We investigate whether ordinary quantification over objects is an extensional phenomenon, or rather creates non-extensional contexts; each claim having been propounded by prominent philosophers. It turns out that the question only makes sense relative to a background theory of syntax and semantics (here called a grammar) that goes well beyond the inductive definition of formulas and the recursive definition of satisfaction. Two schemas for building quantificational grammars are developed, one that invariably constructs extensional grammars (in which quantification, in (...) particular, thus behaves extensionally) and another that only generates non-extensional grammars (and in which quantification is responsible for the failure of extensionality). We then ask whether there are reasons to favor one of these grammar schemas over the other, and examine an argument according to which the proper formalization of deictic utterances requires adoption of non-extensional grammars. (shrink)

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the (...) structure of predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory. (shrink)

Realist theories about fictional entities must explain the fact that, in ordinary contexts people deny, apparently in all seriousness, that there are such things as the Big Bad Wolf and Santa Claus. The usual explanation treats these denials as involving restricted quantification: The speaker is said to be denying only that the Big Bad Wolf and Santa Claus are to be found among real or actual things, not that there are no such things at all. This is unconvincing. The (...) denials may just as naturally be phrased as “The Big Bad Wolf and Santa Claus don't exist”, and claims of nonexistence seem not to admit of interpretations corresponding to statements of restricted quantification. Ordinary denials of the existence of fictional entities constitute a severe difficulty for realist theories. (shrink)

This edited volume explores the intersection of medicine and philosophy throughout history, calling attention to the role of quantification in understanding the medical body. Retracing current trends and debates to examine the quantification of the body throughout the early modern, modern and early contemporary age, the authors contextualise important issues of both medical and philosophical significance, with chapters focusing on the quantification of temperaments and fluids, complexions, functions of the living body, embryology, and the impact of quantified (...) reasoning on the concepts of health and illness. With insights spanning from the sixteenth century to the nineteenth century, this book provides a wide-ranging overview of attempts to ‘quantify’ the human body at various points. Arguing that medicine and philosophy have been constantly in dialogue with each other, the authors discuss how this provided a strategic opportunity both for medical thought and philosophy to refine and further develop. Given today’s fascination with the quantification of the body, represented by the growing profusion of self-tracking devices logging one’s sleep, diet or mood, this collection offers an important and timely contribution to an emerging and interdisciplinary field of study. -/- . (shrink)

Model evaluation for long term climate predictions must be done on quantities other than the actual prediction, and a comprehensive uncertainty quantification is impossible. An ad hoc alternative is provided by coordinated model intercomparisons which typically use a “one model one vote” approach. The problem with such an approach is that it treats all models as independent and equally plausible. Reweighting all models of the ensemble for performance and dependence seems like an obvious way to improve on model democracy, (...) yet there are open questions on what constitutes a “good” model, how to define dependency, how to interpret robustness, and how to incorporate background knowledge. Under¬standing those issues has the potential to increase confidence in model predictions in modeling efforts outside of climate science where similar challenges exist. (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 infinitary 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 infinitary 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 infinitary rules of inference in their reasoning. (shrink)

Illustrates the prevalence of implicit quantification in deontic assertions in ordinary language.

This extended collection of papers is the result of putting recent ideas on quantification to work on a wide variety of languages.

When viewed as the most comprehensive theory of collections, set theory leaves no room for classes. But the vocabulary of classes, it is argued, provides us with compact and, sometimes, irreplaceable formulations of largecardinal hypotheses that are prominent in much very important and very interesting work in set theory. Fortunately, George Boolos has persuasively argued that plural quantification over the universe of all sets need not commit us to classes. This paper suggests that we retain the vocabulary of classes, (...) but explain that what appears to be singular reference to classes is, in fact, covert plural reference to sets. (shrink)

Quantificational arguments can take scope outside of temporal adjunct clauses, in an apparent violation of locality restrictions: the sentence few secretaries cried after each executive resigned allows the quantificational NP each executive to take scope above few secretaries. I show how this scope relation is the result of local operations: the adjunct clause is a temporal generalized quantifier which takes scope over the main clause (Pratt and Francez, Linguistic and Philosophy 24(2), 187–222. [2001]), and within the adjunct clause, the quantificational (...) argument takes scope above the implicit determiner which forms the temporal generalized quantifier. The paper explores various relations among quantificational arguments across clause boundaries, including temporal clauses that are modified internally by a temporal adverbial and temporal clauses with embedded sentential complements. (shrink)

