Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All—that is, All ϕs are ψ—or Most. Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth (...) predicate. In this paper I solve the problem by showing how Kleene's strong scheme, and Kripke's theory based on it, can in a natural way be extended to accommodate the full range of generalized quantifiers. (shrink)

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)

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)

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 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)

So far, we have focused on discourse reference to atomic individuals and specific times, events, and states. The basic point of the argument was that all types of discourse reference involve attention-guided anaphora (in the sense of Bittner 2012: Ch. 2). We now turn to discourses involving anaphora to and by quantificational expressions. Today, we focus on quantification over individuals but the analysis we develop will directly generalize to other semantic types. The basic idea is that quantification is (...) one more species of top-level anaphora--to wit, anaphora to top-ranked sets. (shrink)

Can we believe that there are non-existent entities without commitment to the Meinongian metaphysics? This paper argues we can. What leads us from quantification over non-existent beings to Meinongianism is a general metaphysical assumption about reality at large, and not merely quantification over the non-existent. Broadly speaking, the assumption is that every being we talk about must have a real definition. It’s this assumption that drives us to enquire into the nature of beings like Pegasus, and what our (...) relationship as thinkers is to them. However, I argue this assumption only holds if you think your language, and in particular that aspect of it to do with referring to entities works in a specific way. This is the specific way generally assumed by the discipline called ‘Semantics’. I sketch out an alternative, call it global expressivism, in which talk of referring is given an expressivist, speech-act theoretic treatment. If we accept that our talk of the non-existent works as the global expressivist tells us it does, then the question of the metaphysical nature of non-existent entities is utterly void. You might say that Pegasus is empty of any metaphysical nature. Since the non-existent lacks any metaphysical nature, the metaphysics of the non-existent, Meinongianism, as a form of inquiry, lacks a subject matter, despite the fact that we talk happily, and indeed unavoidably, of the non-existent. (shrink)

Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory as framework for our semantic theory provides a resolution of this problem, at least if a broadly Fregean interpretation of type theory is (...) assumed. However, the intelligibility of this interpretation has been questioned. In this paper I introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification. This alternative emerges very naturally by reflecting on the features on which the type-theoretic solution of the problem of unrestricted quantification relies. Although this alternative theory is formulated in a non-classical logic, it preserves the deductive strength of classical strict type theory in a natural way. The ideas developed in this paper make crucial use of Russell’s notion of range of significance. (shrink)

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...) intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for higher-order and substitutional analyses of special quantifiers. (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)

According to the interpretational theory of logical validity (IR), logical validity is preservation of truth in all interpretations compatible with the intended meaning of logical expressions. IR suffers from a seemingly defeating objection, the so-called cardinality problem: any instance of the statement ‘There are n things’ is true under all interpretations, since it can be written down using only logical expressions that are not to be reinterpreted; yet ‘There are n things’ is not logically true. I argue that the cardinality (...) problem is indeed a serious problem for IR, when understood in terms of ‘asymmetry of information’. I then argue that IR can be rehabilitated by making quantifiers context-sensitive: what we do not reinterpret is the Kaplanian character of a quantifier, rather than its content. ‘There are n things’ is false in a context where fewer than n things are relevant, so it is not logically true in IR. I finally discuss some objections and ramifications of my account: I discuss how to make space for the possibility of an explicitly absolutely general quantifier in my framework, how terms can be logical even though context-sensitive, and how to recapture classical logic within my framework. (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)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of generalizations, (...) not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

What explains the truth of a universal generalization? Two types of explanation can be distinguished. While an ‘instance-based explanation’ proceeds via some or all instances of the generalization, a ‘generic explanation’ is independent of the instances, relying instead on completely general facts about the properties or operations involved in the generalization. This intuitive distinction is analyzed by means of a truthmaker semantics, which also sheds light on the correct logic of quantification. On the most natural version of the semantics, (...) this analysis vindicates some claims made—without a proper defense—by Michael Dummett, Solomon Feferman, and others. Where instance-based explanations are freely available, classical logic is shown to be warranted. By contrast, intuitionistic logic remains warranted regardless of what explanations are available. (shrink)

