The ongoing process of revising and rethinking the foundations of economic theory leads to great complexities and contradictions at the heart of economics. ‘Economics of innovation’ provides a fertile challenge to standard economics, and one that can help it overcome its many criticisms. This authoritative book from Cristiano Antonelli provides a systematic account of recent advances in the economics of innovation. By integrating this account with the economics of technological change, this exceptional book elaborates an understanding of the (...) effects of the introduction of new technologies. This excellent, comprehensive account from respected expert Antonelli will be much appreciated within the innovation economics community, yet it is also a book that should be read by all those with either a private or professional interest in economic theory. (shrink)

El concepto de "inmanencia" ha adquirido una creciente relevancia en el campo filosófico contemporáneo. Dos destacados pensadores franceses, Gilles Deleuze y Franfois Jullien, le han otorgado un lugar fundamental en sus investigaciones. El propósito de este artículo es indagar el diálogo, poco explorado aún, entre ambos autores. Nuestra hipótesis de trabajo propone los siguientes ejes de análisis: primero, comparamos los usos de la expresión "absolutización de la inmanencia", acuñada por el sinólogo a fin de relativizar la trascendencia en el pensamiento (...) chino y luego empleada por Deleuze en el marco de la creencia en este mundo. En segundo lugar, examinamos las críticas que Jullien le dirige a Deleuze respecto a la relación entre la filosofía y la sabiduría. En tercer lugar, confrontamos sus perspectivas divergentes sobre la inmanencia en tanto "plano" (Deleuze) y como "fondo" (Jullien). Finalmente, ponemos de manifiesto la dificultad presente en ambos autores para pensar la idea de inmanencia. The concept of "immanence" has acquired substantial relevance within the contemporary philosophical field. Two influential french thinkers, Gilles Deleuze and Franfois Jullien, have conferred this concept a fundamental standing in their research. The purpose of this work is to explore the dialogue between both authors as this exploration has not been concluded. Our hypothesis puts forward the following axes of analysis. First, we shall compare the usage of the expression "absolutization of immanence" coined by the sinologist in order to put in perspective the idea of transcendence in Chinese thought. This expression was then applied by Deleuze within the frame of the belief in this world. Second, we shall examine Jullien's critique of Deleuze concerning the relationship between Philosophy and Wisdom. Third, we shall confront the divergent perspectives on immanence: as "plane" (Deleuze) and as "buttom" (Jullien). Finally, we shall show the difficulty to ponder the idea of immanence in both authors. (shrink)

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)

Frege's logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the "neologicist" approach of Hale and Wright. Less attention has been given to Frege's extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of (...) a concept C, together with extra-logical axioms governing such a predicate, and show that arithmetic can be obtained in such a framework. As a philosophical payoff, we investigate the status of the so-called Hume's Principle and its connections to the root of the contradiction in Frege's system. (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 proposes a cost-benefit analysis of argumentation, with the aim of highlighting the strategic considerations that govern the agent's decision to argue or not. In spite of its paramount importance, the topic of argumentative decision-making has not received substantial attention in argumentation theories so far. We offer an explanation for this lack of consideration and propose a tripartite taxonomy and detailed description of the strategic reasons considered by arguers in their decision-making: benefits, costs, and dangers. We insist that the (...) implications of acknowledging the strategic dimension of arguing are far-reaching, including promising insights on how to develop better argumentation technologies. (shrink)

While second-order quantifiers have long been known to admit nonstandard, or interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretationgeneral” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.

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)

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)

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.

The general aim of this work is to show the importance of the adressee's mind as planned by the author of a speech act or of a norm; in particular, how important are the expected motivations for goal adoption. We show that speech acts differ from one another for the different motivations the speaker is attempting to obtain from the hearer. The description of the participants' social positions is not sufficient. Important conflicts can arise which are not relative to what (...) to do, but to the different motives requested by the speaker. This view is applied to norms, pointing out that what is required by a norm is not only a behaviour but also a mental attitude, and that the prescribed mind might be even more important than the prescribed behaviour. Norms don't want just behavioural conformity, but also that this conformity implies an acknowledgement and a reinforcement of both the authority and the norm itself. Norms ask for submission. Any form of norm is aimed at influencing the addressee by changing his or her mind. (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.

