Reading through the Corpus Aristotelicum we come across a group of expressions meant to indicate predicative relations, which lead us to think that Aristotle connected predication to a part-whole relation. He frequently calls the ‘εἴδη’, “species”, ‘μέρη’, “parts”, of their genera. More generally, the universal is said to contain that of which it is true. In a parallel way, what is contained by something is also what is under something else. Again, it is quite common for him to consider (...) the species as partaking of their genera. Although the relation of partaking is normally used to qualify the way in which species are related to their genera, sometimes also the relation between particulars and species or even genera is expressed in terms of partaking. (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)

Originally published in 1981. This is a book for the final year undergraduate or first year graduate who intends to proceed with serious research in philosophical logic. It will be welcomed by both lecturers and students for its careful consideration of main themes ranging from Gricean accounts of meaning to two dimensional modal logic. The first part of the book is concerned with the nature of the semantic theorist's project, and particularly with the crucial concepts of meaning, truth, and semantic (...) structure. The second and third parts deal with various constructions that are found in natural languages: names, quantifiers, definite descriptions, and modal operators. Throughout, while assuming some familiarity with philosophical logic and elementary formal logic, the text provides a clear exposition. It brings together related ideas, and in some places refines and improves upon existing accounts. (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)

This book details how quantification can serve both as evidence and as an instrument of government, whether when dealing with statistics on employment, occupational health and economic governance, or when developing public management or target-driven policies. In the process, it presents a thought-provoking homage to Alain Desrosières, who pioneered ways to study large numbers and the politics underlying them. It opens with a summary of Desrosières's contributions to the field in which several generations of researchers detail how this statistician (...) and historian profoundly influenced them. This tribute, based on personal testimonies, bears witness to the vitality of the school of thought and analytical framework Desrosières initiated. Next, a collection of essays explores the statistical argument in the neoliberal era, examining issues such as counting the homeless in Europe, measuring the performance of public services, and quantifying the effects of public action on the unemployed in France. The third part details the uses of quantification. It reveals that although statistics are frequently used to the advantage of those in power, they can also play a vital role in challenging and resisting both the conventions underlying the measurements as well as the measurements themselves.Featuring the work of economists, historians, political scientists, sociologists, and statisticians, this title provides readers with a thoughtful look at an influential figure in the history of statistics. It also shows how statistics are used to direct public policy, the degree of conflict that is possible in their production, and the disputes that can develop around their uses. (shrink)

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)

This paper critically examines the debate between William of Ockham and his contemporary Peter Auriol on how to account for the intension and remission of forms. Peter Auriol denies that an added degree of a quality such as the theological virtue of charity could be anything other than something which is neither a universal nor an individual and which cannot be grasped by intuition, but must be posited in order to account for the possibility that an accidental form can vary (...) in intensity. Ockham aims at proving that Auriol’s account is inconsistent. In my opinion, Ockham does not succeed, nor does he succeed in defending a consistent account of the metaphysics underlying the intension and remission of forms. Indeed, he conceives of the degree of a quality as a part of the intensified quality which, while being an individual that is really distinct from the quality and can be picked out, forms a unity with it in such a way that the union of the degree and the quality is itself an individual. Ockham fails to distinguish the notion of maximal resemblance holding between a quality’s degree and the quality from the notion of maximal resemblance which holds between individuals of the same species. In the end, he is led to give up the idea that a degree is an individual that can be picked out in order to protect the core thesis of his nominalism about universals. (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)

In Parts of Classes and "Mathematics is Megethology" David Lewis shows how the ideology of set membership can be dispensed with in favor of parthood and plural quantification. Lewis's theory has it that singletons are mereologically simple and leaves the relationship between a thing and its singleton unexplained. We show how, by exploiting Kit Fine's mereology, we can resolve Lewis's mysteries about the singleton relation and vindicate the claim that a thing is a part of its singleton.

