A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of (...) analysis is driven by exploiting the Curry–Howard correspondence. In particular, deducibility of identicals is shown to correspond to the computational property of eta expansion, which is essential in the characterization of propositional identity. (shrink)

An anti-realist theory of meaning suitable for both logical and proper axioms is investigated. As opposed to other anti-realist accounts, like Dummett-Prawitz verificationism, the standard framework of classical logic is not called into question. In particular, semantical features are not limited solely to inferential ones, but also computational aspects play an essential role in the process of determination of meaning. In order to deal with such computational aspects, a relaxation of syntax is shown to be necessary. This leads to a (...) general kind of proof theory, where the objects of study are not typed objects like deductions, but rather untyped ones, in which formulas have been replaced by geometrical configurations. (shrink)

Cet article propose d’étudier les critiques avancées par Michael Dummett à l’encontre de l’argument consistant à faire appel à l’omniscience de Dieu pour justifier la thèse du réalisme sémantique (c’est-à-dire la thèse selon laquelle la signification et la vérité de nos énoncés seraient déterminées par une réalité indépendante de nous et de nos états cognitifs). Pour Dummett, un tel argument est en effet illégitime, car il contient une pétition de principe qui est à son tour induite par une erreur d’analyse (...) logico-linguistique. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

We study how to postpone the application of the reductio ad absurdum rule (RAA) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of RAA, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.

We study how to postpone the application of the reductio ad absurdum rule ) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of \, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.

A widely debated issue in philosophy of logic concerns the possibility of an inferentialist account of classical logic. Many proposals to show that classical logic satisfies the requirements of inferentialist semantics (such as harmony) demand to modify the ordinary natural deduction rules. In this paper, we try to explain why the ordinary natural deduction rules for classical logic are not harmonious and therefore not directly justifiable within an inferentialist framework. We show however that an indirect justification of classical logic, passing (...) through negative translation, can be acceptable from an inferentialist point of view. (shrink)

A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to give (...) a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator. (shrink)

We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely (...) axiomatizable in first-order logic. (shrink)

Editorial NoteThe following Discussion Note is an edited transcription of the discussion on G. Aldo Antonelli’s paper “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals”, held among participants at the IHPST-UC Davis Workshop Ontological Commitment in Mathematics which took place, in memoriam of Aldo Antonelli, at IHPST in Paris on December, 14–15, 2015. The note’s and volume’s editors would like to thank all participants in the discussion for their contributions, and Alberto Naibo, Michael Wright and (...) the personnel at IHPST for their technical support. (shrink)

What is racism? is a timely question that is hotly contested in the philosophy of race. Yet disagreement about racism’s nature does not begin in philosophy, but in the sociopolitical domain. Alberto G. Urquidez argues that philosophers of race have failed to pay sufficient attention to the practical considerations that prompt the question “What is racism?” Most theorists assume that “racism” signifies a language-independent phenomenon that needs to be “discovered” by the relevant science or “uncovered” by close scrutiny of (...) everyday usage of this term. (Re-)Defining Racism challenges this metaphysical paradigm. Urquidez develops a Wittgenstein-inspired framework that illuminates the use of terms like “definition,” “meaning,” “explanation of meaning,” and “disagreement,” for the analysis of contested normative concepts. These elucidations reveal that providing a definition of “racism” amounts to recommending a form of moral representation—a rule for the correct use of “racism.” As definitional recommendations must be justified on pragmatic grounds, Urquidez takes as a starting point for justification the interests of racism's historical victims. (shrink)

Desde la perspectiva de las ciencias jurídicas y, en particular, del derecho internacional ambiental, la presente intervención aborda la emergencia de un Derecho internacional contemporáneo y acude a las ideas del cosmopolitismo blando y la vertiente normativa del constitucionalismo global, como debates filosóficos-jurídicos que podrían cimentar un terreno fértil, un sustrato material, para incidir en las fuentes formales de creación de normas internacionales para enfrentar los problemas globales ambientales. En ese sentido, hace mención a la emergencia y reconocimiento del derecho (...) humano al ambiente sano y saludable como un derecho humano autónomo y exigible, desde su vertiente sustantiva y procesal, lo que puede vislumbrase como el embrión de una ciudadanía global ambiental. (shrink)

