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)

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)

In constructional ontology, entities emerge by construction, that is, from the application of constructors to objects. We explore this approach to ontology, focusing on three modules: the constructors, the inputs to the constructors, and the constructional process. Our aim is to identify and assess some key theoretical choices arising in an ontology of this kind.

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)

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.

Il saggio ricostruisce l’utilizzo da parte di Gramsci del tema del “merito” nel suo discorso sulla scuola e l’educazione. Negli scritti pre-carcerari la critica ai privilegi delle classi più abbienti viene svolta sulla base di una rivendicazione dei meriti dei tanti soggetti di famiglie proletarie impossibilitati a coltivarli e farli valere. Nei _Quaderni dal carcere_ tale posizione viene inserita nel quadro di uno Stato Nuovo, in cui la classe dirigente viene selezionata su un corpo sociale interamente messo in grado di (...) partecipare cognitivamente all’autogoverno del lavoro. Vengono anche segnalati significativi parallelismi con i concetti bourdesiani di habitus e riproduzione. (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)

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)

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)

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)

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)

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.

Bank Street College of Education professor Salvatore Vascellaro is a leading advocate of taking children and teachers into a wider world as the key to improving our struggling schools. Combining practical and theoretical guidance, Out of the Classroom and into the World visits a rich variety of classrooms transformed by innovative field trip curricula--showing how students’ hearts and minds are opened as they discover how a suspension bridge works, what connects them to the people and places of their neighborhood, (...) and as they come to understand the ecosystem of a river by following it to its source. Vascellaro shows, equally, that what teachers can offer children is fueled by their own engagement with the world, and he offers stunning examples of teachers awakened by their direct experiences with the social issues plaguing American society--from the flood-torn areas of New Orleans to the mining areas of West Virginia. Based on the core principles of progressive pedagogy, and the wisdom gained from Vascellaro’s experience as a teacher, school administrator, and teacher educator, Out of the Classroom and into the World is a direct retort to test scores and standards as adequate measures of teaching and learning--an inspiring call and major new resource for anyone interested in reinvigorating America’s classrooms. (shrink)

This article addresses the questions “why do we still have to read Kant today?”, “what kind of responses can he give us in the era of global terrorism?”. In other terms, today, “What does it mean to orient oneself in thinking?”. Because his concept of renewed religious laity, distant from both fanatic fundamentalism and indifferent secularism, becomes the compass we can only rely on and authentically trust in the relationship with the other. Issues identified on reading the interesting kantian work, (...) studied during the last academic year and discussed in the meeting of the 17th March 2017 between Liceo Classico “La Farina” and DICAM of the University in Messina, in the context of the project Tradition and Contemporaneity, set by the Italian Philosophical Society (SFI). (shrink)

Abstract: L’articolo si propone di individuare i caratteri costitutivi della cura attraverso un’analisi simbolica della parabola del buon Samaritano, nella quale il rapporto con l’altro presuppone la nostalgia del totalmente Altro. Key words: simbolo, liberazione, responsabilità, agape, attraversare, coscienza.

È la morte la cartina al tornasole che rivela l’atteggiamento esistenziale che si concretizza nel rapporto con l’altro. Dal modo in cui la si valuta, e, conseguentemente, dal modo in cui si vive, dipende il grado di autenticità della propria esistenza. Per argomentare la suddetta tesi ricorreremo al racconto di Tolstòj La morte di Ivàn Il’íc.

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)

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)