism lectures period, would not have understood ontological questions to be first and foremost questions of quantification. He would take fundamentality to be important too, which explains in part his assertions to the effect the the values of individual variables have a reality not attributable to values of higher-order variables, even ineliminable higher-order variables. (shrink)

This article identifies and formalizes the logical features of analogous terms that justify their use in deduction. After a survey of doctrines in Aristotle, Aquinas, and Cajetan, the criteria of “analogy of proper proportionality” are symbolized in first-order predicate logic. A common genus justifies use of a common term, but does not provide the inferential link required for deduction. Rather, the respective differentiae foster this link through their identical proportion. A natural-language argument by analogy is formalized so as to exhibit (...) these criteria, thereby showing the validity of analogical deduction. (shrink)

Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of nonmaximality in plural definites by Križ (2016) to explain how context disambiguates donkey sentences. We propose that the denotations of such sentences produce truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to generate the standard judgments of the literature. Building on Muskens’s (1996) Compositional (...) Discourse Representation Theory and on ideas from supervaluation semantics, the semantic analysis defines a general schema for quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pronouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier. (shrink)

The problem with ontological commitment is that when we symbolize the statements that we make about what 'exists' or what is 'real', they do not always translate to exactly that which we intend to express. In this essay, I explore the relation between 'Reality' and how we describe reality. I evaluate the accounts of three prominent philosophers on the topic, address their shortcomings, and introduce my own account; which I call "The Natural Definition of Reality".

When our choice affects some other person and the outcome is unknown, it has been argued that we should defer to their risk attitude, if known, or else default to use of a risk avoidant risk function. This, in turn, has been claimed to require the use of a risk avoidant risk function when making decisions that primarily affect future people, and to decrease the desirability of efforts to prevent human extinction, owing to the significant risks associated with continued human (...) survival. I raise objections to the claim that respect for others’ risk attitudes requires risk avoidance when choosing for future generations. In particular, I argue that there is no known principle of interpersonal aggregation that yields acceptable results in variable population contexts and is consistent with a plausible ideal of respect for others’ risk attitudes in fixed population cases. GPI Working Paper No. 20-2022. (shrink)

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the (...) existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition. (shrink)

Metaphysicians frequently appeal to intuition. But when is that appeal useful? I consider that question by focusing on our existential intuitions. In particular, I want to go some way to answering the question of whether, and when, appeal to existential intuitions is useful, by consid-ering the issue in the light of an argument for unrestricted composition. This argument appeals to a difference in the extent to which restricted and unrestricted compositionalists appeal to existential intuitions, and concludes that (...) at the very least, restricted compositionalists are on shak-ier epistemic ground than unrestricted compositionalists. Having outlined this argument for unrestricted composition, I con-sider the nature of the unrestricted existential quantifier in the context of three different metaphysical scenarios about the way the world might be: scenarios that differ with respect to whether the metaphysics of a world completely or uniquely settles the division of that world into ob-jects. I argue that appeal to intuition is not only useful but necessary if we are to determine the intension of ‘exists’ and hence its extension at any given world. But this appeal is not simply an appeal to our brute ex-istential intuitions—our dispositions actually to quantify over a certain domain. Rather, it requires equilibration over a set of worlds in which we consider our ‘quantificational’ dispositions in each world, where, importantly, included in this set of worlds are worlds in which the meta-physics differently settles the division of those worlds into objects. Ul-timately, I argue, our dispositions yield various conditional claims about our concept <existence>. These are conditional claims of the most ab-stract kind: they tell us, for instance, that if there is some natural, unique division of our world into objects, then the unrestricted quantifier ranges over all and only the objects in that domain. But, I will argue, our untu-tored, world-bound dispositions are no guide at all to what actually ex-ists even on the supposition that metaphysics alone does not uniquely or completely settle a natural division of our world into objects. Hence they are no guide to the nature of composition. And to the extent that certain restricted compositionalist views depend on such intuitions, so much the worse for them. Or so I shall argue. (shrink)