It is unknown to what extent medical researchers generalize study findings beyond their samples when their sample size, sample diversity, or knowledge of conditions that support external validity do not warrant it. It is also unknown to what extent medical researchers describe their results with precise quantifications or unquantified generalizations, i.e., generics, that can obscure variations between individuals. We therefore systematically reviewed all prospective studies (n = 533) published in the top four highest ranking medical journals, Lancet, New England Journal (...) of Medicine (NEJM), Journal of the American Medical Association (JAMA), and the British Medical Journal (BMJ), from January 2022 to May 2023. We additionally reviewed all NEJM Journal Watch clinical research summaries (n = 143) published during the same time. Of all research articles reporting prospective studies, 52.5% included generalizations beyond specific national study populations, with the numbers of articles with generics varying significantly between journals (JAMA = 12%; Lancet = 77%) (p < 0.001, V = 0.48). There was no evidence that articles containing broader generalizations or generics were correlated with larger or more nationally diverse samples. Moreover, only 10.2% of articles with generalizations beyond specific national populations reported external validity strengthening factors that could potentially support such extrapolations. There was no evidence that original research articles and NEJM Journal Watch summaries intended for practitioners differed in their use of broad generalizations, including generics. Finally, from the journal with the highest citation impact, articles containing broader conclusions were correlated with more citations. Since there was no evidence that studies with generalizations beyond specific national study populations or with generics were associated with larger, more nationally diverse samples, or with reports of population similarity that may permit extensions of conclusions, our findings suggest that the generalizations in many articles were insufficiently supported. Caution against overly broad generalizations in medical research is warranted. (shrink)

The Generalized Quantifiers Theory, I will argue, in the second half of last Century has led to an important rapprochement, relevant both in logic and in linguistics, between logical quantification theories and the semantic analysis of quantification in natural languages. In this paper I concisely illustrate the formal aspects and the theoretical implications of this rapprochement.

Hossack's 'The Metaphysics of Knowledge' develops a theory of facts, entities in which universals are combined with universals or particulars, as the foundation of his metaphysics. While Hossack argues at length that there must be negative facts, facts in which the universal 'negation' is combined with universals or particulars, his conclusion that there are also general facts, facts in which the universal 'generality' is combined with universals, is reached rather more swiftly. In this paper I present Hossack with three arguments (...) for his conclusion. They all draw, as does Hossack's theory of facts, on views Russell expressed in various writings. Two arguments are based on Russell's explanation of universals as aspects of resemblance; the third on Russell's observation that general propositions do not follow logically from exclusively particular premises. Comparison with other metaphysics of generality show them to be wanting and Russell's and Hossack's accounts superior. (shrink)

The question of Absolute Generality is whether quantifiers are ever as general as can be. Absolutists claim that quantifiers sometimes are absolutely general, while Relativists claim that quantifiers are never absolutely general. Although diverse philosophers have found the Relativist ethos compelling, it has been hard to articulate a consistent thesis which says what the Relativist seems to want to say. In this paper, I offer Relativists a way forward: I argue that what is needed to successfully state Relativism is a (...) way of generalizing that is non-quantificational. After showing how to define such a device of generalization in terms of identity between properties in a higher-order logical language, I use the device to articulate a form of Relativism which I prove to be consistent and which I argue captures the intuitive vision of the Relativist. (shrink)

Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical positions, (...) rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior’s puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives. (shrink)

In this paper, I present an argument for a rational norm involving a kind of credal attitude called a quantificational credence – the kind of attitude we can report by saying that Lucy thinks that each record in Schroeder’s collection is 5% likely to be scratched. I prove a result called a Dutch Book Theorem, which constitutes conditional support for the norm. Though Dutch Book Theorems exist for norms on ordinary and conditional credences, there is controversy about the epistemic significance (...) of these results. So, my conclusion is that if Dutch Book Theorems do, in general, support norms on credal states, then we have support for the suggested norm on quantificational credences. Providing conditional support for this norm gives us a fuller picture of the normative landscape of credal states. (shrink)

