The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is (...) in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information. (shrink)

This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones.

Aldo Antonelli offers a novel view on abstraction principles in order to solve a traditional tension between different requirements: that the claims of science be taken at face value, even when involving putative reference to mathematical entities; and that referents of mathematical terms are identified and their possible relations to other objects specified. In his view, abstraction principles provide representatives for equivalence classes of second-order entities that are available provided the first- and second-order domains are in the equilibrium dictated (...) by the abstraction principles, and whose choice is otherwise unconstrained.entities are the referents of abstraction terms: such referents are to an extent indeterminate, but we can still quantify over them, predicate identity or non-identity, etc. Our knowledge of them is limited, but still substantial: we know whatever has to be true no matter how the representatives are chosen, i.e., what is true in all models of the corresponding abstraction principles. This view is backed up by an “austere” conception of universals, according to which these are first-order objects, i.e., ways of collecting first-order objects. Antonelli thus claims that second-order logic does not import any novel ontological commitment beyond ontology of first-order, naturalistically acceptable, objects. Moreover, in the case of arithmetic, even if Hume’s Principle is construed as described above, Frege’s Theorem goes through unaffected, since there is nothing in its proof that depends on an account of the “true nature” of numbers. A viable construal of logicism is then given by the combination of semantic nominalism and a naturalistic conception of abstraction. [Editors note]. (shrink)

In this paper we show that the Gupta-Belnap systems S# and S* are П12. Since Kremer has independently established that they are П12-hard, this completely settles the problem of their complexity. The above-mentioned upper bound is established through a reduction to countable revision sequences that is inspired by, and makes use of a construction of McGee.

This article introduces and discusses the initial results of a survey focused on the contents, role and effectiveness of company codes of ethics. The article examines the contents of the codes of ethics of companies operating in the private sector in Italy, quoted on the Italian Stock Exchange (Standard& Poor/Mib-Milano Indice Borsa). The purpose of this investigation was to identify any correlations between sector characteristics and the contents of the codes of ethics, which would enable us to map out the (...) main principles followed in writing the companies' codes of ethics. The analysis was conducted in order to ascertain whether there were common factors deriving from the shared ethical questions faced by the companies operating in the same sector of activity. As the first step, the 40 companies were subdivided into three main economic categories -Industrial, Financial and Service. Then the contents of each code of ethics were evaluated and classified in accordance with different criteria. The main categories of classification were based on -general principles, social values, rules of conduct, relationships with third parties, implementation and sanctions. The next objective was to investigate whether these characteristics were due to the regulation of the sector of reference, the existence of sector benchmarks for best practice, or simply companies' voluntary stance on ethical issues. The main conclusions were that the codes of ethics of the Italian companies that we analysed do not seem to show relevant differences traceable to sector of activity, and their adoption is affected by several reasons other than intentionally ethical considerations. (shrink)

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance (...) of each. (shrink)

In line with earlier works, this article argues for a “continuist” interpretation of Brentano’s conception of intentionality. It maintains that Brentano’s conception of intentionality rests on a complex set of notions, which are reduced to a minimal core or applied more fully depending on the complexity of the mental phenomenon under consideration and perspective from which it is analyzed. The article positions this conceptual structure in relation to theories of objects developed within the framework of late- and Neo-Scholastic philosophy where, (...) since the psychic act can relate to its object in different ways, the different types and roles of objects must be distinguished. This theory of objects enables Brentano to reinterpret Aristoteles’s idea of the intentionality of mental phenomena in light of the commentaries and interpretations of Thomas Aquinas while also giving space to other medieval texts. (shrink)

The paper argues against the growing tendency to interpret Brentano’s conception of inner consciousness in self-representational terms. This trend has received support from the tendency to see Brentano as a forerunner of contemporary same-order theories of consciousness and from the view that Brentano models intransitive consciousness on transitive consciousness, such that a mental state is conscious insofar as it is aware of itself as an object. However, this reading fails to take into account the Brentanian concept of object, which is (...) ultimately derived from ancient and medieval philosophy, as well as the secondary, elusive character that Brentano attributes to inner perception. According to Brentano, we have an aspectual but transparent consciousness of transcendent objects, whereas our awareness of our own mental acts is always complete but incidental, and ultimately opaque. Reversing the relationship between intentionality and consciousness faces difficulties at the textual interpretative level, but also raises theoretical problems, for it risks treating Brentano’s theory of mind as a form of subjectivism and idealism. (shrink)

Kleene comincia la sezione §60 di Introduction to metamathematics considerando la questione se la matematica informale, e specialmente la teoria intuitiva dei numeri sia formalizzabile. Il classico teorema di G¨.

