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)

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)

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)

Abstract At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part of the (...) misleading material mode of speech, and as such dismissed, rather than addressed, ontological problems. Central to the analysis in the present paper is the concept of an explication, which was seen by both Carnap and Quine as being of great philosophical importance. It will be shown that the concept of explication played a significant role in how each formulated their mature position on ontology. Both these final positions on ontology can also be seen as a evolving in reaction to Carnap’s flawed handling of ontological matters at the time of Syntax. Carnap, influenced by Tarski’s work on semantics, comes to believe that the concept of reference can be given an acceptable explication, and that by doing so we can see reference to abstract objects as unobjectionable. As a result, Carnap develops a position very different from the one presented in Syntax. Quine strongly rejected the instrumentalism of Syntax, and sought to give an explication of ontological questions that was language independent. This paper closes with a discussion of each’s understanding of the other’s position. (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)

Standard first-order logic plus quantifiers of all finite orders ("SFOLω") faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is (...) removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOLω type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOLω models. (shrink)

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

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)

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)

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 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)

We develop a variant of Least Fixed Point logic based on First Orderlogic with a relaxed version of guarded quantification. We develop aGame Theoretic Semantics of this logic, and find that under reasonableconditions, guarding quantification does not reduce the expressibilityof Least Fixed Point logic. But we also find that the guarded version ofa least fixed point algorithm may have a greater time complexity thanthe unguarded version, by a linear factor.

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)

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)

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)

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

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)

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)

Quantification, understood in the widest possible sense, is a phenomenon of fundamental interest for logic and linguistics and at the same time a phenomenon whose exegesis presents notorious problems in both of these disciplines. The general point to be made in the present essay is this: that there is a lack of understanding of the real nature of quantification, both in natural language and in logic itself, and that this is a direct consequence of a serious defect in (...) Morris’s division of semiotics into three autonomous branches of syntax, semantics, and pragmatics, the study of each of which is supposed to proceed independently of the study of any other. The aim of this paper is thus twofold: on the one hand to show that the real exegesis of quantification may be attained only under a certain interpretation of semiotics as such; and on the other hand to show that the very fact of the attainability of this authentic explanation of the nature of quantification gives grounds to speak of the necessity of reassessing certain notions on which logic, linguistics, and semiotics are currently based. (shrink)

Alternative readings of quantification are considered. The absence of an unequivocal translation into ordinary speech is noted. Some examples are cited which, in the opinion of the author, are a result of equivocal readings of quantification, or unnecessarily restrictive readings which obscure its primary function.

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.

Ramsey defined truth in the following way: x is true if and only if ∃p(x = [p] & p). This definition is ill-formed in standard first-order logic, so it is normally interpreted using substitutional or some kind of higher-order quantifier. I argue that these quantifiers fail to provide an adequate reading of the definition, but that, given certain adjustments, standard objectual quantification does provide an adequate reading.

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)

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 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)

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)

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)

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)

Complexity in our universe, Herbert Simon once noted, generally takes a hierarchical, nearly decomposable form. If our purpose as biologists is to "carve Nature at the joints," then the quantitative biologist's pattern questions must embody some tentative claim of where the explanatory joints are—only after meaningful qualifications can notions of variance and covariance make sense. In morphometrics, specimens and variables alike can be "carved at the joints," with a correspondingly great gain in explanatory power in both versions. Simon's advice is (...) that the competent biologist's measurements should lie entirely within a single organismal component or else deal entirely with one of the joints. In either context, our best contemporary rhetorics of explanation in biology may resemble morphometrics in their frank combination of carefully supervised parallel quantifications that, taken together, result in new qualifications, leading in turn to new quantifications, and so on. In short, the relation between qualitative and quantitative in the organismal biological sciences is not an opposition but a complementarity, and the modern biometrical statistics of organismal form may be a particularly apposite praxis for exploring it. (shrink)

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell (...) successfully antedates Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain. (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)

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)

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)

Quineans have taken the basic expression of ontological commitment to be an assertion of the form '' x '', assimilated to theEnglish ''there is something that is a ''. Here I take the existential quantifier to be introduced, not as an abbreviation for an expression of English, but via Tarskian semantics. I argue, contrary to the standard view, that Tarskian semantics in fact suggests a quite different picture: one in which quantification is of a substitutional type apparently first proposed (...) by Geach. The ontological burden is borne by constant symbols, and truth is defined separately from reference. (shrink)

This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.

