This essay argues that relativist semantics provide fruitful frameworks for the study of the relationships between meaning and truth-conditions, and consequently for the analysis of the logical properties of expressions. After a discussion of the role of intensionality and indexicality within classic double-indexed semantics, I explain that the non-relativistic identification of the parameters needed for the definition of truth and for the interpretation of indexicals is grounded on considerations that are irrelevant for the assessment of the relationships between meaning and (...) truth. (shrink)

We introduce a two‐dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then we prove completeness and a semantic partial cut elimination theorem down to formulas of a certain type.

For arbitrary finite group $G$ and countable Dedekind domain $R$ such that the residue field $R/P$ is finite for every maximal $R$ -ideal $P$ , we show that the localizations at every maximal ideal of two $RG$ -lattices are isomorphic if and only if the two lattices satisfy the same first order sentences. Then we investigate generalizations of the above results to arbitrary $R$ -torsion-free $RG$ -modules and we apply the previous results to show the decidability of the theory of (...) ${\vec Z}C(2)^2$ -lattices. Eventually, we show that ${\vec Z} [i] C(2)^2$ -lattices have undecidable theory. (shrink)

This paper defends a position that parts ways with the positivist view of legal certainty and reasonableness. I start out with a reconstruction of this view and move on to argue that an adequate analysis of certainty and reasonableness calls for an alternative approach, one based on the acknowledgement that argumentation is key to determining the contents, structure, and boundaries of a legal system. Here I claim that by endorsing a dialectical notion of rationality this alternative account espouses an ambitious (...) approach to reasoning in law and conceives of the theory of legal argumentation as the vantage point from which to analyze legal systems and tackle the main problems connected with their existence. Next, I look at what this alternative approach does for the way we should go about treating certainty and reasonableness, considered singularly as well as in their reciprocal relationship. I conclude on this basis that when argumentation receives its due emphasis in law we have to redefine certainty and reasonableness and recast their connection as non-conflictive. (shrink)

In this paper the argument from coherence is submitted to a critical analysis. First, it is argued to be a complex form of coordinative argumentation, structured on various argumentative levels. Then, using the pragma-dialectical theory of argumentation a distinction is brought out between two basic forms of the argument from coherence: in one use this argument occurs as a sequence of two symptomatic arguments; in the other use we have a main symptomatic argument supported by a subordinate pragmatic argument. Finally, (...) from an evaluative point of view it is assessed whether the argument from coherence can be found acceptable as a tool for settling disputes. It is claimed that in general, we can welcome this argumentative structure as sound and fully acceptable provided that we are aware of the interpretative discretion its use implies. (shrink)

Aim of this work is to investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an ω–type schema of inference that naturally interpret the propositional and the predicate until–free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set of (...) extralogical axioms). For each system we provide a syntactic proof of cut elimination and a proof of completeness. (shrink)

To his pupil Nero and to Lucilius (friend and, as metonymy, representative of the entire mankind), Seneca testifies to his pedagogic vocation. With conviction he applies himself to demonstrate the perfect correspondence between the Stoic doctrine and the edu¬cational strategy that he proposes. Firstly, the reciprocity of the relationship between educator and pupil appears fundamental; both further their individual knowledge. Secondly, the limitations of an ethical precept that is not anchored in the intensity and concreteness of human life becomes clearly (...) apparent. Furthermore, it brings to question the weakness of a world vision not inspired by an innovative and original path. The starting point is therefore a rigorous examination of conscience to ultimately reach the revolutionary experience of risk in the moment of the last decision. In the name of truth the wise man must have the courage to embrace fate in order to really understand who he is (in a process of oikeiosis both as experience and as target), and he must instil in his pupils the courage to take risks along their own independent journey. In so doing, self-scrutiny and politics can become intertwined. It is herein that the educator’s risk and responsibilities lie. (shrink)

We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of (...) an environment structure is composed of particular subsets of Rn. The comparison of mereogeometrical theories within these environment structures shows dependencies among primitives and provides (relative) definitional equivalences. With one exception, we show that all the theories considered are equivalent in these environment structures. (shrink)

