The present paper deals with natural intuitionistic semantics for intuitionistic logic within an intuitionistic metamathematics. We show how strong completeness of full first order logic fails. We then consider a negationless semantics à la Henkin for second order intuitionistic logic. By using the theory of lawless sequences we prove that, for such semantics, strong completeness is restorable. We argue that lawless negationless semantics is a suitable framework for a constructive structuralist interpretation of any second order formalizable theory (classical or intuitionistic, (...) contradictory or not). (shrink)

In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability (...) and, on the other, by means of the operator K of epistemic logic. Intuitionistic logic, as reconstructed within this perspective, turns out to be a part of epistemic logic, so that it loses its traditional foundational role, antithetic to that of classical logic. In section 3 we uphold the view that certain consequences of the adoption of atemporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view. (shrink)

Brouwer's theorem of 1927 on the equivalence between virtual and inextensible order is discussed. Several commentators considered the theorem at issue as problematic in various ways. Brouwer himself, at a certain time, believed to have found a very simple counter-example to his theorem. In some later publications, however, he stated the theorem in the original form again. It is argued that the source of all criticisms is Brouwer's overly elliptical formulation of the definition of inextensible order, as well as a (...) certain ambiguity in his terminology. Once these drawbacks are removed, his proof goes through. (shrink)

This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers - both new and previously published - it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer's idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical (...) realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer's work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics. (shrink)

In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, the alleged (...) innocence of mereology and plural quantification is highly controversial and has been criticized by several authors. In the present paper we propose a new approach to megethology based on the theory of plural reference developed in To be is to be the object of a possible act of choice. Our approach shows how megethology can be grounded on plural reference without the help of mereology. (shrink)

Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...) à la Dedekind, as the unique non-logical axiom. We will also sketch a virtual interpretation of the classical continuum involving no other infinite than a countable plurality of individuals. (shrink)

This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)

In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed (...) in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification. (shrink)

In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification . Instead, in the mereological case: (Lewis, 1991, p. 87). The aim of the paper is to (...) argue that one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. (shrink)

In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification (...) are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)

In Parts of Classes [Lewis 1991] David Lewis attempts to draw a sharp contrast between mereology and set theory and to assimilate mereology to logic. He argues that, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – (...) unlike the sum of the given objects – seems to be an abstract entity whose existence is not directly entailed by the existence of the objects themselves. The argument for the innocence of mereology is grounded on the thesis of “Composition as identity”. Lewis analyses two different versions of the thesis: the first is the Strong composition thesis, according to which certain objects are their sum, where the use of “are” would mean that composition is literally identity. The second version is the Weak composition thesis, according to which composition is analogous, under some aspects, to identity. He criticises the first version of the thesis and argues for the second one. In the paper we argue that (T1) arguments for the ontological innocence of mereology are not conclusive. An obvious objection to the Strong composition thesis is that – given certain objects Xs – they cannot be their sum because none of them is the sum. One could reply to this objection by observing that the “are” in the sentence “The Xs are their sum” is to be understood collectively and not distributively. But the crux is that the collective reading fails to generate a new entity, whereas mereology, in particular in Lewis’ use for the reconstruction of set theory as “megethology”, needs to consider sums as real objects. Besides, we contend that Lewis’ argument for the innocence of mereology based on the Weak composition thesis is a petitio principii. The reason is that the aspects of the analogy between composition and identity, which Lewis emphasises, obtain under the presupposition of the existence of sums. But this is just what a denier of innocence would refuse. (T2) Some arguments against the ontological innocence of mereology show a certain ambiguity in the innocence thesis itself. Some defences of the innocence seem to implicitly presuppose that the sum of certain objects Xs is not a genuine entity. Speaking of the sum of the Xs would be just another way of speaking plurally of the Xs. However, the relevant use of sums in mereology treats them as well determined objects. The relevant innocence thesis takes for granted that, though sums are genuine objects, nevertheless their existence does not require any further commitment. (T3) The innocence thesis, apart from Lewis’ defence, seems to depend on a general conception of the nature of objects and on how the notion of ontological commitment is understood. We think that the thesis is the manifesto of a realistic conception of parts and sums. This conception consists of the following clauses: (i) given any object x, it is well determined which parts it possesses; these are in turn objects whose existence is a necessary consequence of the existence of x. (ii) However any objects Xs are given, they automatically constitute a well determined object x which is their sum; (iii) We can refer singularly and plurally to parts and sums of given objects. Obviously, one might wonder if such a conception is really ontologically innocent. One could object that it is not innocent because clauses (i) – (iii) are not. For example, clause (i) could be considered as an ontological commitment to the existence of sums. But the innocence at issue does not concern the above-sketched conception. The innocence is embedded in the conception itself. In other words, someone who argues for clauses (i) – (iii) takes a point of view from which mereology appears to be innocent. For, such a point of view forces us to consider as well determined the parts of any object and does not allow us to separate the existence of certain objects form the existence of their sum. (T4) is the claim that the alleged innocence of mereology is subject to Quine’s notorious criticisms of the set-theoretical interpretation of second order logic. To the purpose, we construct a mereological model of a substantive fragment of set theory, i.e. the one that grounds the principal model semantics of second order logic. First, we construct a mereological model under the assumption of the existence of infinitely many atoms. Then, we replace this assumption with that of the existence of any infinite object (with or without atoms). Finally, let us make a general point about the innocence thesis of mereology. A conclusive argument for that would be a refutation of the thesis that there are only denumerably many entities. For, since the parts of an infinite object constitute a non-denumerable infinity, such an argument would entail that there could be no infinite without a non-denumerable infinity. However, the thesis that any genuine infinity is a denumerable one has had some important advocates. So, a conclusive argument for the innocence of mereology seems to be highly implausible. (shrink)

