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)

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)

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)

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)

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)

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 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)

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.

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)

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)

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 [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)

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.

In an era characterized by fast technological progress that introduces new unpredictable scenarios every day, working in the law field may appear very difficult, if not supported by the right tools. In this respect, some systems based on Artificial Intelligence methods have been proposed in the literature, to support several tasks in the legal sector. Following this line of research, in this paper we propose a novel method, called PRILJ, that identifies paragraph regularities in legal case judgments, to support legal (...) experts during the redaction of legal documents. Methodologically, PRILJ adopts a two-step approach that first groups documents into clusters, according to their semantic content, and then identifies regularities in the paragraphs for each cluster. Embedding-based methods are adopted to properly represent documents and paragraphs into a semantic numerical feature space, and an Approximated Nearest Neighbor Search method is adopted to efficiently retrieve the most similar paragraphs with respect to the paragraphs of a document under preparation. Our extensive experimental evaluation, performed on a real-world dataset provided by EUR-Lex, proves the effectiveness and the efficiency of the proposed method. In particular, its ability of modeling different topics of legal documents, as well as of capturing the semantics of the textual content, appear very beneficial for the considered task, and make PRILJ very robust to the possible presence of noise in the data. (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)

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)

Our usual method" is an expression that Aristotle uses in a passage of the Politics (I.1, 1252a17-20) to describe the technique of subdividing a composite object of study into the elements that make it up, in order to study the possible combinations. What theory is the basis for this method? Is it really a usual method for Aristotle? Enrico Rini responds to these questions, starting with the analysis of some passages of the Aristotelian corpus that refer to concepts of (...) the part and the whole. From these passages, Rini attempts to extrapolate a theory that Aristotle states explicitly only on occasion. The mereology that emerges from this study is not a formal theory, unlike the logical mereology present today, and therefore takes into account different types of the whole and the part, with a scope that has applications for the field of biology. (shrink)

Diatoms are important protists that generate one fifth of the oxygen produced annually on earth. These aquatic organisms likely derived from a secondary endosymbiosis event, and they display peculiar genomic and structural features that reflect their chimeric origin. Diatoms were one of the first models of cell division and these early studies revealed a range of interesting features including a unique acentriolar microtubule‐organising centre. Unfortunately, almost nothing is known at the molecular level, in contrast to the advances in other experimental (...) organisms. Recently the full genome sequences of two diatoms have been annotated and molecular tools have been developed. These resources offer new possibilities to re‐investigate the mechanisms of cell division in diatoms by recruiting information from more intensively studied organisms. A renaissance of the topic is further justified by the current interest in diatoms as a source of biofuels and for understanding massive diatom proliferation events in response to environmental stimuli. (shrink)

Vanity and pride have been condemned by Christian thinkers for centuries. Therefore, it may seem curious that Paul-Henri Thiry, Baron d’Holbach, one of the fiercest critics of religion, decried these passions. Holbach’s work is interspersed with remarks about vanity and pride which have gone unnoticed in the literature. This chapter analyzes Holbach’s account of vanity, delving into the role it plays in the establishment and maintenance of religion. I show that the desire for prestige is at the very core of (...) religious practices, which aim to justify the alleged superiority of man over nature. Holbach’s well-known critique of religion, therefore, cannot be fully understood without reference to his lesser known account of vanity and pride. The study of these passions is also essential to grasping Holbach’s conception of philosophy and how the philosophe should be: an individual free from prejudices, who has abandoned every trace of vanity in order to move forward in their journey towards the truth. (shrink)

The World Health Organization has published a global priority list of antibiotic-resistant bacteria to guide research and development of new antibiotics. Every pathogen on this list requires R&D activity, but some are more attractive for private sector investments, as evidenced by the current antibacterial pipeline. A “pipeline coordinator” is a governmental/non-profit organization that closely tracks the antibacterial pipeline and actively supports R&D across all priority pathogens employing new financing tools.

This paper develops Richard Wollheim’s claim that the proper appreciation of a picture involves not only enjoying a seeing-in experience but also abiding by a standard of correctness. While scholars have so far focused on what fixes the standard, thereby discussing the alternative between intentions and causal mechanisms, the paper focuses on what the standard does, that is, establishing which kinds, individuals, features and standpoints are relevant to the understanding of pictures. It is argued that, while standards concerning kinds, individuals (...) and features can be relevant also to ordinary perception, standards concerning standpoints are specific to pictorial experience. Drawing on all this, the paper proposes an ontology of depiction according to which a picture is constituted by both its visual appearance and its standard of correctness. (shrink)

In the first part of this paper, published in issue 1 of Augustinianum 63 (2023), 9-45, we examined the question of whether Irenaeus of Lyons depended on the Exposition of Logia about the Lord of Papias of Hierapolis. In this second and final part we focus on the way Irenaeus used information which, since the first decades of the second century, had been attributed to presbyters of Asia and then in particular on the way he identifies the succession of presbyters (...) with that of bishops (primarily in Rome). He links the latter with Christian origins but also profoundly alters the function traditionally attributed to the presbyters themselves, within a system he devised in order to respond to urgent problems, in a context quite different from the era in which the traditions to which he appeals were born. (shrink)

How the cilium appeared is still such a poorly defined question that current hypotheses range from a symbiotic spirochaete to a cellular eye. In this paper, the whole question is subdivided into a list of problems which are morphological, physiological and temporal. These problems are examined one by one, in order to analyse the most popular exogenous hypothesis of Margulis as well as other recent exogenous and endogenous hypotheses. To overcome fundamental topological and temporal difficulties, a new endogenous hypothesis is (...) expounded, according to which the cilium derives from a cellular peduncle reinforced with microtubules. This hypothesis implies a geometrical rationale for the ninefold symmetry. In the last paragraph the consequences of the various hypotheses are compared. (shrink)

Il volume affronta i complessi problemi sollevati dalla musica a studiosi, critici, filosofi, e che riguardano cio che ruota attorno a questa arte dalle molteplici facce. Punto chiave della riflessione sono le avanguardie del Novecento, poiché le sue profonde trasformazioni mettono a nudo ed evidenziano, a volte in modo drammatico, gli interrogativi di fondo a cui la musica ci ha sempre posto di fronte. Il tema centrale è il rapporto tra una supposta universalità dell'esperienza musicale in senso lato e la (...) sua innegabile storicità, tema su cui si dibatte nel pensiero occidentale sin dai tempi di Pitagora. Pur essendo un linguaggio chiuso nella sua specificita, la musica ci spinge di continuo ad andare oltre: allude sempre a qualcosa che sta al di fuori dei suoni stessi e ci invita a esplorare i luoghi a cui segretamente tende"--Back cover. (shrink)