What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show (...) how they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

Our aim in this paper is to extend the semantics for the kind of logic of ground developed in (deRosset and Fine, 2023). In that paper, we very briefly suggested a way of treating universal and existential quantification over a fixed domain of objects. Here we explore some options for extending the treatment to allow for a variable domain of objects.

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. (...) I will conclude with some consideration on scope interactions between quantifiers. (shrink)

A generic grounding claim is a grounding claim that isn’t about any particular entity or fact. For example, consider the claim: an act is right in virtue of maximizing happiness. One natural idea is that generic grounding claims state mere regularities of ground. So if an act is right in virtue of maximizing happiness, then every possible right act is right in virtue of maximizing happiness. The generic claim generalizes over particular grounding relations. In this essay, I argue that this (...) simple story is wrong. Generic grounding claims are not merely quantificational; rather, they express real definitions, where real definitions are (in part) claims about essence. My view has two major upshots: ('i') it makes better sense of debates where generic grounding claims are at issue (like debates about moral laws); ('ii') it clarifies the distinction between reductive and non-reductive metaphysical theories. (shrink)

Jc Beall has made several contributions to the theory of restricted quantification in relevant logics. This paper examines these contributions and proposes an alternative account of restricted universals. The alternative is not, however, a theory of relevant restricted universals in any real sense. It is, however, a theory of restricted universals phrased in the most plausible general quantificational theory for relevant logics—Kit Fine’s stratified semantics. The motivation both for choosing this semantic framework and for choosing the particular theory of (...) restricted quantification we use is because they are the best way of dealing with these topics from Beall’s theory-building theory picture of logic, establishing a second point of contact with Beall’s work. (shrink)

Jan Westerhoff defends an account of thoroughgoing non-foundationalism that he calls “irrealism,” which is implicitly modeled on a Madhyamaka Buddhist view. In this paper, I begin by raising worries about the irrealist’s account of human cognition as taking place in a brain-based representational interface. Next, I pose first-order and higher-order challenges to how the irrealist—who defends a kind of global error theory—can sensibly accommodate an unlocalized appearance-reality distinction, both metaphysically and epistemologically. Finally, although Westerhoff insists that irrealism itself is not (...) an ontological theory and that the irrealist’s rejection of absolutely general quantification precludes his commitment to any ultimately true theories, I propose strategies inspired by the Svātantrika commentarial tradition of Madhyamaka for how the irrealist might develop a lightweight account of unrestricted quantification that could be used to advance a lightweight ultimately true theory. This, I suggest, may allow the irrealist to (i) preserve a commitment to an unlocalized appearance-reality distinction, (ii) underwrite a distinction between ordinary veridical states and metaphysically accurate epistemic states, and (iii) provide an explanation for the massive error that he claims characterizes ordinary cognition. (shrink)

Kripke (1977) presents an argument designed to show that the considerations in Donnellan (1966) concerning attributive and referential uses of (definite) descriptions do not, by themselves, refute Russell’s (1905) unitary theory of description sentences (RTD), which takes (utterances of) them to express purely general, quantificational, propositions. Against Kripke, Marga Reimer (1998) argues that the two uses do indeed reflect a semantic ambiguity (an ambiguity at the level of literal truth conditions). She maintains a Russellian (quantificational) analysis of utterances involving attributively (...) used descriptions but attempts to defend the following two claims about utterances involving referentially used descriptions (referential utterances) (1998, p. 89). (shrink)