Girard’s attempts to present his main ideas have been numerous and, according to himself, never fully satisfying: many problems arise when looking for the best way to explain what Mimetic Theory is about, mainly because the order of the discourse and the logic of the underlying long argument, just as the micro level of the analysis and the macro one, are twisted with one another in a hermeneutical circle that can easily be misinterpreted as vicious. A thorough work of analysis (...) of the essential logical features of Mimetic Theory main hypotheses has been done by Jean–Pierre Dupuy. In what follows, we are going to use a few of his concepts in order to set the analysis of secularization and modernity and their consequences both at a micro level, dealing with modern pathologies, and at the macro one, investigating the displacement of the sacred. (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)

One might well wonder about the source of Girard’s knowledge. Where is it thought to have come from in the first place? From what vantage point are we supposed to be surveying the events he claims are originary? And what, then, is the condition for the very possibility of his Christian wisdom? In this paper, I argue that we can put forward a tentative solution by looking at one particular aspect of all the texts that Girard has interpreted: they are (...) all written texts. Analyzing this in detail with the assistance of the proposals of Bernard Stiegler, I will claim that it is writing itself that has afforded us the possibility of paying attention. Moreover, in the second section, I shall also put forward an analysis of the gnoseological condition of the possibility of Christian wisdom. To do so, I expand on Stiegler’s reading of Kant’s notion of schema focusing on its relation with the hermeneutical notion of figura, as presented by Erich Auerbach. Commenting on the common rhetorical setting of both the Critique of Pure Reason and the Bible, I then show that these two written texts address a very similar problem—a critique of the way people judge—and also put forward, surprisingly, much the same solution: to properly judge, it would be better to take into account past examples of judgments and consider that, no matter whether we critique them or not, they will schematize our own experiences and influence our intentionality. (shrink)

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)

Neste texto apresentamos considerações sobre o agendamento midiático-esportivo realizado em relação aos Jogos Pan-americanos Rio/2007, enfatizando aspectos teórico-conceituais da teoria do agendamento (agenda-setting), bem como evidenciando algumas estratégias utilizadas pela mídia no tocante ao evento, como a utilização de elementos da identidade nacional e a figura dos ídolos esportivos.

Butler’s idea of evolution was developed over the publication of four books, several articles and essays between 1863 and 1890. These publications, although never achieving the success expected by Butler, proposed a psychological elaboration of evolution, called ‘unconscious memory’. This was strongly in contrast with the materialistic approach suggested by Darwin’s natural selection. Starting with a historical introduction, this paper aspires to ascertain the logic, meaning and significance of Butler’s idea of ‘unconscious memory’ in the post-Darwinian physiological and psychological Pan-European (...) discussion. Particular attention is devoted to demonstrating that Butler was not only a populariser of science but also an active protagonist in the late Victorian psychological debate. (shrink)

The decolonial theory understands that Western Modernity keeps imposing itself through a triple mutually reinforcing and shaping imprisonment: coloniality of power, coloniality of knowledge, and coloniality of being. Technical design has an essential role in either maintaining or overcoming coloniality. In this article, two main approaches to decolonizing the technical design are presented. First is Yuk Hui’s and Ahmed Ansari’s proposals that, revisiting or recovering the different histories and philosophies of technology produced by humankind, intend to decolonize the minds of (...) philosophers and engineers/architects/designers as a pre-condition for such decolonial designs to take place. I call them top-down approaches. Second is some technical design initiatives that, being developed alongside marginalized/subalternate people, intend to co-construct decolonial sociotechnical solutions through a committed, decolonizing, and careful dialog of knowledge. I call them bottom-up approaches. Once that is done, the article’s second half derives ontological, epistemological, and political consequences from the conjugation of top-down and bottom-up approaches. Such consequences challenge some established or not yet entirely overcome understandings in the philosophy of technology and, in so doing, are meant to represent some steps in PT’s decolonization. Even though both top-down and bottom-up approaches are considered, the article’s main contributions are associated with decolonial technical design practices, whose methodologies and outcomes are important study cases for PT and whose practitioners can be taken as inspiring examples for philosophers who want to decolonize/enlarge PT or make it decolonial. (shrink)

Recovering an ancient debate on the meaning of the Latin word pomoerium, I will show that if John Searle has offered the standard version of social ontology, Maurizio Ferraris has good reasons to claim that his ‘Theory of Documentality’ can go further. Nonetheless, his anti-post-modernism and his blindness about the religious origins of the social objects he deals with, reduce the width of his argument. Complementing his hasty analysis of mimesis with the mimetic theory of religion, violence and the sacred, (...) put forward by René Girard, I will try to show that social objects always hide a scapegoating event and not just a document, as Ferraris would say. Recovering the underlying Derridean paradigm and adding a Girardian reading, such an investigation would turn Ferraris’ static and insufficient analysis into a dynamic ontology of actuality. Thus my aims are: 1) to verify to what extend Ferraris’ theory holds ground, 2) point out, through the application of mimetic theory, certain limits of the theory pertaining to the origins of the social objects investigated, and 3) hint at a new paradigm based on the graft of Derridean thought with the trace of Girardian thoughts on mimesis. (shrink)