Jay Zeman one must keep a bright lookout for unintended and unexpected changes thereby brought about in the relations of different significant parts of the diagram to one another. Such operations upon diagrams, whether external or imaginary, take the place of the experiments upon real things that one performs in chemical and physical research. Chemists have ere now, I need not say, described experimentation as the putting of questions to Nature. Just so, experiments upon diagrams are questions put to (...) the Nature of the relations concerned (4.530). 1 The diagrammatic nature of mathematical reasoning suggests that as my power to create diagrams increases, so too will my capacity for fruitful mathematical reasoning. Peirce's own work involved an unending series of experiments with different diagrammatic notations, all interesting, some difficult, some extremely fruitful. And the diagrammatic notations available are not only a function of some kind of “internal mental activity.” As Dewey has noted, “Breathing is an affair of the air as truly as of the lungs; digesting an affair of food as truly as of tissues of stomach” (Dewey, 15); so analogously is mathematical reasoning an affair of the diagrams available as truly as of the “mind” (which is then not limited to something inside the head, but includes the relevant diagrams, “external” as well as “internal”); so does mathematical reasoning have its “alembics and cucurbits” just as surely as does chemistry. In doing mathematical reasoning, we make of the diagrams “instruments of thought,” and advances in the technology of diagrams can directly affect our patterns of reasoning. I can imagine Peirce spending hours (and dollars) in a modern artists' supply store. (shrink)

The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we (...) can replace a universal proposition about any universe (finite or infinite, countable or uncountable) by a complex proposition (= sentence built up from atomic sentences and the connectives). But from the point of view of communication such a replacement is not possible if the universe is infinite. (shrink)

This book attempts to marry truth-conditional semantics with cognitive linguistics in the church of computational neuroscience. To this end, it examines the truth-conditional meanings of coordinators, quantifiers, and collective predicates as neurophysiological phenomena that are amenable to a neurocomputational analysis. Drawing inspiration from work on visual processing, and especially the simple/complex cell distinction in early vision (V1), we claim that a similar two-layer architecture is sufficient to learn the truth-conditional meanings of the logical coordinators and logical quantifiers. As a prerequisite, (...) much discussion is given over to what a neurologically plausible representation of the meanings of these items would look like. We eventually settle on a representation in terms of correlation, so that, for instance, the semantic input to the universal operators (e.g. and, all)is represented as maximally correlated, while the semantic input to the universal negative operators (e.g. nor, no)is represented as maximally anticorrelated. On the basis this representation, the hypothesis can be offered that the function of the logical operators is to extract an invariant feature from natural situations, that of degree of correlation between parts of the situation. This result sets up an elegant formal analogy to recent models of visual processing, which argue that the function of early vision is to reduce the redundancy inherent in natural images. Computational simulations are designed in which the logical operators are learned by associating their phonological form with some degree of correlation in the inputs, so that the overall function of the system is as a simple kind of pattern recognition. Several learning rules are assayed, especially those of the Hebbian sort, which are the ones with the most neurological support. Learning vector quantization (LVQ) is shown to be a perspicuous and efficient means of learning the patterns that are of interest. We draw a formal parallelism between the initial, competitive layer of LVQ and the simple cell layer in V1, and between the final, linear layer of LVQ and the complex cell layer in V1, in that the initial layers are both selective, while the final layers both generalize. It is also shown how the representations argued for can be used to draw the traditionally-recognized inferences arising from coordination and quantification, and why the inference of subalternacy breaks down for collective predicates. Finally, the analogies between early vision and the logical operators allow us to advance the claim of cognitive linguistics that language is not processed by proprietary algorithms, but rather by algorithms that are general to the entire brain. Thus in the debate between objectivist and experiential metaphysics, this book falls squarely into the camp of the latter. Yet it does so by means of a rigorous formal, mathematical, and neurological exposition – in contradiction of the experiential claim that formal analysis has no place in the understanding of cognition. To make our own counter-claim as explicit as possible, we present a sketch of the LVQ structure in terms of mereotopology, in which the initial layer of the network performs topological operations, while the final layer performs mereological operations. The book is meant to be self-contained, in the sense that it does not assume any prior knowledge of any of the many areas that are touched upon. It therefore contains mini-summaries of biological visual processing, especially the retinocortical and ventral /what?/ parvocellular pathways computational models of neural signaling, and in particular the reduction of the Hodgkin-Huxley equations to the connectionist and integrate-and-fire neurons Hebbian learning rules and the elaboration of learning vector quantization the linguistic pathway in the left hemisphere memory and the hippocampus truth-conditional vs. image-schematic semantics objectivist vs. experiential metaphysics and mereotopology. All of the simulations are implemented in MATLAB, and the code is available from the book’s website. • The discovery of several algorithmic similarities between visison and semantics. • The support of all of this by means of simulations, and the packaging of all of this in a coherent theoretical framework. (shrink)

