We present recent results on the model companions of set theory, placing them in the context of a current debate in the philosophy of mathematics. We start by describing the dependence of the notion of model companionship on the signature, and then we analyze this dependence in the specific case of set theory. We argue that the most natural model companions of set theory describe (as the signature in which we axiomatize set theory varies) theories of $H_{\kappa ^+}$, as $\kappa (...) $ ranges among the infinite cardinals. We also single out $2^{\aleph _0}=\aleph _2$ as the unique solution of the continuum problem which can (and does) belong to some model companion of set theory (enriched with large cardinal axioms). While doing so we bring to light that set theory enriched by large cardinal axioms in the range of supercompactness has as its model companion (with respect to its first order axiomatization in certain natural signatures) the theory of $H_{\aleph _2}$ as given by a strong form of Woodin’s axiom $(*)$ (which holds assuming $\mathsf {MM}^{++}$ ). Finally this model-theoretic approach to set-theoretic validities is explained and justified in terms of a form of maximality inspired by Hilbert’s axiom of completeness. (shrink)

In this detailed study of the republican tradition in the development of the Enlightenment, the central problem of utopia and reform is crystallized in a discussion of the right to punish. Describing the political situation in Europe in the seventeenth and eighteenth centuries, the author shows how the old republics in Italy, Poland and Holland stagnated and were unable to survive in the age of absolutism. The Philosophes discussed the ideal of republicanism against this background. They were particularly influenced by (...) the political and religious radicalism of John Toland, which had survived the English Restoration and was then reaching Europe. Professor Venturi traces the debate on the penal laws and the attempt to relate utopian ideas of society to the practical problem of dealing with man in society, which culminated in the assertion by many Philosophes that an unjust social system necessitated harsh penal laws, thereby rejecting the possibility of reform. (shrink)

The author comments on and criticizes some conclusions of the article by Lubomir Lamy entitled “Beyond Emotion: Love as an Encounter of Myth and Drive.” In addition, she shows evidence that love may be considered an integrated neurobiobehavioral process and, as such, regulated by neural systems and circuits that underlie its emotional, cognitive, and behavioral expressions.

Bernard Bolzano (1781 - 1848) war ein vielseitiger Philosoph. Seine Interessen bedecken alle Bereiche der Logik über Physik bis zur den Wissenschaften des Übersinnlichen. Die moderne Bolzano-Rezeption schätzt an seinem Werk vor allem die mathematischen, logischen und erkenntnistheoretischen Bemühungen. Trotz des großen Stellenwertes, den Mathematik und Logik in der Forschung Bolzanos einnehmen, können sie die beachtliche Dichte der Querverbindungen seines Denkens nicht ausschöpfen. In diesem Band wird eine kritische Rekonstruktion der theologisch-metaphysischen Untersuchungen (anhand seiner Athanasia) Bolzanos geliefert, welche die Wechselwirkungen (...) aufzeigen soll, die zwischen den theologisch-metaphysischen und den logisch-mathematischen Untersuchungen besteht. (shrink)

Ce livre offre une vue d’ensemble sur la mendicité en traversant plusieurs disciplines (histoire, philosophie, littérature) et plusieurs genres littéraires (epos, tragédie, littérature philosophique) et en se déployant sur un arc chronologique qui s’étend de la Grèce archaïque jusqu’au monde judéo-chrétien. L’ouvrage se compose d’une présentation, rédigée par Étienne Helmer, et de onze contributions, organisées en trois volets : I. « Au centre et au bord. Espaces civiques et institutionnels d...

In the Tractatus, it is stated that questions about logical formatting cannot be meaningfully formulated, since it is precisely the application of logical rules which enables the formulation of a question whatsoever; analogously, Wittgenstein’s celebrated infinite regress argument on rule-following seems to undermine any explanation of deduction, as relying on a logical argument. On the other hand, some recent mathematical developments of the Curry-Howard bridge between proof theory and type theory address the issue of describing the “subjective” side of logic, (...) that is, the concrete manipulation of rules and proofs in space and time. It is advocated that such developments can shed some light on the question of logical formatting and its apparently unintelligible paradoxes, thus reconsidering Wittgenstein’s verdict. (shrink)

This paper contributes to the generalization of lattice-valued models of set theory to non-classical contexts. First, we show that there are infinitely many complete bounded distributive lattices, which are neither Boolean nor Heyting algebra, but are able to validate the negation-free fragment of \. Then, we build lattice-valued models of full \, whose internal logic is weaker than intuitionistic logic. We conclude by using these models to give an independence proof of the Foundation axiom from \.