Connectionist attention to variables has been too restricted in two ways. First, it has not exploited certain ways of doing without variables in the symbolic arena. One variable-avoidance method, that of logical combinators, is particularly well established there. Secondly, the attention has been largely restricted to variables in long-term rules embodied in connection weight patterns. However, short-lived bodies of information, such as sentence interpretations or inference products, may involve quantification. Therefore short-lived activation patterns may need to achieve the effect (...) of variables. The paper is mainly a theoretical analysis of some benefits and drawbacks of using logical combinators to avoid variables in short-lived connectionist encodings without loss of expressive power. The paper also includes a brief survey of some possible methods for avoiding variables other than by using combinators. (shrink)

Model evaluation for long-term climate predictions must be done on quantities other than the actual prediction, and a comprehensive uncertainty quantificationUncertainty quantification is impossible. An ad hoc alternative is provided by coordinated model intercomparisonsModel intercomparisons which typically use a “one model one vote” approach. The problem with such an approach is that it treats all models as independent and equally plausible. Reweighting all models of the ensemble for performance and dependence seems like an obvious way to improve on model (...) democracy, yet there are open questions on what constitutes a “good” model, how to define dependency, how to interpret robustnessRobustness, and how to incorporate background knowledgeBackground knowledge. UnderstandingUnderstanding those issues have the potential to increase confidence in model predictions in modeling efforts outside of climate scienceClimate science where similar challenges exist. (shrink)

Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main (...) arguments for and against the possibility of unrestricted quantification, highlighting some of the broader implications of the debate. (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)

Craniology – the practice of inferring intelligence differences from the measurement of human skulls – survived the dismissal of phrenology and remained a widely popular research program until the end of the nineteenth century. From the 1970s, historians and sociologists of science extensively focused on the explicit and implicit socio-cultural biases invalidating the evidence and claims that craniology produced. Building on this literature, I reassess the history of craniological practice from a different but complementary perspective that relies on recent developments (...) in the epistemology of measurement. More precisely, I identify two aspects of the measurement culture of nineteenth-century craniologists that are crucial to understand the lack of validity of craniological inference: their neglect of the problem of coordination for their presupposed quantification of intelligence and their narrow view of calibration. Based on my analysis, I claim that these methodological shortcomings amplified the impact of the socio-cultural biases of craniologists, which had a pervasive role in their evidential use of measurement. Finally, my argument shows how the epistemology of measurement perspective can offer useful tools in debates concerning the use of biological evidence to foster social discourse and for analyzing the relationship between theory, evidence, and measurement. (shrink)

The question of the origin of polyadic expressivity is explored and the results are brought to bear on Bertrand Russell's 1903 theory of denoting concepts, which is the main object of criticism in his 1905 "On Denoting". It is shown that, appearances to the contrary notwithstanding, the background ontology of the earlier theory of denoting enables the full-blown expressive power of first-order polyadic quantification theory without any syntactic accommodation of scopal differences among denoting phrases such as 'all φ', 'every (...) φ', and 'any φ' on the one hand, and 'some φ' and 'a φ' on the other. The case provides an especially vivid illustration of the general point that structural (or ideological) austerity can be paid for in the coin of ontological extravagance. (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 infinitary 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 infinitary 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 infinitary rules of inference in their reasoning. (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)

It is common in metaphysical discourse to make claims like “Everything is self-identical” in which “everything” is intended to range over everything. This sort of “unrestricted” generality appears central to metaphysical discourse. But there is debate whether such generality, which appears to involve quantification over an all-inclusive domain, is even meaningful. To address this concern, Shaughan Lavine and Vann McGee supply competing accounts of the generality expressed by this use of “everything.” I argue that, from the perspective of the (...) metaphysician, neither of their proposals is entirely suitable. But their central insights, as well as their shortcomings, suggest an account which is suitable for metaphysical discourse, what I call “genuinely unrestricted quantification.” For while genuinely unrestricted quantification does not directly supply an account of the metaphysician's “everything,” it disentangles what are properly metaphysical issues from issues concerning how we ought to understand the quantifiers. It makes clear that whether the metaphysician's “everything” is meaningful cannot simply be resolved by supplying an appropriate account of our understanding of quantification. It depends on addressing certain substantive ontological questions. (shrink)