In Voyous, Jacques Derrida develops his argument starting from the presupposition that democracy as such is the entity whose integrity and immunity are at stake and, therefore, under investigation. This gesture reflects the setting in which ten years before, in Foi et savoir, he had cast his reasoning about the logic of immunity. There, it was one of the sources of religion, the immunity of the sacred, that operated according to this logic. The hyphen between these two essays, beside Derrida’s (...) own crossed references, is the genealogical reasoning on the meaning and essence of the concept of democracy: contrary to what Derrida claims, it will be maintained that Athenian democracy had a clear immune matrix, whose constant exercise is clearly defined, in spite of himself, by Vernant, and it will be shown how modern democracy has been forced to change policy. Modern democracy is an entity characterized by an immune deficiency. In order to save Derrida’s intuition from both the collapse of different vantage points and from a quite bizarre reticence in taking into account of the immune value of rituals, our starting point will be René Girard’s œuvre and his reading of the role of immune logic in sacred systems and, more generally, in modernity. The threshold between the auto-immune reaction, immune deficiency and auto-immune disease, between the sacrifice who delimits and constitutes the self and the holocauste du peuple en détail, is the space where, constantly exposed to the risk of auto-denial, democracy lives. (shrink)

Este texto trata da reflexão heideggeriana sobre o conceito de mônada em Leibniz e suas determinações. Os apontamentos de Heidegger sobre o ser a partir do pensamento leibniziano promovem uma abertura fundamental da mônada, trazendo entre outras conseqüências, o perspectivismo e a idéia do ente enquanto pulsão. A limitação ontológica da mônada e sua capacidade de movimentar-se a partir de si mesma resultam em uma noção de representação e delineiam os contornos do ente. Esta discussão intenta demonstrar as possibilidades de (...) compreensão do conceito de mônada partindo das reflexões de Heidegger sobre A determinação do Ser do Ente segundo Leibniz. (shrink)

L'obiettivo del presente articolo è l'osservazione storica delle politiche della memoria nel Brasile contemporaneo, con particolare attenzione al periodo tra il 2019 e il 2022 (governo Bolsonaro). Dall'analisi delle azioni giudiziarie proposte da diversi attori sociali e politici, l'articolo propone una riflessione sulle temporalità coinvolte nelle politiche della memoria nel contesto post-dittatoriale, soprattutto dalla prospettiva delle vittime del regime.

Henry Leonard and Karel Lambert first introduced so-called presupposition-free (or just simply: free) logics in the 1950’s in order to provide a logical framework allowing for non-denoting singular terms (be they descriptions or constants) such as “the largest prime” or “Pegasus” (see Leonard [1956] and Lambert [1960]). Of course, ever since Russell’s paradigmatic treatment of definite descriptions (Russell [1905]), philosophers have had a way to deal with such terms. A sentence such as “the..

This essay proposes that the only publication of the Accademia del Cimento, referred to as Saggi,Footnote11 Accademia del Cimento, Saggi di naturali esperienze fatte nell’ Accademia del Cimento sotto la protezione del serenissimo principe Leopoldo di Toscana e descritte dal segretario di essa Accademia (Firenze: Per Giuseppe Cocchini, 1667). had as one of its main goals the celebration of the House of Medici’s paternity of cutting-edge experiments and instruments during the reign of Grand Duke Ferdinando II. These included Ferdinando II’s (...) thermometers and hygrometers, Torricelli’s experiment and barometer, and Galileo’s pendulum as a clock-regulator. It seems that this agenda went unnoticed, not at the time of its initial circulation, but rather in modern historiography. Christiaan Huygens’s challenged invention of the pendulum clock provides a case study to explore the agenda of this publication and the problem of defining an invention in seventeenth-century Europe. This paper presents for the first time the document that attests to when the first specimen of Huygens’s clock arrived in Florence, disproving the previously believed date of September 1657. The paper argues that over the last two centuries, this error has made the Medici narratives of this dispute appear inconsistent and marginalized them. In light of this new find, they must be reconsidered. (shrink)

Thesis: Macro-level social phenomena are implemented through the (social) actions and minds of the individuals. Without an explicit theory of the agents' minds that founds, agents' behavior we cannot understand macro-level social phenomena, and in particular how they work. AntiThesis: Mind is not enough: the theory of individual (social) mind and action is not enough to explain several macro-level social phenomena. First, there are pre-cognitive, objective social structures that constrain the actions of the agents; second, there are emergent, unaware or (...) non-contractual forms of cooperation, organisation, and intelligence. Synthesis: The real challenge is how to reconcile, cognition with emergence, intention and deliberation with unknown or unplanned social functions and social order . Both objective structures and unplanned self-organising complex forms of social order and social function emerge from the interactions of agents and from their individual mental states; both these structures and self-organising systems feedback on agents' behaviors through the agents' individual minds. (shrink)