In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a (...) perfectly natural first-order quantifier. I argue that this claim is not justified. Quine has shown that we can dispense with first-order quantifiers, by using a family of ‘predicate functors’ instead. I argue that we have no reason to think that it is the first-order quantifiers, rather than Quine’s predicate functors, which are perfectly natural. The discussion of quantification is used to provide some motivation for a general scepticism about Sider’s project. Shamik Dasgupta’s ‘generalism’ and Jason Turner’s critique of ‘ontological nihilism’ are also discussed. (shrink)

The validity of psychological measurement is crucially connected to a peculiar form of epistemic circularity. This circularity can be a threat when there are no independent ways to assess whether a certain procedure is actually measuring the intended target of measurement. This paper focuses on how Gustav Theodor Fechner addressed the measurement circularity that emerged in his psychophysical research. First, I show that Fechner's approach to the problem of circular measurement involved a core idealizing assumption of a shared human physiology. (...) Second, I assess Fechner's approach to this issue against the backdrop of his own epistemology of measurement and the measurement context of his time. Third, I claim that, from a coherentist and historicallysituated perspective, Fechner's quantification can be regarded as a first successful step of a longer-term quantification process. To conclude, I draw from these insights some general epistemological reflections that are relevant to current quantitative psychology. (shrink)

Proper names are generally taken to be count nouns. This paper argues that this is mistaken and that at least in some languages, for example German, names divide into mass and count. Making use of Kayne's (2005, 2010) theory of light nouns, this paper argues that light nouns are part of (simple) names and that a mass-count distinction among light nouns explains the behavior of certain types of names in German as mass rather than count. The paper elaborates the role (...) of light nouns with new generalizations regarding their linguistic behavior in quantificational and pronominal NPs, their selection of relative pronouns in German, and a general difference in the support of plural anaphora between English and German. (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)

I distinguish between a metaphysical and a logical reading of Generality Relativism. While the former denies the existence of an absolutely general domain, the latter denies the availability of such a domain. In this paper I argue for the logical thesis but remain neutral in what concerns metaphysics. To motivate Generality Relativism I defend a principle according to which a collection can always be understood as a set-like collection. I then consider a modal version of Generality Relativism and sketch how (...) this version avoids certain revenge problems. (shrink)

In this article Quine's program for reducing ontology to the semantic level is compared to Aquinas' metaphysical ontology. Some internal inconsistencies of Quine's quantificational account of existence are discussed. Aquinas' account of existence is explicated in response to Quine' mischaracterization of Scholastic ontology. The general nature of an amended logical account of existence incorporating Aquinas' ontological categories is indicated. Finally, recent attempts to harmonize Thomism and analytic philosophy are criticized for failing to note that the quantificational account of existence is (...) motivated by analytic philosophy's rejection of metaphysical ontology. Nothing short of a logical account of existence within the broader framework of the philosophy of being can legitimate the efforts of analytical Thomists. (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)

This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed here, the “Logic (...) of Many” and the “Logic of Plausibility”, that characterize assertions of the kind “many”, and “for a good number of”. Although the notion of simple majority (“more than half”) can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on evidence sets, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers as notions of families of principal filters and reduced topologies, respectively. We prove that both systems are conservative extensions of classical logic that preserve important properties, such as soundness and completeness. Some additional perspectives connecting our approach to flexible reasoning through modulated logics to epistemology and social choice theory are also discussed. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order logic (...) to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

This is a comment on Cian Dorr 'Higher-Order Quantification and the Elimination of Abstract Objects'. The aim of this contribution is to clarify and further develop a view (with its empirical generalizations) on which higher-order objects play a highly restricted role in the ontology of natural language. A sharp distinction is drawn between ontologically dependent objects (events, tropes, qualities, attitudinal objects etc.) and higher-order objects (properties, relations, propositions, etc.). Natural language reflects an ontology of the former, rather than of (...) the latter. (shrink)