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional (...) logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions. (shrink)

E. J. Lowe and others argue that there can be 'uncountable' things admitting of no numerical description. This implies that there can be something without there being at least one such thing, and that things can be identical without being one or nonidentical without being two. The clearest putative example of uncountable things is portions of homogeneous stuff or 'gunk'. The paper argues that there is a number of portions of gunk if there is any gunk at all, and that (...) the possibility of uncountable things is inadequately supported. (shrink)

The use of digital tracking technologies is a widespread phenomenon. Millions of people around the world now track, document, and analyse their physical activities, vital functions, and daily habits through wearable devices, apps, and platforms. The aim is to assess and improve health, productivity, and wellbeing. The current Covid-19 pandemic has accelerated the uptake of tracking technologies. At the heart of this trend lies the quantification of the body, deemed as a key element in medical practice and personal self-care. (...) While often couched in positive promotional terms that highlight its value to users' mental, emotional, and physical health, it is also raising a host of issues and concerns that are at once ontological, ethical, political, social, legal, economic, and aesthetic. The Quantification of Bodies in Health aims to deepen understanding of this growing phenomenon and of the role of self-tracking practices in everyday life. It brings together established and emerging authors working at the intersection of philosophy, sociology, history, psychology, and digital culture, while bridging between philosophical and empirical approaches. A timely topic of extreme relevance and significance, The Quantification of Bodies in Health constitutes a useful and unique companion for anyone interested in the study of body quantification and self-tracking practices. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it (...) has been argued that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

The literature contains a popular argument in favor of the position that conditional attitudes are not simple attitudes with conditional contents but, rather, have a more complex structure. In this paper I show that an analogous argument applies to what we might call quantificational attitudes—like an intention to follow every bit of good advice I receive or a desire to get rabies shots for each bite I incur from an infected bat. The conditions under which these attitudes are satisfied and (...) thwarted are not captured by claiming that they are simple attitudes with quantificational contents. So, the argument supports a novel position—that quantificational attitudes have a more complex structure. After sketching the form of this extra structure, I show how similar considerations count in favor of the existence of genuinely quantificational speech acts. (shrink)

The Philosophical Review, Vol. XCVI, No. 4 (October 1987). Categorically proves that Leibniz's Law (the principle that any instance of _for any x and y, if x=y, then if ...x..., then ..y..._ is true) is not a principle of which is true of natural language objectual quantification.

This paper is about avoiding commitment to an ontology of possible worlds with two primitives: a hyperintensional connective like ‘in virtue of’, and primitive quantification into predicate position. I argue that these tools (which some believe can be independently motivated) render dispensable the ontology of possible worlds needed by traditional anaylses of modality. They also shed new light on the notion of truth-at-a-world.

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. (...) Utilizing recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (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)

When multiple individuals interact in a conversation or as part of a large crowd, emergent structures and dynamics arise that are behavioral properties of the interacting group rather than of any individual member of that group. Recent work using traditional signal processing techniques and machine learning has demonstrated that global acoustic data recorded from a crowd at a basketball game can be used to classify emergent crowd behavior in terms of the crowd's purported emotional state. We propose that the description (...) of crowd behavior from such global acoustic data could benefit from nonlinear analysis methods derived from dynamical systems theory. Such methods have been used in recent research applying nonlinear methods to audio data extracted from music and group musical interactions. In this work, we used nonlinear analyses to extract features that are relevant to the behavioral interactions that underlie acoustic signals produced by a crowd attending a sporting event. We propose that recurrence dynamics measured from these audio signals via recurrence quantification analysis (RQA) reflect information about the behavioral dynamics of the crowd itself. We analyze these dynamics from acoustic signals recorded from crowds attending basketball games, and that were manually labeled according to the crowds' emotional state across six categories: angry noise, applause, cheer, distraction noise, positive chant, and negative chant. We show that RQA measures are useful to differentiate the emergent acoustic behavioral dynamics between these categories, and can provide insight into the recurrence patterns that underlie crowd interactions. (shrink)