W. V. Quine’s criterion of ontological commitment is commonly presented as the slogan: “to be is to be the value of a variable”. More specifically, to be is to be in the domain of values of a bound variable attached to a existential quantifier in the body of a theory. If a sentence of our best available theory quantifies over bachelors, so we conclude that, according to it, there are bachelors. Simplicity and the use of logical apparatus for determining (...) this criterion are responsible for many philosophers to adhere to this standpoint within analytical metaphysics. I will argue that despite this strong influence of the Quinean criterion of ontological commitment in many debates, we find at least three interlinked problems in its original formulation: (1) The criterion depends of a clear definition of theory for the determination of the quantifications counting as entailers of ontological commitments. However, Quine does not present such clear concept of what would be a theory and of how to formalize it. Quine develops this notion under just the metaphor of the knowledge fabric, in which we have a group of sentences, which does not suffice for the required account of ontological commitment. (2) There are distinct possibilities of quantifying over given sentences, which leaves room for different ontological commitments associated with the same statement. In that sense, someone could argue that the Quinean solution would be to endorse just the first order predicate logic. Nonetheless, the Quinean should explain why we ought to be restricted to this logic. (3) The previous problems lead to a possible explosion of the Quinean criterion of ontological commitment, making it trivial, because it permits the quantification over any supposed entities and, hence, that anything can exist. Thus, I will discuss Quine’s criterion of ontological commitment in the light of the abovementioned problems, showing that, unless the Quinean presents a more specific definition of theory beyond just a group of sentences, he leads to an explosion of commitments with different entities. I will conclude that, if you understand ‘theory’ as Alonzo Church’s concept of ‘formalized language’, this knot can be undone. However, Church’s concept is much more akin to Carnap’s linguistic framework than to a notion of knowledge fabric “without borders” as the one proposed by Quine. (shrink)

This paper is about an underappreciated aspect of generics: their non-specificity. Many uses of generics, utterances like ‘Seagulls swoop down to steal food’, express non-specific generalisations which do not specify their quantificational force or flavour. I consider whether this non-specificity arises as a by-product of context-sensitivity or semantic incompleteness but argue instead that generics semantically express non-specific generalisations by default as a result of quantifying existentially over more specific ones.

ABSTRACT: This paper discusses ancient versions of paradoxes today classified as paradoxes of presupposition and how their ancient solutions compare with contemporary ones. Sections 1-4 air ancient evidence for the Fallacy of Complex Question and suggested solutions, introduce the Horn Paradox, consider its authorship and contemporary solutions. Section 5 reconstructs the Stoic solution, suggesting the Stoics produced a Russellian-type solution based on a hidden scope ambiguity of negation. The difference to Russell's explanation of definite descriptions is that in the Horn (...) Paradox the Stoics uncovered a hidden conjunction rather than a hidden existential sentence. Sections 6 and 7 investigate hidden ambiguities in 'to have' and 'to lose' (including inalienable and alienable possession) and ambiguities of quantification based on substitution of indefinite plural expressions for indefinite or anaphoric pronouns, and Stoic awareness of these. Section 8 considers metaphorical readings and allusions that add further spice to the paradox. (shrink)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, (...) too, with its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

In this paper, I argue that Kant's famous critique of the Ontological Argument largely begs the question against that argument, and is no better when supplemented by the modern quantificational analysis of "exists." In particular, I argue that the claim, common to Hume and Kant, that conceptual truths can never entail substantive existential claims is false,and thus no ground for rejecting the Ontological Argument.

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be (...) used with any Copi-style set of inference rules, so it is quite adaptable to many mainstream symbolic logic textbooks. Consequently, PARC may be especially attractive to logic teachers who find Jaskowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules. The PARC system is also keyboard-friendly in comparison to the widely adopted Jaskowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams. (shrink)

In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order (...) domain in terms of definability, can serve a neo-logicist's purposes. The problem, in both cases, is similar: neither Wright nor Hale is sufficiently sensitive to the demands that impredicativity imposes. Finally, I defend my own earlier attempt to finesse this issue, in "A Logic for Frege's Theorem", from Hale's criticisms. (shrink)

This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume different requirements for their arguments are asserted for one single entity, e.g., "the lunch was delicious but took forever". This paper is particularly concerned with copredication sentences with quantification, i.e., cases where the two predicates impose distinct criteria of quantification and individuation, e.g., "Fred picked up and (...) mastered three books." In our solution developed in homotopy type theory and using the rule of existential closure following Heim analysis of indefinites, common nouns are modeled as identifications of their aspects using HoTT identity types, e.g., the common noun book is modeled as identifications of its physical and informational aspects. The previous treatments of copredication in systems of semantics which are based on simple type theory and dependent type theories make the correct predictions but at the expense of ad hoc extensions (e.g., partial functions, dot types and coercive subtyping). The model proposed here, also predicts the correct results but using a conceptually simpler foundation and no ad hoc extensions. (shrink)