We study a modal extension of the Continuous First-Order Logic of Ben Yaacov and Pedersen :168–190, 2010). We provide a set of axioms for such an extension. Deduction rules are just Modus Ponens and Necessitation. We prove that our system is sound with respect to a Kripke semantics and, building on Ben Yaacov and Pedersen, that it satisfies a number of properties similar to those of first-order predicate logic. Then, by means of a canonical model construction, we get that every (...) consistent set of formulas is satisfiable. From the latter result we derive an Approximated Strong Completeness Theorem, in the vein of Continuous Logic, and a Compactness Theorem. (shrink)

Name der Zeitschrift: Byzantinische Zeitschrift Jahrgang: 109 Heft: 1 Seiten: 151-178.

We propose a set theory, called NRFST, in which the Cantorian axiom of infinity is negated, and a new notion of infinity is introduced via non standard methods, i. e. via adequate notions of standard and internal, two unary predicates added to the language of ZF. After some initial results on NRFST, we investigate its relative consistency with respect to ZF and Kawai's WNST.

Comment une nouvelle divinité, munie de ses attributs spécifiques, ses timai et ses épiphanies, peut-elle être créée? Par qui? Et à quelles fins? Qui seront ses prêtres et ses fidèles? La documentation hellénistique confère une perspective historique aux aspects cultuels, sociaux et idéologiques de ces phénomènes religieux et les cultes des souverains sont un cas particulier de l’établissement et de l’acceptation de nouveaux dieux. Les cultes de souveraines n’ont que très récemment reçu l’attention qu’ils méritent. L’article étudie les cas de (...) Bérénice Ire, Arsinoé II et Laodice V afin de fournir de nouvelles interprétations de quelques fêtes dynastiques et d’étudier la relation entre les cultes de souverains et la légitima­tion du pouvoir féminin. La discussion repose surtout sur des papyrus et des inscriptions, mais l’analyse conclusive de l’Idylle XVII de Théocrite montre que la logique poétique de la légitimation du pouvoir entre en résonance avec celle qu’attestent les sources non littéraires. (shrink)

We conjecture that the text of § 9 in Kant's "Doctrine of Virtue" might have been assembled in a wrong order, because of issues in the preparation of the manuscript for publication. We show that textual clues suggest to consider the possibility of reordering two passages in the section, which might yield a more coherent argumentative structure.

Trata-se de uma investigação histórica da neurologia alemã das primeiras décadas do século XIX, representada por Burdach e Carus, e da rela- ção que manteve com pressupostos românticos de abordagem biológica. Carus acentua a necessidade de pesquisar o cérebro pelo viés anatômico e o considera um organismo total, atestando a influência do filósofo Schelling. Burdach, por seu lado, investiga a estrutura cerebral em conexão com a sensibilidade e o processo evolutivo.

In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of a (...) non-standard development. MSC: 03E30, 03E35. (shrink)

Di un concetto come quello di morfologia viene fatto ampio uso in molti rami dell’indagine scientifica, là dove a esso si fa ricorso per indicare le strutture e i sottostanti processi di formazione che ne costituiscono l’oggetto di studio. Come tale, il concetto assume un significato di ordine generale, che fa sì che a esso si ricorra anche in contesti non strettamente scientifici e dunque con una valenza eminentemente metaforica. Senza tema di esagerazione, si potrebbe anzi affermare che il...