This paper argues that ‘that’-clauses are not singular terms (without denying that their semantical values are propositions). In its first part, three arguments are presented to support the thesis, two of which are defended against recent criticism. The two good arguments are based on the observation that substitution of ‘the proposition that p’ for ‘that p’ may result in ungrammaticality. The second part of the paper is devoted to a refutation of the main argument for the claim that ‘that’-clauses are (...) singular terms, namely that this claim is needed in order to account for the possibility of quantification into ‘that’-clause position. It is shown that not all quantification in natural languages is quantification into the position of singular terms, but that there is also so-called ‘non-nominal quantification’. A formal analysis of non-nominal quantification is given, and it is argued that quantification into ‘that’-clause position can be treated as another kind non-nominal quantification. (shrink)

This paper consists roughly of three parts. In the first part, an attempt has been made to find some tenable interpretation of Hamilton's logic. This results in accepting that Hamilton's logic can be "saved" if it is understood as being an everday language version of Euler's relations, i.e., extensional relations between terms. In the second part, the propositions of Euler and the propositions of Aristotle are compared and found to be interdefinable: every proposition of Aristotle can be defined by (...) a disjunction of Euler's propositions, and every proposition of Euler can be defined by a conjunction of Aristotle's propositions. In the third part, extensional interpretation is applied to the traditional logic. As a result the 19 traditional syllogisms are reduced to 11. (shrink)

In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural (...) quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)

Ontological pluralism is the view that there are different fundamental ways of being. Recent defenders of this view—such as Kris McDaniel and Jason Turner—have taken these ways of being to be best captured by semantically primitive quantifier expressions ranging over different domains. They have thus endorsed, what I shall call, quantificational pluralism. I argue that this focus on quantification is a mistake. For, on this view, a quantificational structure—or a quantifier for short—will be whatever part or aspect of reality’s (...) structure that a quantifier expression carves out and reflects. But if quantificational pluralism is true, then a quantifier should be more natural than its corresponding domain; and since it does not appear to be the case that a quantifier is more natural than its corresponding domain, quantificational pluralism does not appear to be true. Thus, I claim, an ontological pluralist should not be a quantificational pluralist. (shrink)

A broad-scale quantification of the measure of quality for scholarship is under way. This trend has fundamental implications for the future of academic publishing and employment. In this essay we want to raise questions about these burgeoning practices, particularly how they affect philosophy of education and similar sub-disciplines. First, details are given of how an ‘impact factor’ is calculated. The various meanings that can be attached to it are scrutinised. Second, we examine how impact factors are used to make (...) various ‘high stakes’ academic decisions, such as hiring and promotion, funding of research projects and how much money is to be awarded to a particular area. By focusing on a particular practice, problems with the application of the metric generally are outlined. Finally, we offer some general observations about the unintended consequences and other problems arising from the widespread use of this metric, including attempts to ‘game the system’. We argue that the use of impact factors increasingly shapes the kind of topics and issues scholars write on, their choices of methodology, and their choice of publication venues for their work. Technical measures and mechanisms tend to ‘colonise’ the qualitative and professional judgments that must also be part of the process of evaluation, and for which bibliometrics alone cannot offer a substitute. (shrink)

In this paper, a response to Ed Levy's discussion of medical quantification, I reflect on the ambitions of my book Trust in Numbers. I explore the idealized method of randomized clinical trials, revealed in his case study, as a social technology, one endowed with a persuasive scientific rationale but shaped also by political and social demands. The scholarly study of quantification requires not a choice between blind admiration and sweeping rejection, but a nuanced understanding. This should take into (...) account not only the cognitive aspects of science, but also its role in relation to institutions and customs, examined with some specificity. While history is narrowed and distorted when it is written to support a position on some present issue, historical and social studies of science should at least provide tools of criticism. For this, the historian of science must look beyond narrow communities of specialists, and seek a wider perspective on science as an administrative tool and a bearer of cultural and political values. (shrink)

