The variety of residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some (...) parts of the theory of join-completions of residuated \-groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices. (shrink)

In this paper, we aim at highlighting the significance of the A- and B-properties introduced by Finch (Bull Aust Math Soc 2:57–62, 1970b). These conditions turn out to capture interesting structural features of lattices of closed subspaces of complete inner vector spaces. Moreover, we generalise them to the context of effect algebras, establishing a novel connection between quantum structures (orthomodular posets, orthoalgebras, effect algebras) arising from the logico-algebraic approach to quantum mechanics.

Beaucoup de « géomètres » du XIXe siècle - Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, et autres - ont joué un rôle important dans la discussion sur les fondements des mathématiques. Mais, contrairement aux idées d'Euclide, ils n'ont pas identifié «l'espace physique» avec« l'espace de nos sens». Partant de notre expérience dans l'espace, ils ont cherché à identifier les propriétés les plus importantes de l'espace et les ont posées à (...) la base de la géométrie. C'est sur la connaissance active de l'espace que les axiomes de la géométrie ont été élaborés ; ils ne pouvaient donc pas être a priori comme ils le sont dans la philosophie kantienne. En outre, pendant la dernière décade du siècle, certains mathématiciens italiens - De Paolis, Gino Fano, Pieri, et autres - ont fondé le concept de nombre sur la géométrie, en employant des résultats de la géométrie projective. Ainsi, on fondait l'arithmétique sur la géométrie et non l'inverse, comme David Hilbert a cherché à faire quelques années après, sans succès. (shrink)

We introduce Boolean-like algebras of dimension n ($$n{\mathrm {BA}}$$ n BA s) having n constants $${{{\mathsf {e}}}}_1,\ldots,{{{\mathsf {e}}}}_n$$ e 1, …, e n, and an $$(n+1)$$ ( n + 1 ) -ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of $$n{\mathrm {BA}}$$ n BA s share many remarkable properties with the variety of Boolean algebras and with primal varieties. The $$n{\mathrm {BA}}$$ n BA s provide the (...) algebraic framework for generalising the classical propositional calculus to the case of n–perfectly symmetric–truth-values. Every finite-valued tabular logic can be embedded into such a n-valued propositional logic, $$n{\mathrm {CL}}$$ n CL, and this embedding preserves validity. We define a confluent and terminating first-order rewriting system for deciding validity in $$n{\mathrm {CL}}$$ n CL, and, via the embeddings, in all the finite tabular logics. (shrink)

In recent research, some of the present authors introduced the concept of an $n$-dimensional Boolean algebra and its corresponding propositional logic $n\textrm{CL}$, generalizing the Boolean propositional calculus to $n\geq 2$ perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for $n\textrm{CL}$, named $n\textrm{LK}$. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that $n\textrm{LK}$ enjoys the cut admissibility property. The latter relies on the generalization to the $n$-ary case (...) of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters. (shrink)

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present paper. We especially focus on quasivarieties whose generators either are subalgebras of the standard square quasi-MV algebra S , or can be obtained therefrom (...) through the addition of some fixpoints for the inverse. (shrink)

Biological and Cultural Bases of Human Inference addresses the interface between social science and cognitive science. In this volume, Viale and colleagues explore which human social cognitive powers evolve naturally and which are influenced by culture. Updating the debate between innatism and culturalism regarding human cognitive abilities, this book represents a much-needed articulation of these diverse bases of cognition. Chapters throughout the book provide social science and philosophical reflections, in addition to the perspective of evolutionary theory and the central assumptions (...) of cognitive science. The overall approach of the text is based on three complementary levels: adult performance, cognitive development, and cultural history and prehistory. Scholars from several disciplines contribute to this volume, including researchers in cognitive, developmental, social and evolutionary psychology, neuropsychology, cognitive anthropology, epistemology, and philosophy of mind. This contemporary, important collection appeals to researchers in the fields of cognitive, social, developmental, and evolutionary psychology and will prove valuable to researchers in the decision sciences. (shrink)

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

In the present paper we continue the investigation of the lattice of subvarieties of the variety of √′ P quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same (...) variety. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

This is an excerpt from the contentThe reasons that drive individuals to develop new technologies and to disseminate them in new products and processes, and the capacity to develop original solutions to technological problems, can be analysed with the concepts typical of individual and social cognitive psychology. Various aspects of cognitive activity address innovation. In particular, the capacity to grasp the latent questions and needs of the market that lies behind the possibility to identify opportunities for new products or services; (...) the means of generating solutions that can respond effectively to the realisation of these new opportunities; problem solving processes in the identification of new procedures that underpin process inventions and new manufacturing techniques; the risk of innovative behaviour and the contexts that can favour a greater or lesser propensity to develop innovative solutions. The best historical example of the two stages of the identification of the problem/opportunity and the generation of. (shrink)