Next SectionWe discuss the thesis formulated by Hintikka (1973) 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.

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)

I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an relation. Next, I sketch a different approach that is more adequate than PQL for capturing plural aspects of (...) natural language semantics and logic. I conclude with a criticism of the claim that PQL should replace natural language for specific philosophical or scientific purposes. (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)

BackgroundThe rating of perceived exertion scales with respiratory and muscular illustrations are recognized as simple and practical methods to understand individual psychometric characteristics in breathing and muscle exertion during exercise. However, the implementation of respiratory and muscular RPE to quantify training load in futsal training camps has not been examined. This study investigates respiratory and muscular RPE relationships during domestic training camps and overseas training camps in an under 20 futsal national team.MethodsData collected from eleven field players were used for (...) comparison in this study. All players reported Borg CR10 RPE and 7-scales respiratory RPE and muscular RPE after training sessions and matches. Additionally, total distance covered and training impulse were used to quantify external and internal loads via the Polar Team Pro system. Paired-sample t-tests were used to compare the RPECR10, RPErespiration, RPEmuscle, TD, and TRIMP between DTC and OTC. Furthermore, linear regression was performed to determine the relationships among all RPE scales, TD, and TRIMP.ResultsThe RPECR10, TD, and TRIMP showed significant difference between DTC and OTC. Furthermore, linear regression analyses showed significant correlation between RPErespiration and RPEmuscle, RPECR10 and RPErespiration, and RPECR10 and RPEmuscle.ConclusionPictorial RPErespiration or RPEmuscle can be used as an alternative to quantify perceived measures of internal loads during DTC and OTC in futsal players. Interpretation of perceived measures of training load and cardiac-related responses in association with external training loads during short-term training camps would be useful in further understanding the demands of futsal players’ experience in these circumstances. (shrink)

In my book, Worlds and Individuals, Possible and Otherwise , I use the novel idea of modal tense to respond to a number of arguments against modal realism. Peter van Inwagen’s million-carat-diamond objection is one of them. It targets the version of modal realism by David Lewis and exploits the fact that Lewis accepts absolutely unrestricted quantification. The crux of my response is to use modal tense to neutralize absolutely unrestricted quantification. Seahwa Kim says that even when equipped (...) with modal tense, I am unsuccessful, given my view of reality and the proper use of modal tense in speaking of reality. I counter her attempt at resurrecting van Inwagen’s objection and clarify how we should use modal tense and how we should talk about reality. (shrink)

We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize (...) all collective quantification in natural language. (shrink)

What do we quantify when we attempt to quantify semiotic systems and theories? How sound are potential quantifications in terms of interpretive values within some varieties of semiotic theory? We will make a distinction between formalization and quantification in order to understand what to quantify, how to quantify it and why quantification may be a desirable outcome for semiotic theory. The implications of this stance may be relevant and philosophically interesting in light of the naturalized project of biosemiotics. (...) In this paper we will try to understand some ideas behind the rationale of formalizing and quantifying semiotic phenomena and discuss whether this possibility can or should map to functionalized descriptions of semiosis and the sign. (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 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.

Following David Lewis, Ted Sider has famously argued that unrestricted first-order quantification cannot be vague. His argument was intended as a type of reductio: its strategy was to show that the mere hypothesis of unrestricted quantifier vagueness collapses into the claim that unrestricted quantification is precise. However, this short article considers two natural reconstructions of the argument, and shows that each can be resisted. The theme will be that each reconstruction of the argument involves assumptions which advocates of (...) vague quantification have independent reason to reject. (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)

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)