In this paper I argue that dispositionalism is the metaphysical theory that can best contribute to the construction of a metaphysical model for Molecular Gastronomy. Molecular Gastronomy is better explained if physical and chemical theories, which lie at the heart of Molecular Gastronomy, and cooking phenomena in general are described in terms of dispositions. This is the reason why trying to construct a metaphysical model for Molecular Gastronomy by using a dispositional metaphysics is a challenge worth taking on. I will (...) thus explore what happens when we bring dispositions in the kitchen, and so the intersection between food, science and metaphysics. The main aim of the paper is then to pave the way toward the development of a metaphysical model for the physical and the chemical aspects behind Molecular Gastronomy. In the first section, I will briefly reconstruct the history of Molecular Gastronomy, give a definition of it and outline its program. In the second section, I will describe the version of dispositionalism that I adopt in this paper. In the third section, I will sketch a dispositional model for Molecular Gastronomy by relying on two case studies. In the fourth and final section I will draw my conclusions and raise some issues deserving further investigation. (shrink)

Dispositionalism is the theory of modality according to which all (metaphysical and natural) modal truths are made true by some actual irreducibly dispositional property. The relationship between Dispositionalism and time is yet to be satisfactorily explored. In this paper we contribute to this task by examining how Dispositionalism deals with ‘dated truths’: propositions involving a specific time, e.g. “It might rain at 12.30”. We examine two possible accounts: the first, 'Dated Manifestations Strategy', is the idea that powers are very fine-grained, (...) and tend towards temporally very specific manifestations. We argue that such strategy should not be adopted, for it leads to unnecessary violations of ontological parsimony; it is unable to accommodate an ontology of platonic universals; and it is incapable of offering a principled explanation of the forward-looking nature of powers. We offer an alternative account, the "Duration Strategy", which relies on an independently determined arrow of time and the existence of some “duration facts” that specify how long a power takes to bring about its manifestation. We argue that the Duration Strategy is to be preferred. We then flesh out the account by exploring the connection between powers, duration facts, and processes. (shrink)

This book continues the editors' work of highlighting and re-evaluating the contributions of the most important political scientists who have gone before.

This book fills an important gap in the growing reflective literature on the political science discipline: it consists of a series of 'objective' profiles of the 'Masters of Political Science', written by political scientists who have read and studied their work and who are therefore in a position to evaluate the nature of their contributions.

Italy is one of the advanced industrial democracies with the smallest number of women elected to public office. Current literature has focused on several structural, institutional and cultural factors to explain such a gender gap in political participation and representation. However, one of the most basic forms of political participation, political discussion, has not received a thorough investigation. This article analyses gender differences in the attitudes and the habits of talking about politics with relatives, friends and social acquaintances during the (...) Italian 2006 electoral campaign. The main argument is that the analysis of political discussion may shed new light on how Italian women approach politics and help explain their reluctance to be involved in political activities in terms of elected office and party membership. (shrink)

How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...) of language. (shrink)

Il termine cohousing č utilizzato, a livello internazionale, per indicare le forme di co-abitazione che rispondono essenzialmente a strategie di tipo elettivo da parte di nuclei familiari e/o singoli che decidono di stabilire la propria residenza stabile in strutture abitative pensate per offrire oltre che spazi di vita privati anche luoghi di condivisione. Diverse sono le forme e, ancor piů, i significati, che a questo particolare tipo di convivenza le persone attribuiscono: solidarietÀ, scambievolezza, comunitÀ di vita. Il contributo propone una (...) piccola ricognizione dei principali modelli presenti oggi in Italia. (shrink)

We analyze axioms and postulates as speech acts. After a brief historical appraisal of the concept of axiom in Euclid, Frege, and Hilbert, we evaluate contemporary axiomatics from a linguistic perspective. Our reading is inspired by Hilbert and is meant to account for the assertive, directive, and declarative components of modern axiomatics. We will do this by describing the constitutive and regulative roles that axioms possess with respect to the linguistic practice of mathematics.

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.

There is a tension between Dispositionalism––the view that all metaphysical modality is grounded in actual irreducible dispositional properties––and the possibility of time travel. This is due to the fact that Dispositionalism makes it much harder to solve a potentiality-based version of the grandfather paradox. We first present a potentiality-based version of the grandfather paradox, stating that the following theses are inconsistent: 1) time travel is possible, 2) powers fully ground modality, 3) self-defeating actions are impossible, 4) time-travellers retain their intrinsic (...) powers upon time-travelling, and 5) time-travellers are ordinary agents with basic intrinsic potentialities. We then consider a number of potential solutions, and find them wanting. We argue that the metaphysical impossibility of performing a self-defeating action acts as a necessary perfect mask––while time-travel lets us “slip” the potentiality under the mask, thus generating the contradiction. We conclude considering what are the options for the dispositionalist. (shrink)

In this paper, we examine the logics of essence and accident and attempt to ascertain the extent to which those logics are genuinely formalizing the concepts in which we are interested. We suggest that they are not completely successful as they stand. We diagnose some of the problems and make a suggestion for improvement. We also discuss some issues concerning definability in the formal language.