In Parts of Classes David Lewis attempts to draw a sharp contrast between mereology and set theory and he tries to assimilate mereology to logic. For him, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – unlike (...) the sum of the given objects – seems to be an abstract entity whose existence is not directly entailed by the existence of the objects themselves. The argument for the innocence of mereology is grounded on the thesis of composition as identity. In our paper we argue that: arguments for the ontological innocence of mereology are not conclusive. Some arguments against the ontological innocence of mereology show a certain ambiguity in the innocence thesis itself. The innocence thesis seems to depend on a general conception of the nature of objects and on how the notion of ontological commitment is understood. Specifically, we think that the thesis is the manifesto of a realistic conception of parts and sums. Quine‟s notorious criticism of the set-theoretical interpretation of second order logic seems to be reproducible against Lewis‟defence of mereology. To the purpose we construct a mereological model of a substantive fragment of set theory, adequate to ground the set-theoretical semantics of second order logic. (shrink)

The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use (...) in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priest’s claim that the entailment connective expresses the notion of logical consequence. (shrink)

In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as a theory of logical concepts. (...) Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism. (shrink)

We introduce an epistemic version of validity and completeness of first order logic, based on the notions of ideal agent and fictional model. We then show how the perspective here considered may help to solve an epistemic puzzle arising from Gödel's second incompleteness theorem.

This paper investigates the question of how we manage to single out the natural number structure as the intended interpretation of our arithmetical language. Horsten submits that the reference of our arithmetical vocabulary is determined by our knowledge of some principles of arithmetic on the one hand, and by our computational abilities on the other. We argue against such a view and we submit an alternative answer. We single out the structure of natural numbers through our intuition of the absolute (...) notion of finiteness. (shrink)

MartinoEnrico.* * Intuitionistic Proof Versus Classical Truth, The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics. Logic, Methodology and the Unity of Science; 42. Springer, 2018. ISBN: 978-3-319-74356-1 ; 978-3-030-08971-9, 978-3-319-74357-8. Pp. xiii + 170.

