We introduce a sequent calculusBfor a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic. quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterizeBpositively: reflection, symmetry and visibility.A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with a metalinguistic link between assertions, (...) and if its syntactic inference rules are obtained by solving that equation. All connectives of basic logic satisfy reflection.To the control of weakening and contraction of linear logic, basic logic adds a strict control of contexts, by requiring that all active formulae in all rules are isolated, that is visible. From visibility, cut-elimination follows. The full, geometric symmetry of basic logic induces known symmetries of its extensions, and adds a symmetry among them, producing the structure of a cube. (shrink)

The duality between general frames and modal algebras allows to transfer a problem about the relational (Kripke) semantics into algebraic terms, and conversely. We here deal with the conjecture: the modal algebra A is subdirectly irreducible (s.i.) if and only if the dual frame A* is generated. We show that it is false in general, and that it becomes true under some mild assumptions, which include the finite case and the case of K4. We also prove that a Kripke frame (...) F is generated if and only if the dual algebra F* is s.i. The technical result is that A is s.i. when the set of points which generate the dual frame A* is not of zero measure. (shrink)

We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with (...) a metalinguistic link between assertions, and if its syntactic inference rules are obtained by solving that equation. All connectives of basic logic satisfy reflection. To the control of weakening and contraction of linear logic, basic logic adds a strict control of contexts, by requiring that all active formulae in all rules are isolated, that is visible. From visibility, cut-elimination follows. The full, geometric symmetry of basic logic induces known symmetries of its extensions, and adds a symmetry among them, producing the structure of a cube. (shrink)

Pretopologies were introduced in [S], and there shown to give a complete semantics for a propositional sequent calculus BL, here called basic linear logic, as well as for its extensions by structural rules,ex falso quodlibetor double negation. Immediately after Logic Colloquium '88, a conversation with Per Martin-Löf helped me to see how the pretopology semantics should be extended to predicate logic; the result now is a simple and fully constructive completeness proof for first order BL and virtually all its extensions, (...) including the usual, or structured, intuitionistic and classical logic. Such a proof clearly illustrates the fact that stronger set-theoretic principles and classical metalogic are necessary only when completeness is sought with respect to a special class of models, such as the usual two-valued models.To make the paper self-contained, I briefly review in §1 the definition of pretopologies; §2 deals with syntax and §3 with semantics. The completeness proof in §4, though similar in structure, is sensibly simpler than that in [S], and this is why it is given in detail. In §5 it is shown how little is needed to obtain completeness for extensions of BL in the same language. Finally, in §6 connections with proofs with respect to more traditional semantics are briefly investigated, and some open problems are put forward. (shrink)

Within the technical frame supplied by the algebraic variety of diagonalizable algebras, defined by R. Magari in [2], we prove the following: Let T be any first-order theory with a predicate Pr satisfying the canonical derivability conditions, including Löb's property. Then any formula in T built up from the propositional variables $q,p_{1},...,p_{n}$ , using logical connectives and the predicate Pr, has the same "fixed-points" relative to q (that is, formulas $\psi (p_{1},...,p_{n})$ for which for all $p_{1},...,p_{n}\vdash _{T}\phi (\psi (p_{1},...,p_{n}),p_{1},...,p_{n})\leftrightarrow \psi (...) (p_{1},...,p_{n})$ ) of a formula $\phi ^{\ast}$ of the same kind, obtained from φ in an effective way. Moreover, such $\phi ^{\ast}$ is provably equivalent to the formula obtained from φ substituting with $\phi ^{\ast}$ itself all the occurrences of q which are under Pr. In the particular case where q is always under Pr in φ, $\phi ^{\ast}$ is the unique (up to provable equivalence) "fixed-point" of φ. Since this result is proved only assuming Pr to be canonical, it can be deduced that Löb's property is, in a sense, equivalent to Gödel's diagonalization lemma. All the results are proved more generally in the intuitionistic case. (shrink)

Global properties of canonical derivability predicates in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, (...) interpolation and the fixed point theorem. (shrink)

