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)

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)

The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...) one which uses higher-order resources. (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)

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)

In an era increasingly characterized by pluralism and globalization, intercultural pedagogy represents a starting point for addressing the challenges that today’s society confronts us with daily. Throughout history, cultures have changed through interactions, exchanges, and hybridization, leading to the formation of an increasingly pluralistic and multicultural society. Against this background, it is crucial to develop approaches based on dialogue and mutual recognition. However, acceptance and willingness to encounter require an educational path that is promoted by schools from childhood, especially in (...) view of the monocultural mentality that too often characterizes more and more people and prevents the opening of a path that counteracts ethnocentrism in favor of a broader perspective. From this point of view, intercultural pedagogy proves to be the only approach that can guarantee the formation of individuals ready to create a truly multicultural society. (shrink)

Issu d’une journée d’étude organisée le 12 septembre 2017 à la Fondation Hardt pour l’étude de l’Antiquité classique, ce volume embrasse, à travers des contributions constituant autant de touches successives, la diversité des discours et pratiques philosophiques inspirés par le langage des cultes à mystères sous l’Empire romain. À cette époque, comme l’a montré la célèbre étude de Pierre Hadot (Exercices spirituels et philosophie antiques, Paris 1987), la spéculation philosophique est étroite...

Cette enquête est motivée par la coexistence dans l’Antiquité tardive de trois mots exprimant d’une façon différente la lecture : ἀνάγνωσις, qui signifie « lire à haute voix » ; συνανάγνωσις, c’est-à-dire « lire avec quelqu’un » ; ἔντευξις, qui, parmi différentes significations, présente celle de « lecture » au sens général. À partir du V e siècle ap. J.-C., leur emploi est strictement lié à deux phénomènes importants : le premier est l’introduction des mots ἀνάγνωσις et συνανάγνωσις dans la (...) pratique d’enseignement de l’école néoplatonicienne comme synonymes indiquant une lecture exégétique des œuvres anciennes par le maître ; le deuxième concerne la diffusion de la formule « ceux qui lisent » (ἐντυγχάνοντες) ou « ceux qui vont lire » (ἐντευξόμενοι) dans les avertissements au lecteur des premiers commentaires composés directement sous forme écrite dans l’Antiquité tardive. Cette étude vise à démontrer que dans le milieu de l’école néoplatonicienne le couple ἐντυγχάνοντες / ἐντευξόμενοι est en rapport de conséquence avec le couple ἀνάγνωσις / συνανάγνωσις, exprimant un point de vue différent sur le destinataire : en effet, l’ἀνάγνωσις / συνανάγνωσις, en tant que pratique orale, est immédiatement reçue par l’élève, qui possède les aptitudes et les compétences appropriées pour comprendre ; le commentaire, en revanche, en tant que transposition de l’enseignement à l’écrit, doit faire face à deux difficultés : l’explicitation ponctuelle du sens caché dans les textes anciens que les lecteurs ont déjà sous les yeux (ἐντυγχάνοντες) ; et la persuasion d’un public de lecteurs (ἐντευξόμενοι), qui liront le commentaire. (shrink)

Proclus, successor of the School of Athens in the fifth century AD, is one of the last great voices of a pagan polytheistic world in crisis in the face of the gradual rise of Christianity. His writing bears witness not only to one of the most influential metaphysical representations for the constitution of the idea of a philosophical "system" based on a complex "language game" based on the conceptual sphere of "order" and "unity", but also of an attempt to reconcile (...) rhetorics with philosophy. In the three chapters in which the book is structured (style, system, unity), then, a conscious intention is evident in Proclus, to adapt the content of his systematic metaphysics to literary form. Hence there is a consistency traced in Proclus' stylistic choices, with the aesthetic norms of a rhetorical canon, probably established in the cycle of readings of the Neoplatonic school. His writing bears witness not only to one of the most influential metaphysical representations for the constitution of the idea of a philosophical "system" based on a complex "language game" based on the conceptual sphere of "order" and "unity", but also of an attempt to reconcile rhetorics with philosophy. In the three chapters in which the book is structured (style, system, unity), then, a conscious intention is evident in Proclus, to adapt the content of his systematic metaphysics to literary form. Hence there is a consistency traced in Proclus' stylistic choices, with the aesthetic norms of a rhetorical canon, probably established in the cycle of readings of the Neoplatonic school. The way in which expressive "art" is subordinated in Proclus to philosophy is one of the most emblematic examples of a development in late antiquity, that of the enkuklios paideia - the union of all the arts necessary for the formation of man - that would later constitute in the Latin world the cycle of liberal arts. (shrink)

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)