Those who want to interpret the quantifier ? (3 x) (. . .x. . .)'as having no existence commitment often fail to distinguish between this objective and that of merely changing the values of the variables. The confusion vitiates solutions of the singular existence anomalies which purport to be based on a non?existential interpretation of the quantifier. An example of one who makes the distinction but still interprets the particular quantifier non?existentially is offered by Czeslaw Lejewski. Objection to the classical (...) interpretation of the quantifiers often runs hand in hand with aversion to extensional logic. However, it is at least arguable that such an aversion is the result of underestimating the resources of extensional logic. These points arc discussed in the wake of Professor Marcus's recent paper in this journal ?Interpreting Quantification? (shrink)

This article addresses nominal quantification in English in relation to discrete and continuous quantity, the two semantic categories of discrete and continuous / mass being analysed as interpretations of syntax. It re-examines the hypothesis of non-quantifiable continuous nouns as well as some theoretical questions such as overloaded definitions, unexploited oppositions or notions found without an explicit definition, as is sometimes the case with the concept of collective. The study then proceeds to examine semantic multiplicity in connection with grammatical number. (...) Plural is examined in association with numerals and fuzzy quantifiers. The singular category also also yields interpretations of multiplicity, whether with mass-nouns or with discrete collective nouns. This, together with the possible conversion of the latter into mass-nouns, draws one’s attention to a mode of reference shared by mass nouns and collective discrete nouns. (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)

Brentano's innovations in logical theory are considered in the context of his descriptive psychology, with its distinction between differences in quality and in object of mental phenomena. Objections are raised to interpretations that depend on a parallel between Urteil and assertion of a proposition. A more appropriate parallel is drawn between the assertion as subject to description in a metalanguage and the Urteil as secondary object in inner perception. This parallel is then applied so as to suggest a reinterpretation of (...) substitutional quantification, rendering the substitutional interpretation immune to problems that often arise as to the relation between substitutional range and referential range. (shrink)

This paper will attempt to integrate (1) some new reflections on the implications for ontology of Monistic interpretations of formulae in quantification theory, with (2) a review of earlier material that I have published on such implications, and with (3) a sketch of several points made by others which bear on related issues. I hope that a review of these moves and issues might indirectly help the reader in dealing with two strange questions. (A) Does the development of modern (...) quantification theory with its ways of systematically formalising relational inferences throwany light on Ontology, on the question of What There Is for scientists and applied mathematicians to study? (B) Are there any analogies between Monist interpretations of quantification theory and the attraction of holding down the number of basic entities in physics by viewing some as mere modes of other more ‘really basic’ ones? More directly I try to throw sympathetic light on more traditional philosophers of science like Leibniz and Spinoza. (shrink)

In this paper, I discuss the quantificational variability of Cheyenne indeterminates: the variety of interpretations they can receive and the grammatical contexts that condition these interpretations. Building on analyses of indeterminates in other languages, such as Kratzer and Shimoyama (2002), I present a Hamblin-style analysis of Cheyenne indeter- minates. The proposal builds on the analysis of declaratives and interrogatives argued for in Murray (2010). This analysis can account for the quantificational variability of indeterminates in the scope of propositional operators as (...) well as the scope of illocutionary mood markers. The analysis is formalized in an independently motivated update semantics (Update with Centering, Bittner 2011), which automatically provides the required alternatives. (shrink)

The paper maintains that Frege's quantification of sentence positions motivates his identification of sentences as proper names of truth-values; that this identification is fully compatible with the Context Principle; that the relation of a thought to its truth-value is the primary case of the relation of sense to meaning. The paper offers a reconstruction of Frege's defense of in pp. 33-5 of “On Sense and Meaning”O artigo sustenta que a quantificação Fregeana sobre posições de sentença motiva sua identificação de (...) sentenças como nomes próprios de valores de verdade; que esta identificação é inteiramente compatível com o Princípio do Contexto; que a relação de um pensamento com o seu valor de verdade é o caso primário da relação do sentido para com o significado. O artigo oferece uma reconstrução da defesa de Frege de nas pp. 33-5 de “Sobre o Sentido e o Significado”. (shrink)