Neste artigo, propõe-se uma leitura das categorias no tratado aristotélico homônimo como um primeiro esboço de uma ontologia regional, centrada nas substâncias sensíveis. Tendo por foco substância, quantidade, qualidade, relativo, agir e sofrer, este trabalho busca expor as duas estratégias principais que Aristóteles parece empregar para chegar a uma lista das categorias: (a) características básicas, cuja satisfação ou não satisfação de cada uma determina a natureza categorial de cada item e (b) a propriedade única que caracteriza cada categoria em contraste (...) com todas as outras. São, então, feitas considerações para vincular esse primeiro esboço ontológico a temas discutidos nos livros Lambda e Zeta da Metafísica, de modo a sugerir as direções principais que a sua ontologia nova (e geral) seguirá ao evoluir para uma teoria unificada da substância. (shrink)

The search for a synthesis between formalism and constructivism, and meditation on Gödel incompleteness, leads in a natural way to conceive mathematics as dynamic and plural, that is the result of a human achievement, rather than static and unique, that is given truth. This foundational attitude, called dynamic constructivism, has been adopted in the actual development of topology and revealed some deep structures that had remained hidden under other views. After motivations for and a brief introduction to dynamic constructivism, an (...) overview is given of the changes it induces in the practice of mathematics and in its foundation, and of the new results it allows to obtain. (shrink)

Martin-Löf Type Theory is both an important and practical formalization and a focus for a charismatic view of the foundations of mathematics. Per Martin-Löf's work has been of huge significance in the fields of logic and the foundations of mathematics, and has important applications in areas such as computing science and linguistics. This volume celebrates the twenty-fifth anniversary of the birth of the subject, and is an invaluable record both of areas of currentactivity and of the early development of the (...) subject. Also published for the first time is one of Per Martin-Löf's earliest papers. (shrink)

This essay will discuss how the Theory of Communicative Action incorporates the systemic complexification process and the Systems and Life World duality. Part of this process will be carried out with the discussion of communicative action, as a space for dialogue between people seeking understanding. The process of new forms of understanding and construction of knowledge is possible through the integrative structure of the lifeworld, such as semantic dimension, social space, and historical time. However, there is the other side, the (...) Systems, where the manifestations of crisis and disturbances, the pathologies of society, which in cultural reproduction appear as a loss of meaning of culture, loss of legitimacy of society and in personality, there is a crisis of belonging. (shrink)

This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Lof over the last twenty-five years.

The Oscar Wilde trials (1895) have usually been interpreted either as a historical document which gives insight into the regulation of sexuality in the late nineteenth century, or as literary biography explicating the playwright's life and works. Taking its cue from recent scholarship in ‘law and literature’, and also from Wilde's own conception of the relationship between art and life, this article proposes a reading of the trials which blurs the distinction between legal history and literary criticism by considering them (...) as a form of literature. It argues that the trial transcripts enact and reflect Wilde's vision of what literature is and how it should be read, and as such should be given a place amongst his literary works, alongside such aesthetic manifestos as ‘The Decay of Lying’ and ‘The Critic as Artist’. (shrink)

A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fields as Artificial Intelligence, Database Theory, Physics, and Philosophy. The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each (...) chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject. (shrink)

We introduce the notion of infinitary preorder and use it to obtain a predicative presentation of sup-lattices by generators and relations. The method is uniform in that it extends in a modular way to obtain a presentation of quantales, as “sup-lattices on monoids”, by using the notion of pretopology.Our presentation is then applied to frames, the link with Johnstone’s presentation of frames is spelled out, and his theorem on freely generated frames becomes a special case of our results on quantales.The (...) main motivation of this paper is to contribute to the development of formal topology. That is why all our definitions and proofs can be expressed within an intuitionistic and predicative foundation, like constructive type theory. (shrink)

Formal topology aims at developing general topology in intuitionistic and predicative mathematics. Many classical results of general topology have been already brought into the realm of constructive mathematics by using formal topology and also new light on basic topological notions was gained with this approach which allows distinction which are not expressible in classical topology. Here we give a systematic exposition of one of the main tools in formal topology: inductive generation. In fact, many formal topologies can be presented in (...) a predicative way by an inductive generation and thus their properties can be proved inductively. We show however that some natural complete Heyting algebra cannot be inductively defined. (shrink)