There are plenty of classic paradoxes about conditional obligations, like the duty to be gentle if one is to murder, and about “supererogatory” deeds beyond the call of duty. But little has been said about the intersection of these topics. We develop the first general account of conditional supererogation, with the power to solve familiar puzzles as well as several that we introduce. Our account, moreover, flows from two familiar ideas: that conditionals restrict quantification and that supererogation emerges from (...) a clash between justifying and requiring reasons. (shrink)

Ramsification is a well-known method of defining theoretical terms that figures centrally in a wide range of debates in metaphysics. Prior's puzzle is the puzzle of why, given the assumption that that-clauses denote propositions, substitution of "the proposition that P" for "that P" within the complements of many propositional attitude verbs sometimes fails to preserve truth, and other times fails to preserve grammaticality. On the surface, Ramsification and Prior's puzzle appear to have little to do with each other. But Prior's (...) puzzle is much more general than is ordinarily appreciated, and Ramsification requires a solution to the generalized form of Prior's puzzle. Without such a solution, a wide range of theories will either fail to imply their Ramsey sentences, or have Ramsey sentences that are ill-formed. As a consequence, definitions of theoretical terms given using the Ramsey sentence will be either incorrect or nonsensical. I present a partial solution to the puzzle that requires making use of a neo-Davidsonian language for scientific theorizing, but the would-be Ramsifier still faces serious challenges. (shrink)

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)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception (...) of propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions. (shrink)

For a period of several years the philosopher of science Hasok Chang has promoted various inter-related views including pluralism, pragmatism, and an associated view of natural kinds. He has also argued for what he calls the persistence of everyday terms in the scientific view. Chang claims that terms like phlogiston were never truly abandoned but became transformed into different concepts that remain useful. On the other hand, Chang argues that some scientific terms such as acidity have suffered a form of (...) “rupture”, especially in the case of the modern Lewis definition of acids. Chang also complains that the degree of acidity of a Lewis acid cannot be measured using a pH meter and seems to regard this as a serious problem. The present paper examines some of these views, especially what Chang claims to be a rupture in the definition of acidity. It is suggested that there has been no such rupture but a genuine generalization, on moving from the Brønsted-Lowry theory to the Lewis theory of acidity. It will be shown how the quantification and measurement of Lewis acidity can easily be realized through the use of equilibrium theory and the use of stability constants. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

For computer simulation models to usefully inform climate risk management, uncertainties in model projections must be explored and characterized. Because doing so requires running the model many times over, and because computing resources are finite, uncertainty assessment is more feasible using models that demand less computer processor time. Such models are generally simpler in the sense of being more idealized, or less realistic. So modelers face a trade-off between realism and uncertainty quantification. Seeing this trade-off for the important epistemic (...) issue that it is requires a shift in perspective from the established simplicity literature in philosophy of science. (shrink)

Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operator raises concerns. In this paper, I show that the (...) work of both these elements can be done by a single natural generalization of the logical possibility operator. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

One of the central topics in semantic theory over the last few decades concerns the nature of local contexts. Recently, theorists have tried to develop general, non-stipulative accounts of local contexts (Schlenker, 2009; Ingason, 2016; Mandelkern & Romoli, 2017a). In this paper, we contribute to this literature by drawing attention to the local contexts of subclausal expressions. More specifically, we focus on the local contexts of quantificational determiners, e.g. `all', `both', etc. Our central tool for probing the local contexts of (...) subclausal elements is the principle Maximize Presupposition! (Percus, 2006; Singh, 2011). The empirical basis of our investigation concerns some data discussed by Anvari (2018b), e.g. the fact that sentences such as `All of the two presidential candidates are crooked' are unacceptable. In order to explain this, we suggest that the local context of determiners needs to contain the information carried by their restrictor. However, no existing non-stipulative account predicts this. Consequently, we think that the local contexts of subclausal expressions will likely have to be stipulated. This result has important consequences for debates in semantics and pragmatics, e.g. those around the so-called "explanatory problem" for dynamic semantics (Soames, 1982; Heim, 1990; Schlenker, 2009). (shrink)

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole discussion of (...) these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. (shrink)