The widespread use of brain imaging techniques encourages conceiving of neuroscience as the forthcoming “mindscience.” Perhaps surprisingly for many, this conclusion is still largely unwarranted. The present paper surveys various shortcomings of neuroscience as a putative “mindscience.” The analysis shows that the scope of mind (both cognitive and phenomenal) falls outside that of neuroscience. Of course, such a conclusion does not endorse any metaphysical or antiscientific stance as to the nature of the mind. Rather, it challenges a series of assumptions (...) that the undeniable success of neuroscience has fostered. In fact, physicalism is here taken as the only viable ontological framework – an assumption that does not imply that the central nervous system exhausts the physical domain. (shrink)

What is the role of education in a world where we no longer have a clear vision of the future and where the idea of a single, universal model of humanity seems like the residue of a bygone age? What role should educators play in a world where young people find themselves faced with deep uncertainty about their future, where the prospects of securing a stable, long-term career seem increasingly remote and where intensified population movements have created more diverse communities (...) in which different cultures find themselves living side by side, no longer bound together by the belief that the other would eventually be assimilated into ‘our' culture? Faced with the bewildering features of our liquid modern world, many young people are inclined to withdraw - in some cases into the online world of games and virtual relationships, in other cases into anorexia, depression, alcohol or even drug abuse, hoping to find shelter from a world perceived as more and more dangerous. Others launch into more violent forms of behaviour, like street gangs and the looting carried out by young people who have been excluded from the temples of consumption but are eager to participate in the ceremony. And all this happens while our politicians look on, uncomprehending and indifferent. In this short book Zygmunt Bauman - the leading social theorist of our liquid modern world, here in conversation with Riccardo Mazzeo - reflects on the predicament of young people today and on the role of education and the educator in a world where the certainties of our predecessors can no longer be taken for granted. (shrink)

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.

We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...) where such logics respectively correspond to: i) Meyer and Slaney’s Abelian logic [31]; ii) Galli et al.’s logic of equilibrium [21]; iii) a new logic of “preservation of truth degrees”. (shrink)

Any attempt to understand the meaning of Charles Sanders Peirce’s philosophy must necessarily involve the study of his maxim of pragmatism, first formulated in 1878. The maxim is the basis for Peirce’s pragmatism, and its development is a fundamental thread that allows the overall meaning of his system to be grasped. Furthermore, the maxim cannot be separated from the entire body of Peirce’s speculations. In his 2020 paper, Jon Alan Schmidt compiled a rich chronological list of passages that show how (...) Peirce reworked the maxim. We intend to supplement Schmidt’s paper with an analysis that examines the various stages of the maxim’s theoretical development in a chronological order. Furthermore, we will propose a contextualisation of the intrinsic meaning of the maxim and its use within Peirce’s philosophical system. (shrink)

Gupta has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements to the (...) revision-theoretic framework. We prove that there is a precise equivalence between trembling-hand perfect equilibria in two-player normal games and a revision-theoretic property. We then introduce lexicographic choice of action as a way to represent players’ expectations, which allows our analysis to reach full generality. Finally, we provide an example of the versatility of revision theory as applied to strategic interaction by formalizing a risk-and-compensation procedure of strategic choice in the revision-theoretic framework. (shrink)

The author outlines one form of analytical legal realism as the junction of three main theses. According to its first main thesis, interpretive sentences in legal discourse are ascriptive sentences with no cognitive function. According to the second thesis, the law is the set of norms in force, i.e. the norms actually applied in the past and predictably applied in the future by law-applying agencies. The third thesis is that legal science as a cognitive activity must not be confused with (...) legal scholarship. Although legal scholars do engage in cognitive activities, their work mainly consists in non-cognitive activities such as interpretation and legal construction. | An earlier version of this statement was published in Revus 19 in Italian, French, and Croatian. (shrink)