This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework linking Woodin’s generic absoluteness results for second order number theory and the theory of universally Baire sets to model companionship and show that (with the required care in details) a $$\Pi _2$$ -property formalized in an appropriate language for second order number theory is forcible (...) from some $$T\supseteq \mathsf {ZFC}+$$ large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T. In particular we show that the first order theory of $$H_{\omega _1}$$ is the model companion of the first order theory of the universe of sets assuming the existence of class many Woodin cardinals, and working in a signature with predicates for $$\Delta _0$$ -properties and for all universally Baire sets of reals. We will extend these results also to the theory of $$H_{\aleph _2}$$ in a follow up of this paper. (shrink)

In this article we analyze the method of forcing from a more philosophical perspective. After a brief presentation of this technique we outline some of its philosophical imports in connection with realism. We shall discuss some philosophical reactions to the invention of forcing, concentrating on Mostowski’s proposal of sharpening the notion of generic set. Then we will provide an overview of the notions of multiverse and the related philosophical debate on the foundations of set theory. In conclusion, we connect this (...) modern debate and Mostowski’s proposal, suggesting a way to analyze the notion of genericity within the framework of a multiverse structure. (shrink)

In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.

In this paper we provide an analysis of dynamic dispositionalism. It is usually claimed that dispositions are dynamic properties. However, there is no exhaustive analysis of dynamism in the dispositional literature. We will argue that the dynamic character of dispositions can be analyzed in terms of three features: (i) temporal extension, (ii) necessary change and (iii) future orientedness. Roughly, we will defend the idea that dynamism entails a continuous view of time, to be analyzed in mathematical terms, where intervals are (...) its constitutive elements, whose duration lasts as much as a certain change takes to occur (in support of i). Such changes are the necessary components for the flowing of time because we think there cannot be time without change, (thus supporting ii) and that the forward-looking feature of properties is what determines the direction of time (as per iii). The paper is structured in 5 sections. In the first section, we set the problem: we outline and criticize some dispositional theories that defend an unsatisfying notion of dynamism. In the second, third and fourth sections we defend each desideratum for a disposition to be dynamic. Finally, we draw some conclusions and consider potential future research. (shrink)

This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics and logics containing the provability operator as the primary modal operator.

ABSTRACT Despite the increasing interest in science exhibitions, there has been hardly any work on mobile science exhibitions and their role within science diplomacy – a gap this thematic issue is meant to fill. Atomic mobile exhibitions are seen here not only as cultural sites but as multifaceted strategic processes of transnational nuclear history. We move beyond the bipolar Cold War history that portrays propagandist science exhibitions as instances of a one-way communication employed to promote the virtues of the two (...) major and conflicting political powers. Instead, Science Diplomacy on Display follows mobile atomic exhibitions as they move across national borders and around the world, functioning as spaces for diplomatic encounters. Exhibitions play a vital role not only in the production of knowledge and the formation of political worldviews but also as assets in diplomatic negotiations and as promoters of a new worldview in which nuclear stands at the centre. They are powerful iconic diplomatic devices, that is systems of representations that capture the diplomatic processes in action and make the nitty-gritty details of international relations visible. This issue seeks to trace the multiple and often contradictory meanings that mobile exhibitions took on for various actors. (shrink)

We present a case study for the debate between the American and the Australian plans, analyzing a crucial aspect of negation: expressivity within a theory. We discuss the case of non-classical set theories, presenting three different negations and testing their expressivity within algebra-valued structures for ZF-like set theories. We end by proposing a minimal definitional account of negation, inspired by the algebraic framework discussed.

The organization of the mobile atomic exhibition, Mostra Atomica, designed by the United States Information Service to travel through Italy in 1954–55, had to meet technical, scientific, artistic, and political challenges. The head of the group in charge of the exhibition was architect Peter G. Harnden whose pedigree in the intelligence and training in architecture were an ideal match for leading the unit dedicated to exhibitions. The political sensitivity of the Mostra Atomica also required the intervention of the Italian Ministry (...) of the Interior to guarantee safe mobility and secure shows. In every major town, American and British diplomats attended the local opening ceremony, while the very symbol of science diplomacy was Enrico Fermi, whose recorded message praised international cooperation. All in all, the USIS campaign promoting peaceful applications of nuclear physics was successful in reaching and involving Italian society. Visual and spatial aesthetics were particularly relevant: the geometrical design of the exposition rooms conveyed a strong sense of modernity that contrasted with the artistic heritage of Italian cities. The present article is based on archival files, newspaper reports, and photographs that document who was responsible for planning, setting up, and reporting this Cold War propaganda event. (shrink)

Il tema di questo saggio č la linea di demarcazione che distingue e separa uomo e animale dagli albori della civiltÀ occidentale. Attraverso una rilettura critica di momenti e forme di tale linea, il discorso qui sviluppato propone di riconoscere i concetti di uomo e di animale, quali sono stati finora pensati e applicati, come artefatti umani che hanno tenuto in scarsa o nessuna considerazione il fatto che nella demarcazione sono insiti una vicinanza e un rapporto e insieme un'alteritÀ con (...) cui il pensiero non puň piů evitare di misurarsi. (shrink)

We offer tableaux systems for logics of essence and accident and logics of non-contingency, showing their soundness and completeness for Kripke semantics. We also show an interesting parallel between these logics based on the semantic insensitivity of the two non-normal operators by which these logics are expressed.