Beginning from some passages by Vācaspati Miśra and Bhāskararāya Makhin discussing the relationship between a crown and the gold of which it is made, this paper investigates the complex underlying connections among difference, non-difference, coreferentiality, and qualification qua relations. Methodologically, philological care is paired with formal logical analysis on the basis of ‘Navya-Nyāya Formal Language’ premises and an axiomatic set theory-based approach. This study is intended as the first step of a broader investigation dedicated to analysing causation and transformation in (...) non-difference. (shrink)

El presente trabajo busca exponer las premisas y la fundamentación teológica que subyace a la moral de Pedro Abelardo, con el fin de mostrar cómo en el sistema filosófico de dicho autor, conocido por su racionalismo, hay una justificación que extralimita dicho sistema. Para ello, se expondrá la terminología clave de su moral, la aplicación práctica de dichos conceptos, y una serie de objeciones tanto teológicas como filosóficas.

Este artículo busca problematizar parcialmente la constitución ontológica de la noción de praxis hegemónica en Antonio Gramsci; producir una definición de posthegemonía como posición política y no como doctrina; arriesgar la noción de que, de haber una “ontología” posthegemónica, convendría asentarla bajo tacha en el lugar de un posible pensamiento de la diferencia ontológica; describir brevemente un espacio de praxis emergente en el que la noción posthegemónica se hace explícita; y regresar a Antonio Gramsci a partir de una posible entrada (...) en crisis del concepto de hegemonía en su obra misma. (shrink)

Con esta ceremonia culminan los actos del otorgamiento del título de Doctor Honoris Causa de la Universidad de Buenos Aires al filósofo, maestro de maestros, Thomas Moro Simpson.De este modo nuestra Universidad, siguiendo una noble idea iniciada por los romanos mucho antes de que existieran las universidades, la idea de destacar la labor de aquellos ciudadanos que hubieran contribuido notablemente a mejorar la vida de la ciudad común, ha resuelto hacer público su reconocimiento de los excepcionales méritos intelectuales, éticos y (...) académicos de nuestro querido Tomás Simpson. He sido encargado de recordar ahora, sumariamente, ante la comunidad universitaria y, con eso, ante nuestra comunidad simpliciter, algunos de los motivos que condujeron a esta resolución. (shrink)

Gregorio Klimovsky argumentó en contra de los análisis sintacticistas de la noción de lenguaje. En este trabajo se examinan sus argumentos, destacando su vínculo con las discusiones recientes sobre universalidad expresiva, y se plantean algunas réplicas atendibles. Luego se adopta un enfoque general de la cuestión que resulta incompatible con el sintacticismo estricto pero que permite una reformulación aceptable, vinculada con una idea minimalista sobre el alcance de la teoría semántica. Gregorio Klimovsky argued against syntactical analyses of the notion of (...) language. In this paper I examine his arguments, noting their links with recent discussions of universal expressibility, and raise some plausible objections. Afterwards I adopt a general approach to the issue which is incompatible with strict syntacticism but allowing an acceptable reformulation, associated with a minimalist notion of the scope of the semantic theory. (shrink)

The present paper is a continuation of a previous one by the same title, the content of which faced the issue concerning the relations of coreference and qualification in compliance with the Navya-Nyāya theoretical framework, although prompted by the Advaita-Vedānta enquiry regarding non-difference. In a complementary manner, by means of a formal analysis of equivalence, equality, and identity, this section closes the loop by assessing the extent to which non-difference, the main issue here, cannot be reduced to any of the (...) former. The following sections of this study will focus on the assessment of the eventual possibility of causation and transformation in non-difference. (shrink)

Focusing especially on Science and the Modern World, this article explores Whitehead's understanding of the social contexts and repercussions of mathematical and scientific abstraction. It investigates his remarks on the need to offset pernicious practices of abstraction in the context of a renewed concern with the link between conceptuality and materiality in social theory. Whitehead's inquiry into the problematic legacy of Galileo and scientific materialism is then contrasted with a different diagnosis of the abstractive maladies of modern society, the one (...) put forward under the Marxist rubric of `real abstraction'. While both stances allow us to explore the social repercussions of abstractive practices, it is argued that an understanding of the practically abstract character of capitalism permits us to identify the limits of Whitehead's pedagogical wish to reform our culture of abstraction. (shrink)