Es innegable que la noción de epoché fue crucial para el surgimiento y el posterior desarrollo de la tradición fenomenológica. Si bien la resignificación que Husserl hace de ésta es sumamente original, él mismo se detiene a reconocer en la filosofía antigua el mérito de haber encontrado el camino idóneo para acceder a la subjetividad trascendental. En el siguiente trabajo buscaré, por un lado, definir la epoché tal como se origina en el pensamiento de los sofistas para luego pasar a (...) analizar el modo en el que Husserl logra reversionar dicha noción hasta convertirla en el método predilecto que nos permite arribar a la esfera trascendental. Por otro lado, continuaré rastreando la evolución de la epoché para llegar a su abandono en la filosofía de Sartre. En relación con esto último, me interesa preguntarme si el existencialismo reniega de la suspensión del juicio por considerarla inapropiada o si, más bien, se trata de una supresión parcial del método fenomenológico. Me propongo defender esta segunda tesis, alegando que, en realidad, la epoché no es una noción que esté totalmente ausente en la filosofía de Sartre sino que se mantiene vigente en términos de angustia existencial. (shrink)

I present a view of conscious perception that supposes a processual unity between the activity in the brain and the perceived event in the external world. I use the rainbow to provide a first example, and subsequently extend the same rationale to more complex examples such as perception of objects, faces and movements. I use a process-based approach as an explanation of ordinary perception and other variants, such as illusions, memory, dreams and mental imagery. This approach provides new insights into (...) the problem of conscious representation and phenomenal consciousness. It is a form of anti- cranialism different from but related to other kinds of externalism. (shrink)

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

This study investigates interpersonal processes underlying dialog by comparing two approaches, interactive alignment and interpersonal synergy, and assesses how they predict collective performance in a joint task. While the interactive alignment approach highlights imitative patterns between interlocutors, the synergy approach points to structural organization at the level of the interaction—such as complementary patterns straddling speech turns and interlocutors. We develop a general, quantitative method to assess lexical, prosodic, and speech/pause patterns related to the two approaches and their impact on collective (...) performance in a corpus of task-oriented conversations. The results show statistical presence of patterns relevant for both approaches. However, synergetic aspects of dialog provide the best statistical predictors of collective performance and adding aspects of the alignment approach does not improve the model. This suggests that structural organization at the level of the interaction plays a crucial role in task-oriented conversations, possibly constraining and integrating processes related to alignment. (shrink)

We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ($$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: $$\textrm{CHL}$$ CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for $$\textrm{CHL}$$ CHL ; moreover, we (...) suggest a possible computational interpretation of its connexive conditional, and we revisit Kapsner’s idea of superconnexivity. (shrink)

The author discusses a number of issues in the theory of legal sources. The first topic is whether sources should be conceived of as acts or texts. The alternatives are connected with two competing theories of legal interpretation (viz., the cognitive theory and the sceptical theory), which entail different concepts of legal rules and law‐making. The second topic is whether a “formal” or a “material” criterion of recognition of sources should be preferred. The third section is devoted to the analysis (...) of rules of change. Four theories of rules of change are discussed, and five kinds of such rules are distinguished. The fourth section concerns judicial law‐making, with special reference to the creation of new legal rules by constitutional courts. (shrink)

We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition (...) implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to [22], in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON. (shrink)

If Unamuno had been able to choose how to be remembered, he would have wanted him to be a poet. This book wants to do justice to that happy possibility. But above all because Unamuno was a poet in the highest sense: he was while writing the same essay as a novel, or theater, letter or verse, and he was also a poet when he passionately lived all the facets of his intense existence. His intellectual work was poetic and his (...) personal relationships, as well as his political activity, also responded to that peculiar Unamunian aesthetic in which the vital horizon is inescapably confused with the tasks of thought." --Translated from back cover. (shrink)

Anger is probably one of the mostly debated basic emotions, owing to difficulties in detecting its appearance during development, its functional and affective meaning (is it a positive or a negative emotion?), especially in human beings. Behaviors accompanied by anger and rage serve many different purposes and the nuances of aggressive behaviors are often defined by the symbolic and cultural framework and social contexts. Nonetheless, recent advances in neuroscientific and developmental research, as well as clinical psychodynamic investigation, afford a new (...) view on the role of anger in informing and guiding many aspects of human conducts. Developmental studies have confirmed the psychophysiological, cognitive and social acquisition that hesitate in the pre-determined sequence appearance of anger and rage in the first two years of life. The so-called affective neurosciences have shown the phylogenetic origin of the two circuits underlying the emergence of anger along with its evolutionary role for promoting survival. This view has been integrated by the psychodynamic theory of motivational systems that attribute a double role to anger: on the one hand, this affect works as an inwardly directed signal concerning a pressure to overcome an obstacle or an aversive situation; on the other hand, anger is also an outwardly directed communicative signal establishing differentiation and conflict within interpersonal relationships and affective bonds. Of course, human peculiar mental functioning requires the appraisal of such signals by higher cortical functions and, there is little doubt that the meaning that orientates individual behaviors is, eventually, construed on a social and cultural level. At the same time, everyday life experiences as well as clinical insights into psychopathic, narcissistic and borderline personality pathology clearly illustrate the necessity to correctly interpret and give answers to the basic questions raised around the topic of anger as a basic emotion. (shrink)

