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)
Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)
We construct an explicit covariant Majorana formulation of Maxwell electromagnetism which does not make use of vector 4-potential. This allows us to write a “Dirac” equation for the photon containing all the known properties of it. In particular, the spin and (intrinsic) boost matrices are derived and the helicity properties of the photon are studied.
In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...) main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)
Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...) that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)
We give an accurate historical and scientific account of a practically unknown manuscript written by Ettore Majorana in French. The retrieved text deals with Quantum Electrodynamics by using the formalism of field quantization, and it is here reported, for the first time, in English translation. It is likely related to an invited talk for a conference at Leningrad (or Kharkov) in 1933 (or 1934) which, however, Majorana never attended. Probably this manuscript is one of the last missing papers of the (...) “Senatore folder”, given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. (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 biography sheds new light on the life and work of physicist Ettore Majorana (including unpublished contributions), as well as on his mysterious disappearance in March 1938. Majorana is held by many, including Nobel Laureate, Enrico Fermi, to have been a genius of the rank of Galilei and Newton. In this intriguing story, the author, himself a leading expert on the work of Majorana, supplements the existing literature with new insights, anecdotes and personal accounts of contemporaries of Majorana.
What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how (...) they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception. (shrink)
What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a “critical” alternative to traditional plural logic.
According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which dispenses with (...) plural properties and thus undermines the semantic argument in favor of the plural conception of reality. (shrink)
Workplaces are often described as places in which individuals are motivated by their self-interests and in which negative events like time pressure, anxiety, conflict with co-workers, miscomprehensions, difficulties in solving problems, not-transmitted or not-exchanged information that lead to mistakes, and in some cases to injuries, stress or control, are part of everyday life. Such situations are often the result of the limited comprehension of needs, skills, or information available to colleagues, supervisors, subordinates, clients or providers. However, workplaces are also places (...) in which employees take care of clients, support colleagues and subordinates, are enthusiastic about their job, are motivated by leaders that encourage employees to transcend their own self-interests for the good of the group or the organization and provide them with the confidence to perform beyond expectations. Thus positive relationships at work are becoming a new interdisciplinary domain of inquiry. Within this positive relationships framework, in this paper we focus on a positive component of workplaces, and particularly on an individual cognitive and emotional process that has an important role in the workplace because it facilitates interpersonal relations and communications: it is the perspective taking process. In order to describe perspective taking, we will refer to some empirical studies and particularly to the review published by Parker, Atkins and Axtell in 2008 on the International Review of Industrial and Organizational Psychology. Perspective taking is a well established psychological construct, investigated both in the field of human development, as an important component of reasoning and moral development, and also in social and clinical psychology, where it is considered a component of social behaviors and of the therapeutic process. It has also been conceptualized in different ways. Duan and Hill describe three approaches to explain reasons for perspective taking behavior: a dispositional approach, that considers empathy as a relatively stable trait or a general ability; a cognitive-affective experience influenced by situational conditions; and finally as a multiphased experiential process. However, although in modern organizations working cooperatively and taking into account customers’ needs and experiences are becoming even more important, very few studies have considered perspective taking process within organizations. This is interesting because taking into account the perspective of others may contribute to more collaborative workplaces, where it is pleasant to work, as also enlighted in the title of the Parker, Atkins and Axtell’s paper: “Building better workplaces” is one of the possible outcomes of perspective taking. This paper aims to make available to a large audience such studies and, in relation to the topic of the conference organized by “Psychology and Communion”, consider connections between this concept and ideas and writings by Chiara Lubich. (shrink)
A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...) We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic. (shrink)
In light of the close connection between the ontological hierarchy of set theory and the ideological hierarchy of type theory, Øystein Linnebo and Agustín Rayo have recently offered an argument in favour of the view that the set-theoretic universe is open-ended. In this paper, we argue that, since the connection between the two hierarchies is indeed tight, any philosophical conclusions cut both ways. One should either hold that both the ontological hierarchy and the ideological hierarchy are open-ended, or that neither (...) is. If there is reason to accept the view that the set-theoretic universe is open-ended, that will be because such a view is the most compelling one to adopt on the purely ontological front. (shrink)
Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to order should be accounted for (...) without altering the standard formulation of plural logic. In particular, sensitivity to order does not call for a fine-grained notion of plural reference. We point out that the phenomenon in question is quite broad and that current proposals are not equipped to deal with the full range of cases in which order plays a role. Then we develop an alternative and unified account, which locates the phenomenon not in the way in which plural terms can refer, but in the meaning of special expressions such as 'in that order' and 'respectively'. (shrink)
1. OverviewSeveral natural languages such as English contain prima facie different kinds of referential and quantificational expressions. In particular, natural languages can contain singular forms of reference and quantification, as in, e.g., ‘Cecilia is Italian’ and ‘There is a basket of apples on the counter’. But they can contain also plural forms of reference and quantification, as in, e.g., ‘Cecilia and Francesca met in Cathedral Square’ and ‘There are some apples on the counter’. Famously, some sentences in natural language containing (...) plural expressions cannot be formalized in first-order logic, as, e.g. the so-called Geach-Kaplan sentence: This kind of sentence requires at least the expressive power of second-order logic for its logical form to be captured appropriately.The very notions of plural reference and plural quantification are not new in the philosophical landscape.1 But it was from the mid-80s on, starting with the seminal work in [Boolos, 1998a; b], that so-called plural logic gained the attention of the community of logicians, philosophers in general, and philosophers of mathematics in particular.2 Ever since, more and more literature has been produced on it in several areas, e.g., logic and its philosophy, philosophical logic, and philosophy of mathematics, as well as philosophy of language, semantics, and linguistics.3. (shrink)
In the semantic debate about plurals, pluralism is the view that a plural term denotes some things in the domain of quantification and a plural predicate denotes a plural property, i.e. a property that can be instantiated by many things jointly. According to a particular version of this view, untyped pluralism, there is no type distinction between objects and properties. In this article, I argue against untyped pluralism by showing that it is subject to a variant of a Russell-style argument (...) put forth by Timothy Williamson and that it clashes with a plural version of Cantor’s theorem. I conclude that pluralists should postulate a type distinction between objects and properties. (shrink)
This study provides a scoping review of the recent conceptual developments about the deviant work behavior and counterproductive work behavior constructs. It also examines the specific types of deviant work behavior that have been more consistently investigated in the last decade, and whether they cover the interpersonal or organizational type of deviant behavior. In addition, individual, group, and organizational predictors of deviant work behaviors are examined. A scoping review of reviews was conducted on Scopus and Web of Science databases and (...) 54 studies published from 2010 to June 2021 were taken into account. Results show that more recent conceptualizations are based on well established models in the literature and consider the hierarchical structure of these two constructs. Recent reviews examine the relationships of deviant work behavior with job performance and ethical behavior constructs, the multilevel nature of deviant work behavior, and the consequences for the actor of the deviance. The specific types of deviant work behavior more frequently reviewed in the last decade are workplace abuse, incivility, ostracism, bullying and sexual harassment, and abusive and destructive leadership; this evidence suggests a much greater attention to interpersonal, rather than organizational, forms of deviant work behavior. Regarding antecedents, results show the continuing prevalence of personality factors antecedents. Limitations of the study and theoretical and practical implications for the field are also provided. (shrink)
After analysing Habermas's philosophical evolution from his theory of interests to his late pragmatic realism, I will focus on the problems of this last conception, trying to draw a plausible way out which avoids both naturalistic reductionism and a too weak form of realism.
Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the (...) cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting. (shrink)
This article considers historical facts and investigates the particular relationship between a factual and a valuative dimension within them. The operation is an autopsy of a particular historical fact, which works as an example. On this basis, the article will elucidate the similarities and the differences between historical facts and natural facts, with an emphasis on the observation that the former are more subject to the influence of interpretation than the latter. This feature of historical facts explains why social and (...) political struggles for recognition arise with respect to historical events. (shrink)
Wittgenstein: Epistemology Although Ludwig Wittgenstein is generally more known for his works on logic and on the nature of language, but throughout his philosophical journey he reflected extensively also on epistemic notions such as knowledge, belief, doubt, and certainty. This interest is more evident in his final notebook, published posthumously as On Certainty (1969, henceforth … Continue reading Wittgenstein: Epistemology →.