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)

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)

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)

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.

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.

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)

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)

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 →.

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.

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)

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)

In Resp. 509c7 and 9 Socrates declares that he has omitted many things in the exposition of the analogy between the supreme Good and the sun. In fact Socrates’ exposition leaves some questions open which are seminal with regard to the interpretation of the aforesaid analogy : 1) Why Plato designates the sun as analogon of the Good? 2) Why the original manifestation of the Good consists in a plurality of intelligible beings? 3) Why the original manifestation of the Good (...) consists not only in a purely objective intelligible being, but also in an intellect, that is in a form of consciousness? 4) How can be explained the fact that Plato perceives the Good as origin not only of intelligible, but also of physical reality? While the first question can be simply answered by referring to the infinite manifestativity of the Good, the other three questions require a significant effort in the field of speculation. Basing on some clues given by Plato in the exposition of the analogy between the Good and the sun, this article attempts to answer these questions by conjecturing that Plato could have presupposed the image of an infinite sphere consisting in intelligible light. This image, which could have already been presupposed by Parmenides, would offer a conceptual background capable of explaining on the one hand the unity of intelligibility and intellect characterizing the original manifestation of the Good, on the other hand why in Plato’s perspective the Good can be perceived as origin not only of intelligible, but also of physical light. (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)

Personality research has functioned under the prevailing influence of middle-level theorizing sufficiently long to justify consideration of the effects of this approach. Despite improvements in precision and testability of hypotheses, with resulting increases in volume of research, the pervasive effect of several practical dangers of middle-level theorizing are identified. These involve the unappreciated failure to test comprehensive theories when concepts from them have been extirpated, overly-weak justification of research methods, a vanity of small differences, and insufficient theoretical precision in framing (...) empirical efforts. Ways of avoiding these dangers are explored, and it is concluded that the most promising is a comparative analytic stance toward inquiry that reconsiders comprehensive theorizing without courting ambiguity and imprecision. (shrink)

This paper reports the framework, method and main findings of an analysis of cultural milieus in 4 European countries. The analysis is based on a questionnaire applied to a sample built through a two-step procedure of post-hoc random selection from a broader dataset based on an online survey. Responses to the questionnaire were subjected to multidimensional analysis-a combination of Multiple Correspondence Analysis and Cluster Analysis. We identified 5 symbolic universes, that correspond to basic, embodied, affect-laden, generalized worldviews. People in this (...) study see the world as either a) an ordered universe;b) a matter of interpersonal bond;c) a caring society;d) consisting of a niche of belongingness;e) a hostile place. These symbolic universes were also interpreted as semiotic capital: they reflect the capacity of a place to foster social and civic development. Moreover, the distribution of the symbolic universes, and therefore social and civic engagement, is demonstrated to be variable across the 4 countries in the analysis. Finally, we develop a retrospective reconstruction of the distribution of symbolic universes as well as the interplay between their current state and past, present and future socio-institutional scenarios. (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)

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)

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)

Liberal theory seems to be caught in an impasse. On the one hand, since it has social order as its object, it appears to be committed to resolving the problem of disagreement between the various conceptions; on the other, insofar as it is philosophical theory, it seems destined to cause conflict. How, then, can liberalism offer a solution which guarantees the duration in time of a society, without, however, proposing a theory that would merely be one among others? And how (...) can it do this without adopting reductionist strategies, and by trying to remain faithful to the idea that a society should be ordered by a conception of justice? This is the paradox of liberal political philosophy. And this same paradox is the theme that Rawls confronts in Political Liberalism. (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)

This article intends to characterize the constructive function that the Indeterminate Duality may have played in Plato’s oral teaching. Far from being in itself – as some testimonia seem to suggest – the primary origin of evil, as origin of multiplicity the Indeterminate Duality can be perceived as intrinsically presupposed by Plato’s identification of the source of being with the supreme Good. The notion of good implicates for Plato namely an unconditioned impulse to relationality, which indicates that the supreme Good (...) is to be considered as supreme origin not only of unity, but also of multiplicity and alterity. In the absence of multiplicity and alterity, no real relation, and, therefore, no real manifestation of the Good could in fact take place. As a consequence, the Indeterminate Duality may be considered as source of that original differentiation as well as of that generativity without which the supreme Good would be discordant with its goodness. (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)

Aim of this paper is to outline a new evolutionary interpretation of aesthetic emotions, in the light of the most recent developments in Evolutionary Biology, in particular the so-called “Extended Synthesis of Evolution” (Pigliucci-Müller 2010). Focussing on the biological concept of homology, the Author argues that, in order to effectively understand role and evolutionary value of aesthetic emotions, it should be asked not “what aesthetic emotions are for?”, rather “what kind of constraints and homologies influence the specific “shape” of human (...) aesthetic emotions?”. In a few words, we should move from a functionalist approach to human aesthetic emotions towards a morphological one. (shrink)

Herder is usually considered to be one of the mayor sources of the aesthetics of empaty. The present contribution aims at offering a brief rewiew of some main places in Herder aesthetical theory and at reconstructing the genesis of the family of concepts including fühlen, Gefühl, Mitfühlen, Familiengefühl, in order to understand their relationship with regard to the theory of knowledge, the aesthetics, the politics.