RESUMEN En este artículo abordamos la cuestión del poder en el pensamiento de Deleuze. Según nuestra hipótesis, no hay en su obra un único concepto de poder sino diferentes enfoques no incompatibles entre sí pero que no se dejan reducir a un solo punto de vista. Esta variedad de abordajes puede ser reunida alrededor de dos posiciones generales adoptadas por Deleuze: primero, tiende a relativizar su eficacia respecto de otros elementos más fundamentales, realzando así los límites o la impotencia del (...) poder; segundo, le quita valor con relación a otras entidades y procesos en los que deposita su apuesta filosófica. Nos proponemos desarrollar estas perspectivas a fin de ofrecer un panorama integral de una temática relevante de la filosofía política deleuziana. ABSTRACT In this article, we address the question of power in Deleuze's thinking. According to our hypothesis, there is not a single concept of power in his work, but different approaches not incompatible with each other but that cannot be reduced to a single point of view. This variety of approaches can be gathered around two general positions about power, adopted by Deleuze: first, he tends to relativize its effectiveness with respect to other more fundamental elements, thus enhancing the limits or impotence of power; second, he takes away value in relation to other entities and processes in which he places his philosophical commitment. We intend to develop these perspectives in order to offer a comprehensive overview of a relevant theme of Deleuzian political philosophy. (shrink)

El artículo se propone establecer, a partir de una lectura sistemática de la obra de Pierre Bourdieu, algunas relaciones conceptuales entre poder y constitución social del tiempo. Partiendo del supuesto de que el tiempo, el modo en que lo experimentamos, concebimos y empleamos, es una construcción social, se tratan de identificar algunas de las maneras en que el poder interviene en esos procesos de construcción, tarea para la cual la obra de Bourdieu es no sólo estratégica sino insoslayable, pues está (...) entre las pocas que se han ocupado en profundidad de ambos temas. El artículo identifica primero las coordenadas generales del tratamiento bourdiano de ambas cuestiones, diferenciando cinco dimensiones del tiempo social: la del tiempo como experiencia práctica, como recurso, como coacción estructural, como representación del pasado y del futuro y como tensión existencial. En cada una, luego, se elaboran relaciones concretas entre poder y tiempo, que se pasan en limpio globalmente en las conclusiones. (shrink)

Este artículo presenta un enfoque de la creatividad de la acción que, sin renunciar a los logros alcanzados por diversas tradiciones sociológicas, apuesta por la imaginación como clave filosófica complementaria para continuar su desarrollo. Se diagnostica primero el lugar restringido que la creatividad ha tenido en la sociología de la acción; se ofrece después una precisión de “creatividad”, a partir de la noción de “contingencia”; ulteriormente se propone un esquema general para situar la imaginación en distintos niveles de la acción; (...) y, finalmente, se muestran tres caminos de desarrollo posible, según se haga de la imaginación un fenómeno de la conciencia, del lenguaje o de la psique. (shrink)

In this paper, we sketch out a simple scheme to evaluate different ways in which Western society has coped with the momentous and hidden problem of envy; afterward, we consider the consequences for the constitution of the social space that these changes entail. We will argue that envy, when considered as a primal feeling, can shed light on René Girard’s notion of metaphysical desire and on diasparagmos rituals. Then, taking into account Jean-Pierre Dupuy’s endogenous fixed point thesis—concerning the constitution of (...) autotranscendent social structures that configure themselves around an attractor, a fixed point, revealed to be a product of the process of constitution, an effect and not a cause—we will consider envy as the main feedback in the system. Starting from this theoretical scenario, we will envisage three steps—on a line sketched according to mimetic theory—marked by the particular conditions and role of the feedback. We will show what kind of balance was guaranteed to Athens (taken as an exemplar archaic society, starting from its self-representation as given by Sophocles in Oedipus the King) by the complementary rituals of pharmakos and ostrakos; what equilibrium was offered to Christian medieval social structures by the doctrine of the deadly sins; and, finally, we will take a look at our own secularized society. Our aim is to apply René Girard’s theory systematically, to show how the philosophy of history that we can infer from his works can help us to detect a curious and at the same time quite dramatic change as far as the homeostatic equilibrium of our society is concerned. Thanks to this exercise, we will be able to show how the transcendental social space— by which we mean the region of possible outcomes, in terms of constraints and possibilities, of a human life in a social context—is constituted through the victimage mechanism as defined by Girard and how this constitution is affected by the performative unveiling of the mechanism itself. (shrink)

The purpose of this note is to acknowledge a gap in a previous paper — “The Complexity of Revision”, see [1] — and provide a corrected version of argument. The gap was originally pointed out by Francesco Orilia (personal communication and [4]), and the fix was developed in correspondence with Vann McGee.

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)

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)