The New Realism Manifesto by Maurizio Ferraris criticises hermeneutics and postmodernism for their passive and conservative positions, claiming that they are responsible for having delegitimised all philosophical reflection on reality and ontology and favoured the affirmation of a “show-biz” society and a proprietary personalisation of politics. Gianni Vattimo answers this thesis, accusing realism of colluding both with the hierarchy of the powers-that-be and with technocracy and claiming the left-wing orientation of hermeneutics. But to be fair, Vattimo has noticeably changed his (...) own position with respect to the years of “weak Thought”, when every hypothesis of political intervention on reality and every project of transformation were excluded. Hermeneutics today merits being considered a sort of new and revolutionary “philosophy of praxis” in which a weakened Marxism joins up (improbably) with Nietzsche and Heidegger’s thought. Although bitter, the conflict between these positions, which openly claim an emancipationist orientation, is an indication of a process of radicalization of Italian philosophy that is also confirmed by the recent theses of other authors. However, in the absence of a rediscovery of that reality which more than any other has been obscured by postmodernism – the reality of work and the material processes of production and social reproduction – and in the absence of a real subject interested in an overall transformation of the contemporary world, the risk is that such radicalisation of the intellectual classes will stay incomplete and remain within a theoretical debate that is incapable of changing the imbalances and relations of subordination and dominion present in society. (shrink)

Tra le figure più importanti del dibattito filosofico italiano del Novecento, Antonio Banfi ha svolto nell'Italia del secondo dopoguerra anche un ruolo politico di rilievo come senatore del PCI. La sua interpretazione del marxismo ha presentato una forte accentuazione umanistica. Tra i suoi scolari filosofi e storici della filosofia come Giulio Preti, Enzo Paci, Remo Cantoni, Paolo Rossi. Il saggio prende in esame la prima fase della riflessione filosofica di Banfi, nella quale ha una importanza decisiva la conoscenza diretta del (...) dibattito tedesco tra le due guerre mondiali, in primo luogo della fenomenologia di Husserl e della ontologia di N. Hartmann. I Principi di una teoria della ragione - libro apparso alla fine degli anni '20 - e poi una serie di incisivi saggi degli anni '30 documentano una conoscenza approfondita e critica di un dibattito di cui mostrerà di nutrirsi in misura decisiva l'interpretazione di Banfi non solo di Hegel, ma anche di Marx. Among the leading philosophers in Italy during the 20th century, Antonio Banfi played an important role not only in the cultural debate during the 1930s and the 1940s, but also in the political scene of post-war Italy, advocating - as a representative of the Italian Communist Party in Italian Senate - a liberal, humanist view of Marxism. Among his students were influential philosophers and historians of philosophy such as Giulio Preti, Enzo Paci, Remo Cantoni and Paolo Rossi. This paper investigates the first phase of Banfi's philosophical development, an analysis of which must include a scrutiny of Banfi's deep indebtedness to German debate between the two World Wars, primarily Husserl's phenomenology and Hartmann's critical ontology. Banfi's phenomenological apprenticeship at the school of Husserl, and the sensitive and critical attitude of his presentation of the German debate in his Principi di una teoria della ragione, are of substantial importance in nourishing his later interpretation of Hegel and Marx. (shrink)

Il saggio propone una traccia di ricerca per l’elaborazione di una teoria politica della cooperazione, ovvero per la considerazione del fenomeno cooperativo come caratterizzato da una peculiare modalità di azione collettiva, non ricompresa nella celebre distinzione hirschmaniana tra Exit, Voice e Loyalty. Chi partecipa all’impresa cooperativa non crede nelle possibilità di successo sia dell’opzione voice che di quella exit, ma pratica una forma diversa di azione che si basa sulla fiducia in se stessi e nei soci che hanno interessi comuni. (...) Questa forma di azione collettiva può essere preliminarmente definita come entry. L’entry riporta all’interno del mercato chi aveva scelto l’opzione exit, conservando al tempo stesso quella carica di contestazione delle relazioni capitalistiche tipica dell’opzione voice. L’impresa cooperativa, in virtù di questa doppia caratteristica dell’azione dei suoi soci, rappresenta quindi un’opzione, oltre che economica, anche politica. (shrink)

In this paper, I present a critique of inclusive positivism. Inclusive positivism is an untenable position, I argue, because the connection between law and critical morality is conceptual and thus more than merely an accident or a possibility: at the foundation of law we find social facts, but we also and importantly find moral evaluations. This thesis is supported by an argument showing in essence that law cannot exist apart from justification and that justification is a morally coloured practice. For (...) justification proceeds from directives freighted with values. A directive in turn acquires values (and so becomes justifiable) by meeting certain requirements: not those of instrumental reason or of prudential reason, but those of morality, and not just any morality, but critical morality. (shrink)