INDICE -/- Note biografiche Introduzione, di Riccardo Faucci -/- Parte I - Da Verri a Toniolo 1. Jeremy Bentham: Contemporary Interpretations, di M.D.A. Freeman 2. Su Helvétius, Beccaria e Bentham, di Letizia Gianformaggio 3. L'etica utilitaristica di Pietro Veti, di Vincenzo Polignano 4. ll liberismo interventista di Vincenzo Emanuele Sergio, di Anna Li Donni 5. Il concetto di " felicità pubblica, nella << Genesi del diritto penale » di Romagnosi, e il rapporto Romagnosi-Bentham, di Robertino Ghiringhelli 6. « La (...) più grande felicità per il maggior numero » all'Accademia dei Georgofili ( 18)0-1850), di Gabriella Gioli 7. Una nota su Manzoni critico dell'utilitarismo, di Maurizio Mori 8. Sul concetto di utile in Francesco Ferrara e in Maffeo Pantaleoni, di Daniela Parisi Acquaviva 9. Sul pensiero sociale cristiano di fronte all'edonismo, di Luciano Avagliano 10. Giuseppe Toniolo e il recupero cattolico dell'utile e del valore, di Anna Camaiti -/- Parte II Aspetti di storia del pensiero economico nell’età classica -/- 1. La filosofia economica di Thomas Hobbes, di Marco Bertozzi 2. Ordinamento del sapere, modelli metodologici ed economia politica in Adam Smith, di Sergio Cremaschi 3. Elementi classici nel pensiero di Adam Smith: giurisprudenza romana e morale stoica, di Gloria Vivenza 4. Il “lusso” negli economisti italiani del Settecento, di Cosimo Perrotta 5. Prezzi naturali, prezzi di mercato e legge degli sbocchi nel dibattito fra Malthus e Ricardo, di Lilia Costabile 6. Marx e la moneta, di Roberto Petrini -/- . (shrink)

The manuscript UCLA 170/624 contains Galileo’s proof of the center of gravity of the frustum of a cone, which was ultimately published as Theoremata circa centrum gravitatis solidorum in Discorsi e dimostrazioni matematiche intorno a due nuove scienze. The UCLA copy opens the possibility of giving a fuller account of Theoremata dating and development, and it can shed light on the origins of this research by the young Galileo. A comparison of the UCLA manuscript with the other extant copies is (...) carried out to propose a new dating for the composition of the Theoremata. This dating will then be reconsidered in light of the mathematical content. The paper ends with a complete description of the content of the UCLA manuscript and the edition of Galileo’s text there contained. (shrink)

: Traditional mind-body identity theories maintain that consciousness is identical with neural activity. Consider an alternative identity theory – namely, a mind-object identity theory of consciousness. I suggest to take into consideration whether one’s consciousness might be identical with the external object. The hypothesis is that, when I perceive a yellow banana, the thing that is one and the same with my consciousness of the yellow banana is the very yellow banana one can grab and eat, rather than the neural (...) processes triggered by the banana. The bottom line is that one’s conscious experience of an object is the object one experiences. First, I outline the main hypothesis and the relation between mind, body, and object. Eventually, I address a series of traditional obstacles such as hallucinations, illusions, and commonsensical assumptions. Keywords: Identity Theory; Mind/Body Problem; Consciousness; Hallucinations; Illusions Le esperienze sono oggetti. Verso una teoria dell’identità della mente in quanto oggetto Riassunto: Le teorie dell’identità tra mente e corpo di tipo tradizionale hanno affermato una relazione di identità tra coscienza e attività neurale. Si consideri una teoria dell’identità di carattere alternativo – propriamente una teoria dell’identità che intenda la coscienza come un oggetto. Suggerisco di considerare la possibilità che la coscienza di qualcuno possa essere trattata come identica a un oggetto del mondo esterno. Sulla base di questa ipotesi, quando percepisco una banana gialla, ciò che coincide con la mia coscienza della banana gialla è proprio la banana gialla che si può prendere e mangiare, piuttosto che il processo neurale innescato dalla banana. In definitiva l’esperienza cosciente di un oggetto che ciascuno ha è l’oggetto che si esperisce. In una prima parte, procederò con il delineare l’ipotesi principale e la relazione tra mente, corpo e oggetto. Successivamente cercherò di risolvere alcuni problemi di tipo tradizionale, quali le allucinazioni, le illusioni e gli assunti di senso comune. Parole chiave: Teoria dell’identità; Problema mente/corpo; Coscienza; Allucinazioni; Illusioni. (shrink)

