It is commonly assumed that linguistically the Rigveda is a heterogeneous collection of texts. Since the early days of Vedic scholarship, researchers have tried to correlate grammatical properties with individual parts of the Rigveda, aiming at identifying layers and strata. In this article we review stratifications proposed in previous literature and assess the support for these strata by performing statistical analyses with allomorphic linguistic features that have been claimed to bear signals of stratification. In addition, we run a cluster analysis (...) exploring how the books are grouped given the same allomorphic linguistic data. Our results show that once we control for metrical positioning, prosodic structure, and content, the allomorph distributions do not lend significant support for any of the proposed stratifications. Moreover, the cluster analysis favors the assumption that book 10 occupies a special position, but overall differences across the ten books of the Rigveda are not substantial. (shrink)

Philanthropic venture capital, like traditional venture capital, provides funding and value-added services to a portfolio of entrepreneurial firms. However, TVC differs from PhVC, as the primary goal of TVC is to maximize the economic return of its investments. In contrast, PhVC firms expect their portfolio companies to perform well in terms of both social and economic returns. Using both American and European firms, this paper explores and compares the human capital in PhVC and TVC firm founders. Our results show that (...) there are key differences in both general and specific human capital between these firm types. While both TVC and PhVC firm founders have high levels of commercial experience, TVC firm founders tend to hold degrees in science, engineering, business, and law more frequently than PhVC firm founders. PhVC founders also differ from TVC founders by having greater work experience in the social sector. (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.

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)

Written by the great medieval Jewish philosopher Maimonides, The Guide of the Perplexed attempts to explain the perplexities of biblical language--and apparent inconsistencies in the text--in the light of philosophy and scientific reason. Composed as a letter to a student, The Guide aims to harmonize Aristotelian principles with the Hebrew Bible and argues that God must be understood as both unified and incorporeal. Engaging both contemporary and ancient scholars, Maimonides fluidly moves from cosmology to the problem of evil to the (...) end goal of human happiness. His intellectual breadth and openness makes The Guide a lasting model of creative synthesis in biblical studies and philosophical theology. (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)

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 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)

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)

Introduction to a special issue based on a summer school on set theory and high-order logic.

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.

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)

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)

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)

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)

Questo saggio, risultato del lavoro seminariale svolto presso la Fondazione Centro Studi Campostrini, avanza una proposta teoricasulla base di un’ipotesi. L’ipotesi è che quando usiamo il vocabolariodella credenza diciamo qualcosa di specifico e irriducibile adaltre nozioni. Alla ricerca del nucleo di irriducibilità e specificitàdella credenza Giuseppe Di Salvatore scarta tutte quelle forme dicredenza che dipendono in maniera più o meno diretta da unaconsiderazione in termini di conoscenza o da un’implicazione dellaverità. Se alcuni tipi di giustificazione della credenza possono essereutili (...) a individuarne l’irriducibilità, solo le credenze primitive, unacomplessa nozione di “credenza soggettiva” e un originale modellofiduciario della credenza fungono da buoni candidati per difenderela specificità della credenza. Dopo la discussione di alcune tesi diLudwig Wittgenstein e il ricorso a fonti eterogenee, da William Jamesa Henry Habberley Price fino a Niklas Luhmann, l’autore proponela nozione originale di “credenza progressiva” come il migliorcandidato che confermi l’ipotesi di partenza. In essa una precisaidea di rischio e la fiducia, al cui dibattito è dedicata un’ampiaattenzione, contribuiscono a delineare la credenza progressivainsieme ad alcuni suoi aspetti soggettivi, così profilandola comeuna postura sperimentale. Il saggio si completa con una riflessionesulla peculiarità della questione filosofica della credenza religiosa,la quale viene approcciata nella sua preliminare generalità, quindiconfrontata con la credenza progressiva. (shrink)

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)

Is it achievable to read aesthetic experience as a modular adaptation, and what would be its implication on the image of man, on aesthetics and on evolutionary theory itself? An alternative path is offered by evolutionary morphology, starting from the elaboration of a biologic concept of organism and from the notion of homology of function as a system of interconnections organized in a hierarchy. We deduce the possibility of thinking the peculiar innovation of aesthetic experience in an evolutionary way.

Building on the literature on hybrid organizations, this manuscript explores the relationship between the organizational activity of social enterprises backed by venture philanthropy investors and income inequality. Using Ashoka’s portfolio of Indian social enterprises as empirical context of Western venture philanthropy investing activity, our results suggest that Indian municipalities with social enterprises that have received venture philanthropy investments experience a decrease in income inequality level and when these social enterprises are dominated by a collectivistic organizational identity orientation the effect is (...) stronger. Our findings have implications for the research on hybrid organizations, financing of social entrepreneurship and grand ethical challenges. (shrink)

In the following paper, I would like to reconsider the paradigm of “classical” philosophical anthropology in the perspective of postmodernity. I plead in favor of an anthropological project continuing the tradition of Lebensphilosophie, especially Otto Friedrich Bollnow’s claim for an anthropology without images. In fact, I present here a few considerations about a hermeneutic approach to anthropology. I try to make plausible that anthropology should not investigate the nature of the human being and his place in the cosmos, but rather (...) describe identities in a practical sense. Its task is dual: it has to give a critical understanding of the unconscious images that form identities, both at a social and personal level; at the same time, it has to make appeal to a sense of responsibility for others and for the shaping of one’s personal way of life. The mythological figure of Hermes, guide of souls and protector of transitions, is perfectly suited to this dual role of a hermeneutic anthropology, which not only makes theory, but also creates awareness and new opportunities for human advancement. (shrink)

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)

Summary This paper concentrates on the literary sources of the battle of Delion and reopens the debate on the relevance of Euripides’ Supplices for the narrative of this event. Thucydides is read with a particular focus on the speech of Pagondas, which can be understood through the current reconstruction of the history of Boiotia in the latter half of the fifth century BCE. Finally, Diodorus is considered as a useful source for a few pieces of information on the aftermath of (...) the battle that have previously been disregarded. (shrink)

Name der Zeitschrift: Klio Jahrgang: 99 Heft: 2 Seiten: 399-419.

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 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)

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)