The Vitruvian Man of Leonardo da Vinci is one of the most famous and most studied drawings over the world as well as one of the most reproduced ones, e.g. in coins, space suit patches, books and movies. The aim of the present work is to discuss the Vitruvian Man as a figurative representation of the Leonardo’s scientific method. Our analysis is based on scientific elements both present in the drawing and provided by Leonardo in his approach to this drawing. (...) Our thesis is that the square symbolizes the measurable physical world and that the man inscribed within the square refers to the physics measurement process based on the operational definition of quantities, including the measurement unit system and the quantities conversion factors. Therefore, the measurement process is fundamental for the Leonardo’s approach to the scientific knowledge, albeit, the drawing also suggests that this latter does not correspond with the true knowledge. The circle, which has a different center with respect to the square, symbolizes the truth, to which the man inscribed in the square yearns, without ever achieving it, the truth being reachable only by the man inscribed within the circle. (shrink)

A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we (...) present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)

Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.

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.

The paradox that appears under Burali-Forti’s name in many textbooks of set theory is a clever piece of reasoning leading to an unproblematic theorem. The theorem asserts that the ordinals do not form a set. For such a set would be—absurdly—an ordinal greater than any ordinal in the set of all ordinals. In this article, we argue that the paradox of Burali-Forti is first and foremost a problem about concept formation by abstraction, not about sets. We contend, furthermore, that some (...) hundred years after its discovery the paradox is still without any fully satisfactory resolution. A survey of the current literature reveals one key assumption of the paradox that has gone unquestioned, namely the assumption that ordinals are objects. Taking the lead from Russell’s no class theory, we interpret talk of ordinals as an efficient way of conveying higher-order logical truths. The resulting theory of ordinals is formally adequate to standard intuitions about ordinals, expresses a conception of ordinal number capable of resolving Burali-Forti’s paradox, and offers a novel contribution to the longstanding program of reducing mathematics to higher-order logic. (shrink)

The widespread introduction of accreditation procedures contradicts the centrality of freedom in research and teaching which Wilhelm von Humboldt paradigmatically supported. The logic of accreditation propagated during the last decades implies in fact a reversal of Hulmboldt’s perspective: priority is given to standardization and – not necessarily sheer – competition, which shifts the human being into a peripheral position within academic education. With regard to the reductionist anthropology presupposed by accreditation procedures, Humboldt’s Menschenbild manifests a breaking contrastivity. Humboldt in fact (...) intends human beings not as merely biological or psychological subjects, but as spiritual selves capable of a fruitful development with the help of science, whereas science is primarily perceived as spiritual and dialogical activity. This notion of science, which echoes Socrates’ midwifery, could represent a more human alternative to future sceneries in which universities would be exclusively considered as institutions providing services. (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)

This chapter provides an overview of the philosophical and linguistic debate about the logic of plurals. We present the most prominent singularizing analyses of plurals as well as the main criticisms that such analyses have received. We then introduce an alternative approach to plurals known as plural logic, focusing on the question whether plural logic can count as pure logic.

Per l'uomo di oggi, che non spera più nella salvezza alla fine dei tempi ma ha davanti a sé un tempo senza fine, navigare in mare aperto sembra ormai diventato l'unico modo di vivere. Ma quale rotta seguire, dopo il tramonto di ogni certezza e il declino della tradizione giudaico-cristiana in Occidente, due segni distintivi della nostra epoca? Al termine di un lungo e originale itinerario di riflessione sulla modernità, Salvatore Natoli analizza le varie forme del fare e il (...) loro rapporto con quello che dovrebbe essere il vero obiettivo di ogni essere umano: un buon uso del mondo. Partendo dalla distinzione aristotelica tra "agire" e "fare", l'autore si chiede quanto, nella nostra frenetica attività quotidiana, siamo "agenti", soggetti capaci di realizzarsi in ciò che fanno, e quanto invece siamo "agiti", elementi impersonali di una serie causale e anonima di cui non si vede né l'inizio né la fine. Per essere titolari della propria vita, e quindi davvero liberi, non basta infatti conformarsi a ciò che l'organizzazione sociale richiede, ma occorre istituire un rapporto autentico con il proprio desiderio, con la propria corporeità e con gli altri. Così, nella società delle abilità, della tecnica e del saper fare, si ripropone in tutta la sua urgenza la questione delle virtù, intese come "abilità a esistere", in grado di darci stabilità e consistenza. (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)

A realist approach to learning is what I propose here. This is based on a non-epistemic dimension whose presence is a necessary assumption for a concept of learning of a life-world as complementary to learning within a life-world. I develop my approach in opposition to Jürgen Habermas' pragmatic approach, which seems to lack of something from a realist point of view.