This Research Topic aimed at deepening our understanding of the levels and explanations that are of interest for cognitive sci- entists, neuroscientists, psychologists, behavioral scientists, and philosophers of science. Indeed, contemporary developments in neuroscience and psy- chology suggest that scientists are likely to deal with a multiplicity of levels, where each of the different levels entails laws of behavior appropriate to that level (Berntson et al., 2012). Also, gathering and modeling data at the different levels of analysis is not suffi- (...) cient: the integration of information across levels of analysis is a crucial issue. Given such state of affairs, a number of interesting questions arise. How can the autonomy of explanatory levels be properly understood in behavioral explanation? Is reductionism a satis- factory strategy? How can high-level and low-level models be constrained in order to be actually explanatory of both behav- ioral and neurological or molecular evidence? What is the kind of relationship between those models? (shrink)

This is a book about food, philosophy, and intellectual property rights. Taken separately, these are three well-known subjects; but it is uncommon to consider them together. Delivering a rich field of disputes, the book is comprised of 50 case studies, organized around eight themes: images; genericity and descriptiveness; language traps; procedures; menus, recipes, and creativity; boundaries; biotech; and empowerment. The introductory chapter frames the selection of cases and encourages readers to look beyond them, envisaging new lenses to look at food (...) vis-à-vis intellectual property. The terrain encompassed is wide-ranging and reaches out to fine-grained aspects of food products, recipes, and cooking. Conceived for a wide scope of readers, the volume ultimately interrogates the links between food and cultural identity, bringing to the fore the ethical, political, aesthetic worth of culinary arts and gastronomic experiences. This accessible book will be of value to scholars, students, practitioners and others with interests in the areas of intellectual property, food law and food studies. (shrink)

As colleges and universities seek to invigorate ethics education, they need methods to identify where and describe how ethics is already present across their curricula. Meeting this need is complicated by the fact that much ethics education occurs in courses not explicitly focused on ethics or morality. In this paper, we review recent methodological advances before presenting a new Ethics Course Identification Tool (ECIT) that combines application of an expert-derived weighted dictionary and natural language processing methods to identify ethics-related courses (...) based on their titles and course catalog descriptions, even when the terms “ethic” or “moral” are not present. Two studies, the second a pre-registered replication, revealed considerable interrater reliability among experts in ethics education regarding the ethical relevance of courses. Critically, both studies revealed strong correlations between expert judgments and ECIT scores. This empirical evidence points to a shared understanding of ethics education among experts, and it supports the valid use of the ECIT to rapidly and reliably identify ethics-related courses. Based on these findings, we propose that the ECIT can be used both to advance research on trends in ethics education and to help target interventions to improve ethics education at colleges and universities. (shrink)

Who or what is morally considerable? That is to say, what merits direct moral consideration—consideration in light of what it is? Mark Bernstein steers a middle course between the extremes he labels “chauvinism” and “deep ecology.” Chauvinists hold that, at most, all human beings are morally considerable. Deep ecologists are either individualists who hold that every living thing is morally considerable or holists who hold that ecosystems but not their constituent parts are considerable in themselves.

In recent years, the fight against money laundering has emerged as a key issue of financial regulation. The Wolfsberg Group is an important multistakeholder agreement establishing corporate responsibility principles against money laundering in a domain where international coordination remains otherwise difficult. The fact that 10 out of the 25 top private banking institutions joined this initiative opens up an interesting puzzle concerning the conditions for the participation of key industry players in the Wolfsberg Group. The article presents a fuzzy-set analysis (...) of seven hypotheses based on firm-level organizational factors, the macro-institutional context, and the regulatory framework. Results from the analysis of these 25 financial institutions show that public ownership of the bank and the existence of a code of conduct are necessary conditions for participation in the Wolfsberg Group, whereas factors related to the type of financial institution, combined with the existence of a black list, are sufficient for explaining participation. (shrink)

A noção de “interesse público” parece ter uma tradição antiga e profícua nos estudos políticos, em particular nas pesquisas sobre mídia, comunicação e política. No entanto, parece haver um aparente paradoxo entre a própria noção de “interesse” e a ideia de algo “público”: como uma ação ou decisão política pode contemplar a miríade de interesses de grupos e indivíduos diversos? Este artigo delineia alguns aspectos da noção de “interesse” no debate atual sobre comunicação política. Com base em uma pesquisa bibliográfica, (...) este artigo argumenta que, nas últimas décadas, as principais obras sobre o tema têm dedicado menos espaço à noção de 'interesse público' como uma entidade única em favor de uma visão mais nuançada e identitária cultural, noção que contempla a pluralidade de uma esfera pública repleta de novas formas de ativismo e demandas coletivas por espaço, igualdade e visibilidade. (shrink)