The Covid-19 pandemic has further intensified a crisis in the functions and the perception of the state. It has also revealed underlying contradictions in both mainstream and radical ideologies of the state. A desire for the state as guarantor of public welfare vies with fear of the state’s hypertrophic capacities for surveillance and control. Following a brief exploration of the intimate modern connection between plagues and the state, the article tries to map some of the ways in which the state (...) has been at stake in political and theoretical commentaries on the pandemic. Is an epidemiological politics from below, beyond the plague state, possible? Can recent emergency measures be seen as incomplete or inverted anticipations of a communist use of the state of exception? Or is the primacy of the political we are currently experiencing a mere fetish, indissociable from the rule of capital? (shrink)

Angelaki, Volume 16, Issue 3, Page 125-136, September 2011.

In (Fund Math 60:175–186 1967), Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note that all chains in a wpo are well-ordered.) We prove that such maximal chain cannot be found computably, not even hyperarithmetically: No hyperarithmetic set can compute maximal chains in all computable wpos. However, we prove that almost every set, in the sense of category, can compute maximal chains in all computable wpos. Wolk’s original result (...) actually shows that every wpo has a strongly maximal chain, which we define below. We show that a set computes strongly maximal chains in all computable wpo if and only if it computes all hyperarithmetic sets. (shrink)

The question examined in this article is whether the contemporary world system is leading to a world society. World system connotes that we live in an increasingly interdependent world. The author examines the nature of world system in relation to world society. Then the author examines the nature of the world system as a growing interconnected global order, and the yet non-existent world or global society, a society as a network of social relations with mutual expectations and normative consensus. Difference (...) perspectives of world society are discussed, followed by a focus on cosmopolitan ethics and transnational civil society. Institutions of democratic world society and the implications are examined. The author concludes: more and more people come to live in a single world system; a transnational civil society and an international public space are growing; a global communitarian culture and a cosmopolitan ethics are gaining ground. (shrink)

There has been some concern m recent years that economic interests in the biotechnology area could, particularly through patenting, have a constricting influence on scientific research. Despite this concern, there have been no studies of this phenomenon beyond isolated cases. In this article we examine the evolution of the biomedical field of hybridoma/monoclonal antibody research with detailed examples of the three types of patent claims that have emerged there—basic claims, claims on application techniques, and claims on specific antibodies. We analyze (...) the impact of these claims and their legal histories on the free flow of scientific information and, the activity of scientific researchers. We conclude that such patent claims present severe restrictions for both, not only in the monoclonal area but in general, amounting to a subtle but significant shift in the political economy of science and technology. (shrink)

Positional notation and related numerical manipulation techniques of Indian origin were introduced to Europe during the twelfth century through Arabic mediation and vividly described by Fibonacci as modus Indorum, the method of the Indians. This article aims to juxtapose Sanskrit and Latin texts to highlight the connections and differences between matrix and reflection in a complex cultural process of diffusion and assimilation. With reference to positional notation, this contribution examines a conceptual distinction between the graphical notion of position and a (...) logical-classificatory principle hitherto perhaps not fully recognized, although present in the texts of both traditions. The thesis of a consequent diagrammatic conception of positional notation in its origins, as a system of rules relating graphical position and order of magnitude, is also advanced. (shrink)

This article reconsiders Marx’s thinking on religion in light of current preoccupations with the encroachment of religious practices and beliefs into political life. It argues that Marx formulates a critique of the anticlerical and Enlightenment-critique of religion, in which he subsumes the secular repudiation of spiritual authority and religious transcendence into a broader analysis of the ‘real abstractions’ that dominate our social existence. The tools forged by Marx in his engagement with critiques of religious authority allow him to discern the (...) ‘religious’ and ‘transcendent’ dimension of state and capital, and may contribute to a contemporary investigation into the links between capitalism as a religion of everyday life and what Mike Davis has called the current ‘reenchantment of catastrophic modernity’. (shrink)