In this review we highlight the importance of defining the untranslated parts of transcripts, and present a number of computational approaches for the discovery and quantification of alternative transcription start and poly-adenylation events in high-throughput transcriptomic data. The fate of eukaryotic transcripts is closely linked to their untranslated regions, which are determined by the position at which transcription starts and ends at a genomic locus. Although the extent of alternative transcription starts and alternative poly-adenylation sites has been revealed (...) by sequencing methods focused on the ends of transcripts, the application of these methods is not yet widely adopted by the community. We suggest that computational methods applied to standard high-throughput technologies are a useful, albeit less accurate, alternative to the expertise-demanding 5′ and 3′ sequencing and they are the only option for analysing legacy transcriptomic data. We review these methods here, focusing on technical challenges and arguing for the need to include better normalization of the data and more appropriate statistical models of the expected variation in the signal. We highlight the importance of defining the untranslated parts of transcripts, and present a number of computational approaches for the discovery and quantification of alternative transcription start site and alternative poly-adenylation events from standard high-throughput transcriptomic data. We discuss the challenges faced by these methods and argue for the use of better statistical models for dealing with biases in the data and variation in the signal. (shrink)

Anderson-like ontological proofs, studied in this paper, employ contingent identity, free principles of quantification of the 1st order variables and classical principles of quantification of the 2nd order variables. All these theories are strongly complete wrt. classes of modal structures containing families of world-varying objectual domains of the 1st order and constant conceptual domains of the 2nd order. In such structures, terms of the 1st order receive only rigid extensions, which are elements of the union of all 1st (...) order domains. Terms of the 2nd order receive extensions and intensions. Given a family of preselected world-varying objectual domains of the 2nd order, non-rigid extensions of the 2nd order terms belong always to a preselected domain connected with a given world. Rigid intensions of the 2nd order terms are chosen from among members of a conceptual domain of the 2nd order, which is the set of all functions from the set of worlds to the union of all 2nd order preselected domains such that values of these functions at a given world belong to a preselected domain connected with this world. (shrink)

In this paper, a response to Ed Levy's discussion of medical quantification, I reflect on the ambitions of my book Trust in Numbers. I explore the idealized method of randomized clinical trials, revealed in his case study, as a social technology, one endowed with a persuasive scientific rationale but shaped also by political and social demands. The scholarly study of quantification requires not a choice between blind admiration and sweeping rejection, but a nuanced understanding. This should take into (...) account not only the cognitive aspects of science, but also its role in relation to institutions and customs, examined with some specificity. While history is narrowed and distorted when it is written to support a position on some present issue, historical and social studies of science should at least provide tools of criticism. For this, the historian of science must look beyond narrow communities of specialists, and seek a wider perspective on science as an administrative tool and a bearer of cultural and political values. (shrink)

David Lewis‘s Parts of Classes is a great book, in all respects. But one of its most interesting thesis, in my mind, is not its core thesis that standard set theory — ZFC — reduces to classical mereology + plural quantification + a primitive singleton-relation, but rather its sub-thesis of how to understand classical mereology, what Lewis calls the thesis of Composition as Identity: (CAI): a whole is the same portion of reality as its many parts taken (...) together; it is them collectively, they collectively are it. CAI is needed as an assumption for the core thesis of Parts of Classes — the reduction of ZFC — on pain of it being unmotivated.1 But CAI is the most interesting in its own right. It is also as such it is presented by Lewis, and received in the literature. In what follows, I critically assess CAI as Lewis presents it in Parts of Classes. I first argue that Lewis‘s presentation of CAI has been misunderstood in the literature (section 1). I then argue that the best (if not the only) way to understand it entails a slightly revisionary semantics for a certain form of predication (section 2). I finally end by showing that this might create more trouble than it solves for Lewis (section 3). (shrink)

The early history of thermometry is most commonly described as the result of a continuous development rather than the product of a single brilliant mind, and yet scholars have often credited the Italian physician Santorio Santori with the invention of the first thermometers. The purpose of using such instruments within the traditional context of Galenic medicine, however, has not been investigated and scholars have consistently assumed that, being subject to the influence of atmospheric pressure and en­vironmental heat, Santorio’s instruments provided (...) unreliable measurements. The discovery that, as early as 1612, Santorio describes all vacuum-related phenomena as effects of the atmospheric pressure of the air, provides ample room for reconsidering his role in the development of precision instruments and the early history of thermometry in particular. By drawing on a variety of written and visual sources, some unpublished, in the first part of this article I argue that Santorio’s appreciation of phenomena related to the weight of the air allowed him to construct the first thermometers working as sealed devices. Finally, in the second part, I consider Santorio’s use of the thermometer as related to the seventeenth-century medical practice and his way to measure the temperature as based on a wide sample of individuals. (shrink)

Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like The Beatles sing Yesterday, a knowledge representation language should be able to express and reason about plural entities — like the Beatles — and their relationships — like sing — with any possible reading (cumulative, distributive or collective).In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the (...) semantics of sentences, is presented. A twofold extension of theA–C concept language is investigated: (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subsumption of concepts, and to compute recognition of individuals. (shrink)