La brillantezza di molti edifici contemporanei può essere espressa attraverso l'immagine di uno specchio che riflette ciò che sta intorno, impedendo ogni contatto tra interno ed esterno. Ciò porta verso uno scenario articolato e ambiguo, che rappresenta il punto di contatto tra la riflessione architettonica e le formule sempre più spettacolarizzanti della comunicazione mediatica. L'estetica che prende forma da questo “paradigma dello specchio” perde il suo riferimento a una nozione pubblica e condivisa di bellezza, a favore di una sua considerazione (...) come oggetto di scambio individuale. Il concetto di “i-Aesthetics” prova a sintetizzare tale quadro, che diventa sempre più influente in riferimento al giudizio sull'architettura e al legame complessivo che instauriamo con lo spazio. (shrink)

A rigorous ab initio derivation of the (square of) Dirac’s equation for a particle with spin is presented. The Lagrangian of the classical relativistic spherical top is modified so to render it invariant with respect conformal changes of the metric of the top configuration space. The conformal invariance is achieved by replacing the particle mass in the Lagrangian with the conformal Weyl scalar curvature. The Hamilton-Jacobi equation for the particle is found to be linearized, exactly and in closed form, by (...) an ansatz solution that can be straightforwardly interpreted as the “quantum wave function” of the 4-spinor solution of Dirac’s equation. All quantum features arise from the subtle interplay between the conformal curvature acting on the particle as a potential and the particle motion which affects the geometric “pre-potential” associated to the conformal curvature itself. The theory, carried out here by assuming a Minkowski metric, can be easily extended to arbitrary space-time Riemann metric, e.g. the one adopted in the context of General Relativity. This novel theoretical scenario appears to be of general application and is expected to open a promising perspective in the modern endeavor aimed at the unification of the natural forces with gravitation. (shrink)

Ce recueil comprend une vingtaine de mes articles, pour la plupart deja publie par ailleurs. Plusieurs d'entre eux ont paru en francais, la langue que je prefere pour la communication internationale; mais il n'y a pas tout ce que j' ai ecrit ou publie dans cette langue: je n'ai retenu que les etudes concernant la dialectique, la physique et la metaphysique d'Aristote, et parmi celles-ci seulement celles qui me paraissent les plus significatives. J'y ai ajoute cinq traductions d'articles publies en (...) italien ou en anglais et qui me semblaient constituer un complement utile aux theses developpees dans les autres. Le but de cette publication est avant tout de mettre a la disposition d'un public plus large les resultats de mes etudes sur ces differents themes, en lui permettant d'en avoir une vision pour ainsi dire synoptique - au risque de comporter des repetitions, dont je tiens a m'excuser ici. Comme il s'agit d'ecrits s'etendant sur une trentaine d'annees - le plus ancien remonte a 1979, mais il avait ete presente au Symposium Aristotelicum de 1972 -, il est inevitable que, sur plusieurs points, il y ait eu des changements d'opinion. Mais ceux-ci ne sont pas vraiment significatifs et il s'agit dans la plupart des cas de nuances, de differences d'accent ou encore de mises au point. Si j'ai choisi d'inclure ainsi des opinions que je ne soutiens plus de la meme maniere aujourd'hui, c'est dans une intention dialectique, au sens aristotelicien du terme, c'est-a-dire pour fournir tous les arguments en faveur d'une these aussi bien que tous ceux qui lui sont opposes, de maniere a developper les apories dans les deux directions, ce qui, pour Aristote, constitue la meilleure maniere de distinguer le vrai du faux. (shrink)

Le savoir scientifique et le savoir philosophique ont une responsabilité éthique à ne pas mépriser. Ce constat, fait par des savants-philosophes comme Henri Poincaré ou Federigo Enriques, a eu une importance que l’épistémologie du XXe siècle a ignorée, mais qu’il faut aujourd’hui réactiver au nom de valeurs anciennes: l’égalité, la démocratie, l’ouverture, la recherche sans limite dogmatique. L’analyse de l’œuvre d’Enriques nous permet ici de saisir l’enjeu d’une telle démarche.