The main argument of this article is based on a functional disanalogy, between what I will call ‘international humanity-based law’, constituted by human rights and criminal law, and the domestic rule of law. If we adopt a functionalist approach, the attention has to be focused both on Rule of Law’s pragmatical objective – a reasonable stability – and on its means – formalism and legality, for dealing with indeterminacy. Do international key players share such values, embedded in the Rule of (...) Law’s political project? Does humanity-based international law fulfil the requirements of the Rule of Law? The conclusion of this work is that institutions and mechanism to which usually legal scholars refer when stating that a legal order is a Rule of Law, are almost absent in humanity-based international law. That implies that radical indeterminacy is, in humanity issues, a too strong obstacle for achieving the ideal of the Rule of Law. (shrink)

Alain Badiou, Manifesto for Philosophy, Translated, Edited and withan Introduction by Norman Madarasz ISBN - 9780791442197Alain Badiou, Deleuze. The Clamor of Being, Translated and with aPreface by Louise Burchill ISBN - 9780816631391.

En el presente trabajo se interpretan los sentidos teológicos de los términos bíblicos "carne" y "carnalidad" mostrando su carácter ambivalente que surge de binomios cargados tanto de connotaciones negativas como positivas. Se tratará de mostrar que las primeras parten de una interpretación parcial ..

pThere is much theoretical work already underway on the many facets of Badiou#39;s theory of political subjectivation. However, little attention has been directed hitherto to those figures of the subject which cannot be easily identifiable with a universalist or generic orientation. Beginning with Badiou#39;s struggles with the subjectivity of the bourgeois in the seminars that make up his Theorie du sujet , this article tries to track his thinking of the #39;other#39;, non- or anti-universalist subjects of politics, and to think (...) what effects their inclusion within a theory of the subject, and indeed a theory of political praxis, may have. Taking issue with some recent remarks of Badiou on the isomorphies between Islamism and fascism in Logiques des mondes , the article also seeks to develop Badiou#39;s notion of #39;reactive#39; and #39;obscure#39; subjects through a brief engagement with recent interpretations of political Islam./p. (shrink)

Este artículo explora el panorama de la minificción en seis países hispanoparlantes del istmo centroamericano: Guatemala, El Salvador, Honduras, Nicaragua, Costa Rica y Panamá, con el objetivo de contar con una primera mirada a la génesis comparada de la minificción regional, su estado actual y los rasgos propios de la creación minificcional en Centroamérica.

This article concerns the role of haptic perception in the act of enjoying sculptures and it takes as a starting point an unusual experience “in the dark”. Starting with a short description of this experience, some focal theoretical constructs of Art Psychology – in the tradition of Gestalt theory and Rudolf Arnheim – are addressed, namely expressive qualities and perceptual forces and tensions. Revisiting these constructs in a haptic key allows the consideration of aesthetic behaviour in the plastic art domain (...) and the proposal of “naturalistic” research lines aimed at gaining a sharper comprehension of its features. (shrink)

This article seeks to trace the origins of contemporary ‘post-workerism’ in the formulation of concepts of political subjectivity, antagonism and insurrection in Tronti and Negri. In particular, it tries to excavate the seemingly paradoxical position which postulates the increasing immanence of struggles, as based on the Marxian thesis of real subsumption, together with the intensification of the political autonomy or separation of the working class. In order to grasp the political and theoretical proposals of Italian workerism and autonomism, Toscano concentrates (...) on the thesis of a historical transformation of capitalism into an increasingly parasitical and politically violent social relation, a thesis which is grounded in an interpretation of Marx’s notion of ‘tendency’ and which serves as the background to the exploration, especially in Negri, of increasingly uncompromising forms of antagonism. The article focuses especially on Tronti’s so-called ‘Copernican revolution’—giving workers’ struggles primacy in the understanding of capitalism—and critically inquires into the effect of this workerist axiom on Negri’s writings on proletarian sabotage and insurrection in the 1970s. By way of a conclusion, it notes the difficulties in prolonging the workerist gambit in light of capital’s continued effort, as Tronti would put it, to emancipate itself from the working class. (shrink)