Prevention is a pervasive phenomenon. It is about blocking an effect before it happens or stopping it as it unfolds: vaccines prevent (the unfolding of) diseases; seat belts prevent events causing serious injuries; circuit breaks prevent the manifestation of overcurrents. Many disciplines in the information sciences deal with modeling and reasoning about prevention. Examples include risk and security management as well as medical and legal informatics. Having a proper conceptualization of this phenomenon is crucial for devising proper modeling mechanisms and (...) tools to support these disciplines. Forming such a conceptualization is a matter of Formal Ontology. In fact, prevention and related notions have become a topic of interest in this area. In this paper, with the support of Unified Foundational Ontology (UFO), we conduct an ontological analysis of this and other related notions, namely, the notions of countermeasures and countermeasure mechanisms, including the notion of antidotes. As a result of this conceptual clarification process, we propose an ontology-based reusable module extending UFO and capturing the relations between these elements. Finally, we employ this module to address a few cases in risk management. (shrink)

Avicenna is the most influential figure in the intellectual history of the Islamic world. This book is the first comprehensive study of his theory of science, which profoundly shaped his philosophical method and indirectly influenced philosophers and theologians not only in the Islamic world but also throughout Christian Europe and the medieval Jewish tradition. A sophisticated interpreter of Aristotle’s _Posterior Analytics_, Avicenna took on the ambitious task of reorganizing Aristotelian philosophy of science into an applicable model of scientific reasoning, striving (...) to identify conditions of certainty for scientific assertions and conditions of adequacy for real definitions. Riccardo Strobino combines philosophical and textual analysis to explore the scope and nature of Avicenna’s contributions to the logic of scientific reasoning in his effort to recalibrate Aristotle’s model and overcome some of its internal limitations. Focusing on a broad array of philosophical innovations at the intersection of logic, metaphysics, and epistemology, this book casts light on an essential aspect of the thought of the preeminent philosopher and physician of the Islamic world. (shrink)

The paper provides some introductory comments and a preliminary translation of Avicenna’s Burhān, IV, 2. I shall first set the stage by outlining the structure of the book (sec. 1). I will then briefly introduce (sec. 2) a number of notions that are dealt with in the first treatise of the Burhān (e.g. definition, description). Burhān, IV, 2 is split into two parts: the first focuses mainly on Aristotle’s An. Post., B, 4, whereas the second covers some of the topics (...) of B, 5 and B, 6. Accordingly, sec. 3 will be devoted to a cursory presentation of Aristotle’s arguments in An. Post., B, 4 along with a more detailed discussion of its Avicennan counterpart, focusing on the indemonstrability of definition; sec. 4, finally, will be a presentation of the second part of the chapter, concerning the relationship between definition and division. An English translation of the entire chapter is appended to the paper and is accompanied by some notes. (shrink)

Topics in Cognitive Science, Volume 14, Issue 2, Page 327-343, April 2022.

Strict-Tolerant Logic ($$\textrm{ST}$$ ST ) underpins naïve theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical sequent calculus without Cut is sometimes advocated as an appropriate proof-theoretic presentation of $$\textrm{ST}$$ ST. Unfortunately, there is only a partial correspondence between its derivability relation and the relation of local metainferential $$\textrm{ST}$$ ST -validity – these relations coincide only upon the addition of elimination rules and only within (...) the propositional fragment of the calculus, due to the non-invertibility of the quantifier rules. In this paper, we present two calculi for first-order $$\textrm{ST}$$ ST with an eye to recapturing this correspondence in full. The first calculus is close in spirit to the Epsilon calculus. The other calculus includes rules for the discharge of sequent-assumptions; moreover, it is normalisable and admits interpolation. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...) and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

What is the conscious mind? What is experience? In 1968, David Armstrong asked “What is a man?” and replied that a man is “a certain sort of material object”. This book starts from his question but proceeds along a different path. The traditional mind-brain identity theory is set aside, and a mind-object identity theory is proposed in its place: to be conscious of an object is simply to be made of that object. Consciousness is physical but not neural. This groundbreaking (...) hypothesis is supported by recent empirical findings in both perception and neuroscience, and is herein tested against a series of objections of both conceptual and empirical nature: the traditional mind-brain identity arguments from illusion, hallucinations, dreams, and mental imagery. The theory is then compared with existing externalist approaches including disjunctivism, realism, embodied cognition, enactivism, and the extended mind. Can experience and objects be one and the same? (shrink)