This chapter provides an overview of how existential phenomenology has influenced qualitative research methods across a range of disciplines across the social, health, educational, and psychological sciences. It focuses specifically on how the concepts of “existential structures,” or “existentials”—such as selfhood, temporality, spatiality, affectivity, and embodiment—have been used in qualitative research. After providing a brief introduction to what qualitative research is and why philosophers should be interested in it, the chapter provides clear, straightforward examples of how qualitative researchers (...) have used existentials to analyze qualitative data and design qualitative studies. The chapter is intended to introduce philosophers to existential approaches to phenomenological qualitative research, with the aim of facilitating interdisciplinary dialogue and collaboration. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit (...) quantification, but on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules for (...) the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

Relative to an ordinary context, an utterance of the sentence ‘Everything is in the car’ communicates a proposition about a restricted domain. But how does this work? One possibility is that quantifier expressions like 'everything' are context sensitive and range over different domains in different contexts. Another possibility is that quantifier expressions are not context sensitive, but have a fixed, absolutely general meaning, and ordinary utterances communicate a restricted content via Gricean mechanisms. I argue that, contrary to received opinion, the (...) latter view has both a number of methodological and also intuitive advantages over the former. I then reply to three objections to the latter view: the binding argument (due to Stanley and Szabo), the availability-based attack (due to Recanati), and an argument based on Recanati’s scope principle. (shrink)

This chapter discusses ontological commitment to properties, understood as ontological correlates of predicates. We examine the issue in four metaontological settings, beginning with an influential Quinean paradigm on which ontology concerns what there is. We argue that this naturally but not inevitably avoids ontological commitment to properties. Our remaining three settings correspond to the most prominent departures from the Quinean paradigm. Firstly, we enrich the Quinean paradigm with a primitive, non-quantificational notion of existence. Ontology then concerns what exists. We argue (...) that this strengthens the Quinean case against ontological commitment to properties while also newly distinguishing between stronger and weaker forms of nominalism. Secondly, we enrich the Quinean paradigm with the ideology of fundamentality. Ontology then centrally concerns what’s fundamental. We argue that this leaves ontological commitment to properties wide open although Bradleyan regress threatens. Thirdly, we enrich the Quinean paradigm with primitive higher-order quantifiers. Ontology then expands to concern what there higher-order is and what there first-order is. We argue that this naturally but not inevitably incurs ontological commitment to properties. (shrink)

The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same time, those intentional objects do not (...) come for free; rather they are strictly dependent on intentional acts that generally need to have a presence, in one way or another, in the semantic structure of the sentence. (shrink)

This essay introduces a puzzle about the interaction between quantifiers and epistemic modals. The puzzle motivates the idea that whether an object satisfies an epistemically modalized predicate depends on the mode of presentation of the domain of quantification. I compare two ways of implementing this idea, one using counterpart theory, the other using Aloni's 'conceptual covers' theory, and then provides some evidence in favor of the former.

I provide a classification of varieties of pantheism. I argue that there are two different kinds of commitments that pantheists have. On the one hand, there is an ontological commitment to the existence of a sum of all things. On the other hand, there is an ideological commitment: either collectively or distributively, the sum of all things is divine.

This paper deals with the logical form of quantified sentences. Its purpose is to elucidate one plausible sense in which quantified sentences can adequately be represented in the language of first-order logic. Section 1 introduces some basic notions drawn from general quantification theory. Section 2 outlines a crucial assumption, namely, that logical form is a matter of truth-conditions. Section 3 shows how the truth-conditions of quantified sentences can be represented in the language of first-order logic consistently with some established (...) undefinability results. Section 4 sketches an account of vague quantifier expressions along the lines suggested. Finally, section 5 addresses the vexed issue of logicality. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinite rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinite rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinite rules of inference in their reasoning. (shrink)

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in (...) order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of (...) structurally diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

This chapter provides an overview of how existential phenomenology has influenced qualitative research methods across a range of disciplines across the social, health, educational, and psychological sciences. It focuses specifically on how the concepts of “existential structures,” or “existentials”—such as selfhood, temporality, spatiality, affectivity, and embodiment—have been used in qualitative research. After providing a brief introduction to what qualitative research is and why philosophers should be interested in it, the chapter provides clear, straightforward examples of how qualitative researchers (...) have used existentials to analyze qualitative data and design qualitative studies. The chapter is intended to introduce philosophers to existential approaches to phenomenological qualitative research, with the aim of facilitating interdisciplinary dialogue and collaboration. (shrink)