We introduce an implication-free fragment image of ω-arithmetic, having Exchange rule for sequents dropped. Exchange rule for formulas is, instead, an admissible rule in image. Our main result is that cut-free proofs of image are isomorphic with recursive winning strategies of a set of games called “1-backtracking games” in [S. Berardi, Th. Coquand, S. Hayashi, Games with 1-backtracking, Games for Logic and Programming Languages, Edinburgh, April 2005].We also show that image is a sound and complete formal system for the implication-free (...) fragment of LCM , Seventh International Conference on Typed Lambda Calculi and Applications, in: Lecture Notes in Computer Science, vol. 3461, 2005, pp. 11–22. Invited paper]). A simple syntactical description of this fragment was still missing. No sound and complete formal system is known for LCM itself. (shrink)

We study a real valued propositional logic with unbounded positive and negative truth values that we call ‐valued logic. Such a logic is semantically equivalent to continuous propositional logic, with a different choice of connectives. After presenting the deduction machinery and the semantics of ‐valued logic, we prove a completeness theorem for finite theories. Then we define unital and Archimedean theories, in accordance with the theory of Riesz spaces. In the unital setting, we prove the equivalence of consistency and satisfiability (...) and an approximated completeness theorem similar to the one that holds for continuous propositional logic. Eventually, among unital theories, we characterize Archimedean theories as those for which strong completeness holds. We also point out that ‐valued logic provides alternative calculi for Łukasiewicz logic and for propositional continuous logic. (shrink)

The links between the crisis of subprime mortgages and the so-called crisis of European sovereign debt are sometimes concealed, so as to create a veritable sense of shared guilt meant to sanction the legitimacy of the austerity policies that have been imposed by virtuous Northern European countries on the undeserving countries of Southern Europe. We will analyse three main aspects of the current crisis: (1) we will interpret the austerity policies that today characterize the eurozone as the result of financialization; (...) (2) we will define the state of permanent crisis as an instrument of governance characterized by specific economic policies; (3) we will show how all this unfolds at a stage of capitalist development wherein a new constituent process begins to take shape in a fragmented but nonetheless significant manner, and how this process is reclaimed by the very subjectivities upon which the accumulation of cognitive and relational skills depends in order to reproduce itself: the Welfare of the Common. (shrink)

Da uno dei padri fondatori dell’Italia come nazione, un veloce e agile compendio su filosofia, politica risorgimentale e musica, centrato sulle idee e i gusti artistici mazziniani e ambientato nel panorama melodrammatico della prima metà dell’Ottocento, governato dalla maestosa figura di Gioacchino Rossini. Il volume è arricchito anche da un altro breve estratto mazziniano riguardante la musica, proveniente da Dell’Arte in Italia – A proposito del “Marco Visconti” di Tommaso Grossi (1835).

Page's “localist” code, a population code with occasional, maximally firing elements, does not seem to us usefully or testably different from sparse population coding. Some of the evidence adduced by Page for his proposal is not actually evidence for it, and coding by maximal firing is challenged by lower firing observed in neuronal responses to natural stimuli.

This essay tackles head on the argument that sees an inherent paradox in the autonomy of the will as the ground for the authority of the fundamental practical norms. It points out that only on reductive understandings of the autonomy of the will can this idea be qualified as paradoxical, thereby yielding outcomes that either contradict their premises or present autonomy under a false guise. With that done, it will proceed to offer a conception of the autonomy of the will (...) which is not vulnerable to the paradox, and which may therefore be equipped to rest the fundamental practical norms on solid ground. Throughout this discussion, I will rely on constitutivism about practical reasons to specifically defend the twofold conclusion that (a) the paradox of autonomy can be avoided and that, relatedly, (b) if autonomy is properly conceptualised, it is fully equipped and well positioned to ground the authority of the fundamental practical norms. (shrink)

We investigate the consequences of removing the infinitary axiom and rules from a previously defined proof system for a fragment of propositional metric temporal logic over dense time.