This paper investigates the meaning of restricted quantification when the embedded conditional is taken as the conditional of some first-order connexive logics. The study is carried out by checking the suitability of RQ for defining a connexive class theory, in analogy to the definition of Boolean class theory by using RQ in classical logic. Negative results are obtained for Wansing’s first-order connexive logic QC and one variant of Priest’s first-order connexive logic QP. A positive result is obtained for another (...) variant of QP. (shrink)

Although Harry Woolf’s great collective volume Quantification mostly overlooked biology, Thomas Kuhn’s chapter there on the role of quantitative measurement within the physical sciences maps quite well onto the forms of reasoning that actually persuade us as biologists 50 years later. Kuhn distinguished between two contexts, that of producing quantitative anomalies and that of resolving them. The implied form of reasoning is actually C. S. Peirce’s abduction or inference to the best explanation: “The surprising fact C is observed; but (...) if A were true, C would be a matter of course; hence there is reason to suspect that A is true.” This article reviews abduction and the Kuhnian dichotomy in a range of classic examples where quantitative reasoning has ended arguments in the natural sciences. Included are John Snow’s discovery of the cause of cholera, Jean Perrin’s proof that atoms exist, the discovery of the double helix, the Alvarezes’ explanation of the extraterrestrial origin of the Cretaceous-Tertiary extinction, and current examples in passive smoking, ulcers, and the anthropogenicity of global warming. Modern biology is a quantitative science to the extent that we operate by “strong inference,” the insistence that our data are surprising on everybody else’s hypotheses but follow as a matter of course from our own, and that we demand numerical consilience whenever we infer across levels of analysis or across disciplines. (shrink)

A principal goal of this book is to develop and apply the Situation Semantics framework. Jean Mark Gawron and Stanley Peters adopt a version of the theory in which meanings are built up via syntactically driven semantic composition rules. They provide a substantial treatment of English incorporating treatments of pronomial anaphora, quantification, donkey anaphora, and tense. The book focuses on the semantics of pronomial anaphora and quantification. The authors argue that the ambiguities of sentences with pronouns cannot be (...) adequately accounted for with a theory that represents anaphoric relations only syntactically; their relational framework uniformly deals with anaphoric relations as relations between utterances in context. They argue that there is no need for a syntactic representation of anaphoric relations, or for a theory that accounts for anaphoric ambiguities by resorting to two or more kinds of anaphora. Quantifier scope ambiguities are handled analogously to anaphoric ambiguities. This treatment integrates the Cooper Store mechanism with a theory of meaning that provides both a natural setting for it and a convincing account of what, semantically, is going on. Jean Mark Gawron is a researcher for Hewlett Packard Laboratories, Palo Alto. Stanley Peters is professor of linguistics and symbolic systems at Stanford University and is director of the Center for the Study of Language and Information. (shrink)

Special quantifiers are quantifiers like 'something', 'everything', and 'several things'. They are special both semantically and syntactically and play quite an important role in philosophy, in discussions of ontological commitment to abstract objects, of higher-order metaphysics, and of the apparent need for propositions. This paper will review and discuss in detail the syntactic and semantic peculiarities of special quantifiers and show that they are incompatible with substitutional and higher-order analyses that have recently been proposed. It instead defends and develops in (...) formal detail a semantic analysis of special quantifiers as nominalizing quantifiers. On this analysis, special quantifiers involve both singular objectual quantification and implicit on non-singular (higher-order, plural, or mass) quantification. The analysis rests on a range of recent insights and proposals in generative syntactic theory, in particular the recognition of '–thing' as a light noun and a potential classifier as well as recent views of the decomposition of attitudinal and locutionary verbs in syntax. (shrink)

Andrew Bacon, John Hawthorne, and Gabriel Uzquiano have recently argued that free logics—logics that reject or restrict Universal Instantiation—are ultimately not promising approaches to resolving a family of intensional paradoxes due to Arthur Prior. These logics encompass ramified and contextualist approaches to paradoxes, and broadly speaking, there are two kinds of criticism they face. First, they fail to address every version of the Priorean paradoxes. Second, the theoretical considerations behind the logics make absolutely general statements about all propositions, properties of (...) propositions, etc., but because this sort of intensional quantification is always restricted in the logics, they cannot even express those considerations. I present a novel sort of free logic, which rejects the standard Universal Instantiation but validates a restricted form of the rule, and which addresses both kinds of criticism by allowing some propositions to be unrestricted in their quantification. (shrink)