A realist approach to learning is what I propose here. This is based on a non-epistemic dimension whose presence is a necessary assumption for a concept of learning of a life-world as complementary to learning within a life-world. I develop my approach in opposition to Jürgen Habermas' pragmatic approach, which seems to lack of something from a realist point of view.

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)

This article focuses on certain dimensions of Plotinus’ notion of the noetic self, which so far have not received sufficient scholarly atten­tion. The evidence of Enn. V 8 makes clear the assumption about the inexhaustible generativity of the noetic self. This generativity implies an intimate relation with the notions of image and suddenness: the former is intended as a medium of unconditional self-transparency, whereas the latter is understood as pointing to the unlimited newness that is char­acteristic of the noetic life, (...) which, according to Plotinus, consists in an indissoluble unity of identity and alterity. The aforesaid notions make it reasonable to view Plotinus’ concept of noetic self as pointing to a predominantly relational and dynamic ontology, in which essentialism presupposes no staticity whatsoever, but can rather be seen as a perspective that leads to the development of a harmonious and non-narcissistic creativity. (shrink)

We present a reference model for finding evidence of discrimination in datasets of historical decision records in socially sensitive tasks, including access to credit, mortgage, insurance, labor market and other benefits. We formalize the process of direct and indirect discrimination discovery in a rule-based framework, by modelling protected-by-law groups, such as minorities or disadvantaged segments, and contexts where discrimination occurs. Classification rules, extracted from the historical records, allow for unveiling contexts of unlawful discrimination, where the degree of burden over protected-by-law (...) groups is evaluated by formalizing existing norms and regulations in terms of quantitative measures. The measures are defined as functions of the contingency table of a classification rule, and their statistical significance is assessed, relying on a large body of statistical inference methods for proportions. Key legal concepts and reasonings are then used to drive the analysis on the set of classification rules, with the aim of discovering patterns of discrimination, either direct or indirect. Analyses of affirmative action, favoritism and argumentation against discrimination allegations are also modelled in the proposed framework. Finally, we present an implementation, called LP2DD, of the overall reference model that integrates induction, through data mining classification rule extraction, and deduction, through a computational logic implementation of the analytical tools. The LP2DD system is put at work on the analysis of a dataset of credit decision records. (shrink)

This book is the first comprehensive and systematic introduction to the linguistics of humor, exploring not only theoretical linguistic analyses, but also topics from applied linguistics. It will be a valuable resource for students from advanced undergraduate level upwards, particularly those coming to linguistics from related disciplines.

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)

Se è spontaneo associare i concetti di immagine e immaginario, in quanto sembrano due nozioni strettamente legate, non è affatto semplice determinare il modo in cui si configura il loro rapporto. Per tracciare i distingua di tale relazione e i metodi che possono aiutarci a chiarirla, partiremo dalla descrizione della coscienza d’immagine — si tratta di un termine husserliano — per arrivare al mito. La nostra riflessione si dividerà in diversi fasi. Analizzeremo infatti la struttura fenomenica dell’immagine mentale, del segno (...) e del simbolo e seguiremo, brevemente, anche il cammino inverso che va dal simbolo all’immagine. I punti salienti della nostra dimostrazione saranno i seguenti: il rapporto immagine-immaginario non può essere definito in modo univoco, in quanto cambia in base al tipo di immagine; a livello della coscienza d’immagine, un approccio psicologico può rivelarsi utile, poiché il supporto percettivo costituisce un momento essenziale dell’immagine reale; nel caso della phantasia o immagine mentale, il metodo psicoanalitico sembra quello più appropriato, poiché l’assenza del supporto percettivo rende le immagini mentali libere da ogni costrizione. Pertanto la comprensione delle dinamiche affettive-desiranti può fornire una spiegazione al corso apparentemente sregolato di associazioni che qui si manifestano. Per quanto riguarda il segno, il simbolo e il mito, le dimensioni affettiva, percettiva, transizionale e fantastica sono strettamente correlate. Questo tipo di immagini sembrano insistere su “schermi” diversi e pertanto si richiede un approccio metodologico variegato. (shrink)

In Plato’s Republic the prime cause of all things, the Good, is presented both as transcending every form of being and as the supreme Idea, that is to say as the supreme being. The inconsistency between these two characterizations seems to point to the paradoxical relation subsisting between the absolutely transcendent Good and its supreme self-revelation : by revealing itself, the ἀγαϑὸν ἐπέκεινα τῆς οὐσίας constitutes the highest being and therefore has to be considered to be identical with the ἰδέα (...) τοῦ ἀγαϑοῦ; on the other hand its absolute transcendence implies a clear supereminence in regard to the Idea of the Good. This article tries to highlight and illustrate these antinomic aspects of Plato’s notion of the Good with the help of both the so-called ἄγραφα δόγματα and the representation of the Demiurge in Plato’s work. (shrink)