What kind of feeling is shame? Why are we ashamed and what are the consequences that this emotion has on the subject? Is it a private or a "social" emotion? How many types of shame exist? Is vicarious shame always shameful? What are the ways in which art has represented shame? What are the relations between shame, guilt, embarrassment and censorship? Is it possible to be immune to shame? Would "Not being ashamed" count as a virtue or is it a (...) morally reprehensible attitude? Sensibilia. Colloquium on Perception and Experience investigated the different ways in which shame can be described and staged, presupposed and understood. The proposals and the points of view collected in this volume relate in an original and interdisciplinary way different areas of research all equally interested in reflecting on a complex and stratified feeling. The result was a heated debate on (ancient and contemporary) inconvenient, thorny and "shameful" issues. (shrink)

Aggregation methods allow one to replace a large scale dynamical system (micro-system) by a reduced dynamical system (macro-system) governing a small number of global variables. This aggregation of variables can be performed when two time scales exist, a fast time scale and a slow time scale. Perturbation theory allows to obtain an approximated aggregated dynamical system which describes the behaviour of a few number of slow time varying variables which are constants of motion of the fast part of the micro-system. (...) Aggregation methods are applied to the case of the devastation of the great barrier reef by the starfishes. We recall the Antonelli/Kazarinoff model which implies a stable limit cycle for the corals and starfish populations. This prey-predator model describes the interactions between two species of corals and the starfish. Then, we generalize the Antonelli/Kazarinoff model to the case of two spatial patches with a fast part describing the starfish migration on the patches and the human manipulation of the communities by divers and, a slow part describing the growth and the interactions between the populations. We obtain an aggregated model governing the total coral densities on the patches and the total starfish population. This model can exhibit stable limit cycle oscillations and a Hopf bifurcation. The critical value of the bifurcation parameter is expressed in terms of the proportions of coral species and starfish on the two patches. This implies for example that rather than random killing of starfish by the Australian military, it may be better to send teams of divers to outbreaking reefs when they first occur who will then manipulate the community structure to increase protection. (shrink)

This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.

This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.

This book covers the basic guidelines of Vittorio Benussi’s research during the period at Graz and at Padua. It does so in the light of a thorough study of his Nachlass. The book re-evaluates Benussi’s work as a historical piece, and shows how his work is still relevant today, especially in the areas of cognitive psychology and cognitive science. The volume deals with this original and ingenious - though largely ignored - scholar and discusses his work as a leading experimental (...) psychologist. Benussi’s contributions as discussed in this book were particularly relevant in the fields of visual and tactile perception, time perception, forensic psychology, hypnosis and suggestion, unconscious, and emotions. His classical papers are impressive in their originality, energy, range of approaches, experimental skill, the wealth of findings, and the quality of theoretical discussions. This book demonstrates that Benussi was ahead of his time and that his themes, experiments and research programmes are highly relevant to contemporary cognitive psychology. (shrink)