The standard argument to the conclusion that artificial intelligence (AI) constitutes an existential risk for the human species uses two premises: (1) AI may reach superintelligent levels, at which point we humans lose control (the ‘singularity claim’); (2) Any level of intelligence can go along with any goal (the ‘orthogonality thesis’). We find that the singularity claim requires a notion of ‘general intelligence’, while the orthogonality thesis requires a notion of ‘instrumental intelligence’. If this interpretation is correct, they cannot (...) be joined as premises and the argument for the existential risk of AI turns out invalid. If the interpretation is incorrect and both premises use the same notion of intelligence, then at least one of the premises is false and the orthogonality thesis remains itself orthogonal to the argument to existential risk from AI. In either case, the standard argument for existential risk from AI is not sound.—Having said that, there remains a risk of instrumental AI to cause very significant damage if designed or used badly, though this is not due to superintelligence or a singularity. (shrink)

There is a growing movement towards construing some classic debates in ontology as meaningless, either because the answers seem obvious or the debates seem intractable. In this paper, I respond to this movement. The response has three components: First, the members of the two sides of the ontological debates that dismissivists have targeted are using different quantifiers. Second, the austere ontologist is using a more fundamental quantifier than her opponent. Third, the austere ontologist’s more fundamental quantifier is a restriction of (...) her opponent’s quantifier. This response takes seriously the intuition that there is something wrong with the ontological disputes, but does not entail dismissivism. (shrink)

This essay articulates a kind of conservatism that it argues is the most fundamental and important kind of conservatism, viz. existential conservatism, which involves an affirmative and appreciative stance towards the given world. While this form of conservatism can be connected to political conservatism, as seen with Roger Scruton, it need not be, as seen with G. A. Cohen. It is argued that existential conservatism should be embraced whether or not one embraces political conservatism, though it is also (...) shown that existential conservatism imposes constraints on our political thinking. In particular, it is argued that Cohen's ‘luck egalitarianism’ stands at odds with his existential conservatism and that one should be a sufficientarian rather than an egalitarian with regard to economic justice. (shrink)

I argue that academic psychology’s quest to achieve scientific respectability by reliance on quantification and objectification is deeply flawed. Specifically, psychological theory typically cannot support prognostication beyond the binary opposition of “effect present/effect absent”. Accordingly, the “numbers” assigned to experimental results amount to little more than affixing names (e.g., more than, less than) to the members of an ordered sequence of outcomes. This, in conjunction with the conceptual under-specification characterizing the targets of experimental inquiry, is, I contend, a primary (...) reason why psychologists find it difficult to discriminate between competing, explanations of the effects of mind on behavior. Absent well-specified theory capable of enabling precise and detailed quantitative prediction, inferring underlying mental mechanisms from experimental outcomes becomes a difficult, if not impossible, task. (shrink)

This paper describes quantificational structures in Greenlandic Eskimo (Kalaallisut), a language where familiar quantificational meanings are expressed in ways that are quite different from English. Evidence from this language thus poses some formidable challenges for cross-linguistic theories of compositional semantics.

A small but growing number of studies have aimed to understand, assess and reduce existential risks, or risks that threaten the continued existence of mankind. However, most attention has been focused on known and tangible risks. This paper proposes a heuristic for reducing the risk of black swan extinction events. These events are, as the name suggests, stochastic and unforeseen when they happen. Decision theory based on a fixed model of possible outcomes cannot properly deal with this kind of (...) event. Neither can probabilistic risk analysis. This paper will argue that the approach that is referred to as engineering safety could be applied to reducing the risk from black swan extinction events. It will also propose a conceptual sketch of how such a strategy may be implemented: isolated, self-sufficient, and continuously manned underground refuges. Some characteristics of such refuges are also described, in particular the psychosocial aspects. Furthermore, it is argued that this implementation of the engineering safety strategy safety barriers would be effective and plausible and could reduce the risk of an extinction event in a wide range of possible scenarios. Considering the staggering opportunity cost of an existential catastrophe, such strategies ought to be explored more vigorously. (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth (...) and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)