Debates on the moral status of human embryos have been highly and continuously controversial. For many, these controversies have turned into a fruitless scholastical endeavor. However, recent developments and insights in cellular biology have cast further doubt on one of the core points of dissent: the argument from potentiality. In this article we want to show in a nonscholastical way why this argument cannot possibly survive. Getting once more into the intricacies of status debates is a must in our eyes. (...) Not merely intellectual coherence but the standing and self-understanding of current stem cell research might profit from finally taking leave of the argument from potentiality. (shrink)

Across two studies, one of which was pre-registered, we find that a simple questionnaire that measures intellectual virtue and vice predicts how many fake news articles and conspiracy theories participants accept. This effect holds even when controlling for multiple demographic predictors, including age, household income, sex, education, ethnicity, political affiliation, religion, and news consumption. These results indicate that self-report is an adequate way to measure intellectual virtue and vice, which suggests that they are not fully immune to introspective awareness or (...) “stealthy” in the sense that Cassam (2015) argues. This is an important methodological result and may pave the way for future research on intellectual virtue and vice. (shrink)

This article gives a practice-based overview of the implementation aspects of Corporate Responsibility. After discussing the success factors for implementing Corporate Responsibility, the article describes a model for implementing Corporate Responsibility. Special attention is given to the success factors in the subsequent phases of implementation (sensitivity to the organizational environment, awareness of core values and clear leadership), to ensure that the most optimal results attainable for the organization can be reached. The implementation-model is clarified by looking at experiences in implementing (...) Corporate Responsibility at Chiquita. (shrink)

This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...) to define the deductive limit to this hierarchy, that is, its greatest lower deductive bound. The calculus $ \mathcal {C}$min, stronger than $ \mathcal {C}$$\scriptstyle \omega$, is first presented as a step toward this limit. As an alternative to the bivaluation semantics of $ \mathcal {C}$min presented thereupon, possible-translations semantics are then introduced and suggested as the standard technique both to give this calculus a more reasonable semantics and to derive some interesting properties about it. Possible-translations semantics are then used to provide both a semantics and a decision procedure for $ \mathcal {C}$Lim, the real deductive limit of da Costa's hierarchy. Possible-translations semantics also make it possible to characterize a precise sense of duality: as an example, $ \mathcal {D}$min is proposed as the dual to $ \mathcal {C}$min. (shrink)

We give arguments explaining why, when adopting a minimalist approach to constructive mathematics as that formalized in our two-level minimalist foundation, the choice for a pointfree approach to topology is not just a matter of convenience or mathematical elegance, but becomes compulsory. The main reason is that in our foundation real numbers, either as Dedekind cuts or as Cauchy sequences, do not form a set.

This article gives a practice-based overview of the implementation aspects of Corporate Responsibility. After discussing the success factors for implementing Corporate Responsibility, the article describes a model for implementing Corporate Responsibility. Special attention is given to the success factors in the subsequent phases of implementation (sensitivity to the organizational environment, awareness of core values and clear leadership), to ensure that the most optimal results attainable for the organization can be reached. The implementation-model is clarified by looking at experiences in implementing (...) Corporate Responsibility at Chiquita. (shrink)

We prove that the category of Nachbin’s compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we observe that the countable bound on the arity is the best possible: the category of compact ordered spaces is not dually equivalent to any variety of finitary algebras. Indeed, the following stronger results hold: the category of compact ordered spaces is not dually equivalent to any finitely accessible (...) category, any first-order definable class of structures, and any class of finitary algebras closed under products and subalgebras. An explicit equational axiomatisation of the dual of the category of compact ordered spaces is obtained; in fact, we provide a finite one, meaning that our description uses only finitely many function symbols and finitely many equational axioms. In preparation for the latter result, we establish a generalisation of a celebrated theorem by Mundici: our result—whose proof is independent of Mundici’s theorem—asserts that the category of unital commutative distributive lattice-ordered monoids is equivalent to the category of what we call MV-monoidal algebras.Abstract taken directly from the thesis.E-mail: marco[email protected]: https://air.unimi.it/retrieve/handle/2434/812809/1698986/phd_unimi_R11882.pdf. (shrink)

Heterogeneity of Being goes beyond the standard interpretations of Octavio Paz as a thinker of national identity and proposes a radical rethinking of the relationship between literature and philosophy. Dorfsman analyzes how Paz’s “tradition of rupture” properly displays a continuity between self and other, identity and difference, time and space.