La thèse de l’« inexistence intentionnelle » formulée par Brentano a été traditionnellement interprétée comme une théorie de la « relation intentionnelle », autrement dit de la relation entre l’acte mental et son « objet immanent » ou « intentionnel », c’est-à-dire interne à la conscience. Se fondant sur la lecture du fameux passage sur l’intentionnalité de la Psychologie du point de vue empirique , le présent article démontre que l’interprétation ontologique de la théorie de l’intentionnalité du premier Brentano est (...) insoutenable, toute dominante qu’elle est. Pour ce faire, nous partirons des sources de la pensée de Brentano, en particulier de la théorie de la perception et des relatifs d’Aristote, pour rejeter la conception de l’objet immanent ou intentionnel comme entité immanente à la conscience et mettre en évidence la continuité qui existe entre la première conception de Brentano de l’intentionnalité et la seconde, consécutive à ce qu’on définit comme le tournant réiste de sa pensée.Brentano’s thesis of “intentional inexistence” has been traditionally interpreted as a theory of “intentional relationships”, i.e., of the relation between a mental act and its “immanent” or “intentional object”, within consciousness. Starting from the famous passage on intentionality in Psychology from an Empirical Standpoint , the present paper shows that the dominant ontological interpretation of Brentano’s former theory of intentionality is untenable. Proceeding from the sources of Brentano’s thought, in particular from Aristotle’s theory of perception and of relatives, the conception of the immanent or intentional object as an immanent entity to consciousness is rejected. Instead, the continuity between Brentano’s former conception of intentionality and the subsequent one, following the so-called reistic turning-point in his thought, is highlighted. (shrink)

The purpose of this note is to present a simplification of the system of arithmetical axioms given in previous work; specifically, it is shown how the induction principle can in fact be obtained from the remaining axioms, without the need of explicit postulation. The argument might be of more general interest, beyond the specifics of the proposed axiomatization, as it highlights the interaction of the notion of Dedekind-finiteness and the induction principle.

Gian Aldo Antonelli and Cristina Bicchieri. Forward Induction.

Ausgehend von Franz Brentanos berühmter Intentionalitätspassage aus der Psychologie vom empirischen Standpunkt wird dargelegt, daß die vorherrschende ontologische Deutung seines sogenannten frühen Intentionalitätsgedankens unhaltbar ist. Unter Berücksichtigung von Brentanos Quellen, vor allem Aristoteles' Wahmehmungslehre und Theorie der Relativa, wird die Auffassung des sogenannten intentionalen bzw. immanenten Objektes als bewußtseinsimmanenter Entität abgelehnt und die Kontinuität hervorgehoben, die zwischen Brentanos früher und späterer, sogenannter reistischer Intentionalitätsauffassung besteht.

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician–philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically minded philosophers. Mathematical logic continues to play an important role in contemporary philosophy, and (...) mathematically trained philosophers continue to contribute to the literature in logic. For instance, modal logics were first investigated by philosophers and now have important applications in computer science and mathematical linguistics. (shrink)

Strategic interactions have been studied extensively in the area of judgment and decision-making. However, so far no specific measure of a decision-maker's ability to be successful in strategic interactions has been proposed and tested. Our contribution is the development of a measure of strategic ability that borrows from both game theory and psychology. Such measure is aimed at providing an estimation of the likelihood of success in many social activities that involve strategic interaction among multiple decision-makers. To construct a reliable (...) measure of strategic ability, that we propose to call ``Strategic Quotient'' (SQ), we designed a test where each item is a game and where, therefore, the individual score obtained depends on the distribution of choices of other decision-makers taking the test. The test is designed to provide information on the abilities related to two dimensions, mentalization and rationality, that we argue are crucial to strategic success, with each dimension being characterized by two main factors. Principal component analysis on preliminary data shows that indeed four factors (two for rationality, two for mentalization) account for strategic success in most of the strategically simpler games of the test. Moreover, two more strategically sophisticated games are inserted in the test and are used to investigate if and to what extent the four factors obtained by simpler games can predict strategic success in more sophisticated strategic interactions. Overall, the collected empirical evidence points to the possibility of building a SQ measure using only simple games designed to capture information about the four identified factors. (shrink)

A propositional system of modal logic is second-order if it contains quantifiers ∀p and ∃p, which, in the standard interpretation, are construed as ranging over sets of possible worlds (propositions). Most second-order systems of modal logic are highly intractable; for instance, when augmented with propositional quantifiers, K, B, T, K4 and S4 all become effectively equivalent to full second-order logic. An exception is S5, which, being interpretable in monadic second-order logic, is decidable.