It is well known that the interpretation of quantificational expressions in the comparative clause poses a serious challenge for semantic analyses of the English comparative. In this paper, we develop a new analysis of the comparative clause designed to meet this challenge, in which a silent occurrence of the negative degree quantifier no interacts with other quantificational expressions to derive the observed range of interpretations. Although our analysis incorporates ideas from previous analyses, we show that it is able to account (...) for a broader range of facts than other approaches, with a minimum of construction-specific stipulations. We demonstrate that the analysis can be embedded within a general syntactic and semantic architecture for the comparative, and although our analysis focuses on the English data, we give evidence of its potential for crosslinguistic application. We conclude with a discussion of the implications of our approach for the analysis of “split-scope” phenomena in nominal quantification. (shrink)

In Section 1, we questioned the evidence for iteration of tenses, even with abstraction. To permit abstraction would in any case risk neutralizing our distinction between tensed and untensed sentences. Sequence of tense phenomena, far from supporting iteration, were incompatible with it. Instead, we argued, tense always retains its full deictic character; tenses never have scope over each other. The future modal WILL is exceptional (Section 2), but abstraction is not required to deal with this.An important suggestion, first made in (...) Section 1 and developed further in Section 3, would restrict quantification induced by the interpretation of Past to a domain determined by pragmatic factors. When Past serves as a reference time, e.g. when it forms part of would, as inSam believed that he would be in BostonJames bought a stamp that would be priceless then a previous occurrence of Past serves to define the domain relevant to the quantificational element of Past. Without semantic binding or reference, the two cases of Past in such sentences will thus be satisfied by the same interval in the past.The extension of this idea in Section 3, permits an account of the supposed incompleteness of the past tense without invoking a hidden THEN in e.g. I turned the lights off. In this case, restriction of the relevant domain does not proceed via an earlier occurrence of Past but depends solely on discourse factors.In Section 4, the analysis of have given in Part I is modified to introduce an element of ‘pastness’. The relevant sub-interval must be non-final-and perhaps need not even be a sub-interval of the evaluation interval itself. Empirically necessary, this change makes the incompatibility of Pres,have and a definite adverb like at 6 o'clock in a single sentence even harder to explain semantically. However, the vague restrictions on domain imposed by the present tense and relevant to the sub-interval required by an embedded have below it seem clearly pragmatically incompatible with the explicit restriction of that same interval to a very specific interval in the past — a restriction which, we argue, is imposed by a definite time adverb.Thus, Part II represents a consistent, though entirely informal plea for the embedding of the semantics of Part I in a framework in which pragmatic considerations can interact freely with the semantics, to restrict the domains within which quantification is permitted. It is in effect a plea for the introduction of partial models along the lines suggested by Barwise and Perry (1981). The advantages of the basic distinctions between tense, aspect and adverbs introduced in Part I would, we have suggested in the second part, be yet more obvious in such a framework. Formalization in a system of partial models must await further work. (shrink)

This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the sense (...) that they will determine structure on other worldly parts. The main upshot of this will be a clearer grasp of the interaction between modal notions. (shrink)

This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same fact. (...) The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a complex (...) array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (shrink)

There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties relating to the removal of elements. These difficulties are (...) normally overcome by working on the meta-level. This paper offers a comprehensive model in which the various forms of removal are treated on the object level, i.e., as connectives of the object language. (shrink)

There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties relating to the removal of elements. This paper points (...) out the difficulties and offers a comprehensive logical model. (shrink)

Business orientation toward sustainable development goals and the circular economy are relevant research topics today in business theory and practice. The waste recycling sector is a key industry in the circular economy framework for promoting clean production and environmental sustainability. This study analyzes business performance in the recycling sector, focusing on efficiency indicators. The associations between firm efficiency and risk variables were also evaluated. The study goes through several methodological stages, including a Data Envelopment Analysis (DEA) multistage method and multivariate (...) modeling: tobit regression, bootstrap models, and generalized method of moments (GMM). The main results indicate that the average efficiency of waste recycling firms is at a medium level. Large-sized firms achieve higher levels of efficiency than medium-sized and small firms, supporting the economies of scale hypothesis. The evidence also suggests that risk variables (rating score and Zscore) and capital structure are key determinants of firm efficiency in the waste recycling industry. (shrink)