From the early 1840s on, Jeremy Bentham’s utilitarian doctrine aroused the joint interest of Marx and Engels, who saw the English philosopher as one of the forerunners of socialism. Later, however, in the various editions (German, French, English) of Book 1 of Capital (1867/90), Bentham would be sarcastically branded by Marx as a “genius of bourgeois stupidity”. In their youth, both Engels and Marx had independently become interested in Bentham’s ideas, admiring some social-ethical themes, seen as heralding interesting developments for (...) the cause of the proletariat. On Engels’s suggestion, Marx included Bentham’s name, alongside those of the major 18th–19th century English and French exponents of protosocialism, in a planned Library of the most outstanding foreign socialist writers (1845), which however remained only a draft. From his first stay in England (1842/44), the young Engels had embraced in particular the famous utilitarian principle of “the greatest happiness of the greatest number” advocated by Bentham. Marx, on the other hand, after initially praising Bentham’s work, which he had read in a French translation during his exile in Paris (1844), harshly criticized the ambiguous implications of this principle. In fact, he believed thatbehind a misleading progressive façade, it constituted the philosophical equivalent of the later economic theory of labour productivity propounded by D. Ricardo in opposition to the theory of its mere quantitative extension put forward by A. Smith. In the London Manuscripts (1861/63) Marx will reveal the affinity betweenBentham’s principle of the happpiness of the greatest number of people, and Ricardo’s assumption of the ineliminable misery of the minority condemned to productive labour. Based on the collection of Marx’s and Engels’s texts (letters, drafts, notebooks, manuscripts, printed works), made available today thanks to the critical edition by MEGA1, this paper sets out to re-examine, im großen und ganzen, the main moments in their critique of Bentham’s Utilitarianism. (shrink)

Interest in _dream_ and _madness_, conceived as the loss of a world shared with others, and the individual’s entry into a private world governed by a personal logic unrelated to the waking state and to common feeling, recurs in at least three of Kant’s works: _Essay on the Diseases of the Head,_ (1764), _Dreams of a Spirit-Seer_ (1766), and _Anthropology from a Pragmatic Point of View_ (1798). Hegel too, from an early age, showed a strong fascination and a precocious interest (...) in psychopathological matters (states of altered consciousness, prophetic dreams, somnambulism, catalepsy, witchcraft etc.) to which he devoted intriguing reflections in various works from different periods: from the Berne Ms _Philosophy of Subjective Spirit_ (1794/95) to the _Phenomenology _(1807), from the _Philosophical __Propaedeutics_ (1808ff.) to the _Encyclopedia of the Philosophical Sciences_ (1830 3 ). Starting from the remarks of the two philosophers, this paper aims to underline the conceptual links between their thought and that of some renowned psychologists and psychiatrists of the 1800s-1900s (Pinel, Janet, Adler, James, Binswanger, Freud et al.). On the other hand, the paper also seeks to show – within the framework of an idea of _reason_ dating back to Heraclitus (about 544/483 B.C.) – some murky motifs, not always adequately emphasized in the past, found in the figurative and literary works of the late 1700s (e.g. Fuseli’s_ The Nightmare_, Coleridge’s _The Rhyme of the Ancient Mariner_, and, in particular, plate Nr. 43 of the _Caprichos _by Goya, _El sueño de la razón produce monstruos_), where there emerges a «dark side» of psychic activity emblematically described as the cryptic relationship between _dream_ and_ madness._. (shrink)

This novel contributed volume advances the current debate on free will by bridging the divide between analytic and historically oriented approaches to the problem. With thirteen chapters by leading academics in the field, the volume is divided into three parts: free will and determinism, free will and indeterminism, and free will and moral responsibility. The contributors aim to initiate a philosophical discourse that profits from a combination of the two approaches. On the one hand, the analytic tools familiar from the (...) debate – arguments, concepts, and distinctions – can be used to sharpen our understanding of classical philosophical positions. On the other hand, the rich philosophical tradition can be reconstructed so as to inspire new solutions. In recent years, the problem of free will has received special attention in the analytic arena. This is the first anthology to combine historical and analytic perspectives, significantly furthering the debate, and providing a crucial resource to academics and advanced students alike. (shrink)