This paper introduces a generalization of Reiter’s notion of “extension” for default logic. The main difference from the original version mainly lies in the way conflicts among defaults are handled: in particular, this notion of “general extension” allows defaults not explicitly triggered to pre-empt other defaults. A consequence of the adoption of such a notion of extension is that the collection of all the general extensions of a default theory turns out to have a nontrivial algebraic structure. This fact has (...) two major technical fall-outs: first, it turns out that every default theory has a general extension; second, general extensions allow one to define a well-behaved, skeptical relation of defeasible consequence for default theories, satisfying the principles of Reflexivity, Cut, and Cautious Monotonicity formulated by D. Gabbay. (shrink)

In this paper we offer an interpretation of the inner relationship between nihilism and the tragic. With reference to the work of Heinz von Foester and to the sciences of complexity, we will argue that the essential feature of the tragic is “autoreferentiality”. Furthermore, arguing in favor of the use of the theological notion of kenōsis as the most precise description of the “history of nihilism”, we will show that the latter is to be understood in terms of the “weakening”, (...) or lowering of all the reference points generated by autotranscendent, etheronomous, social phenomena. The consequence of nihilism is therefore autoreferentiality. This result will offer the opportunity to see both to what extent we are now, at the end of modernity, living a tragic situation and, eventually, to claim – by recalling that autoreferentiality is also the inner logic of freedom – that the tragic is the outcome of modernity, but not a necessary one. (shrink)

Résumé La section des Persikà consacrée à la vie d’Artoxerxès est en réalité l’histoire des exploits de Mégabyze, un aristocrate qui rivalise avec le roi pendant toute sa vie. L’analyse de la source nous amène à réfléchir sur les motivations qui poussèrent Ctésias à donner une grande importance à Mégabyze et en même temps nous renseigne sur certaines dynamiques historiques et politiques de l’histoire perse du milieu du V e siècle av. J. -C.

In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical construction due (...) to Kleene, and indicate how they can be employed to reconstruct the class of the general recursive functions. We also point at how Revision Rules can be employed to access non-minimal fixed points of partially defined computing procedures. (shrink)

The reflection elaborated in these pages, fleeing all submission to the now abused rhetoric of the prevailing economism, traces in the works of René Girard - the most serious pretender to the legacy of the masters of suspicion - and Jacques Derrida - the last great philosopher of the twentieth century - the constituent elements of a critical paradigm with which to interpret the present time. The volume investigates the multiple correspondences between the different legacies of deconstruction and the most (...) recent developments of mimetic theory through the articulated reconstruction of the reflections, still little known in Italy, of some of the most brilliant contemporary exponents of those traditions. Formulating the features of an ontology of actuality hinged on the notions of mimesis and trace, the author proposes a philosophical diagnosis that recognizes in our time an age in the grip of panic. (shrink)

In this paper we apply the idea of Revision Rules, originally developed within the framework of the theory of truth and later extended to a general mode of definition, to the analysis of the arithmetical hierarchy. This is also intended as an example of how ideas and tools from philosophical logic can provide a different perspective on mathematically more “respectable” entities. Revision Rules were first introduced by A. Gupta and N. Belnap as tools in the theory of truth, and they (...) have been further developed to provide the foundations for a general theory of (possibly circular) definitions. Revision Rules are non-monotonic inductive operators that are iterated into the transfinite beginning with some given “bootstrapper” or “initial guess.” Since their iteration need not give rise to an increasing sequence, Revision Rules require a particular kind of operation of “passage to the limit,” which is a variation on the idea of the inferior limit of a sequence. We then define a sequence of sets of strictly increasing arithmetical complexity, and provide a representation of these sets by means of an operator G(x, φ) whose “revision” is carried out over ω2 beginning with any total function satisfying certain relatively simple conditions. Even this relatively simple constraint is later lifted, in a theorem whose proof is due to Anil Gupta. (shrink)

Spécialiste de la littérature britannique du long dix-huitième siècle, de l’histoire littéraire des femmes et de critique féministe, Jane Spencer nous livre ici un ouvrage qui met les animaux et l’animalité au cœur de la littérature de l’époque dite « des révolutions ». Au moins trois axes de recherche se croisent dans Writing About Animals in the Age of Revolution : un premier, visant à comprendre le rôle joué par les animaux dans la littérature britannique entre la deuxième moitié du (...) xviiie... (shrink)