The existential and universal quantifiers in Japanese both consist of two morphemes: an indeterminate pronoun and a quantificational suffix. This paper examines the distributional characteristics of these suffixes (ka for the existential quantifier and mo for the universal quantifier). It is shown that ka can appear in a wider range of structural positions than mo can. This difference receives explanation on semantic grounds. I propose that mo is a generalized quantifier. More specifically, I assume that the phrase headed by mo (...) is of type ${\langle\langle\alpha, t\rangle, t}$ . Because of its type, mo cannot appear in certain structural positions without causing type mismatch. Ka, on the other hand, is a choice function variable of type ${\langle\alpha/t, \alpha\rangle}$ , and due to its type, its distribution is not as restricted. One of the consequences of this analysis is that there are no quantifier raising or type shifting operations in Japanese that would adequately obviate type mismatch. (shrink)

This paper examines the quantification theory of *9 of Principia Mathematica. The focus of the discussion is not the philosophical role that section *9 plays in Principia's full ramified type-theory. Rather, the paper assesses the system of *9 as a quantificational theory for the ordinary predicate calculus. The quantifier-free part of the system of *9 is examined and some misunderstandings of it are corrected. A flaw in the system of *9 is discovered, but it is shown that with a (...) minor repair the system is semantically complete. Finally, the system is contrasted with the system of *8 of Principia's second edition. (shrink)

We discuss the thesis formulated by Hintikka that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that to account for these phenomena, we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries. The main contribution of the paper is showing how we can add structure to (...) contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments. (shrink)

The format of this book is unusual, especially for a book about linguistics. The book is meant primarily as a research monograph aimed at linguists who have some background in formal semantics, e. g. Montague Grammar. However, I have two other audiences in mind. Linguists who have little or no experience of formal semantics, but who have worked through a basic mathematics for linguists course (e. g. using Wall, 1972, or Partee, 1978), should, perhaps with the help of a sympathetic (...) Montague gramma rian, be able to discover enough of how I have adapted some of the basic ideas in formal semantics to make the developments that I undertake in the rest of the book accessible. Logicians and computer scientists who know about model theoretic semantics and formal systems should be able to glean enough from Chapters I and II about linguistic concerns and techniques to be able to read the remainder of the book, again possibly with the help of a sympathetic Montague grammarian. However, readers should beware. Chapter II is not meant as a general introduction either to formal semantics or to linguistics and while much of the presentation there is going over ground that is already well covered in the literature, the particular formulation and the emphases are very much oriented to the developments to be undertaken later in the book. (shrink)

The paper maintains (1) that Frege's quantification of sentence positions motivates his identification of sentences as proper names of truth-values; (2) that this identification is fully compatible with the 'context principle'; (3) that the relation of a thought to its truth-value is the primary case of the relation of sense to meaning. The paper offers a reconstruction of Frege's defense of (1) in pp. 33-35 of "On Sense and Meaning".

Bainbridge’s well known “Ironies of Automation” Analysis, design and evaluation of man–machine systems. Elsevier, Amsterdam, pp 129–135, 1983. https://doi.org/10.1016/B978-0-08-029348-6.50026-9) laid out a set of fundamental criticisms surrounding the promises of automation that, even 30 years later, remain both relevant and, in many cases, intractable. Similarly, a set of ironies in technologies for sensor driven self-quantification is laid out here, spanning from instrumental problems in human factors design to much broader social problems. As with automation, these ironies stand in the (...) way of many of the promised benefits of these wearable technologies. It is argued here that without addressing these ironies now, the promises of wearables may not come to fruition, and instead users may experience outcomes that are opposite to those which the designers seek to afford, or, at the very least, those which consumers believe they are being offered. This paper describes four key ironies of sensor driven self-quantification: know more, know better versus no more, no better; greater self-control versus greater social control; well-being versus never being well enough; more choice versus erosion of choice. (shrink)