It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...) schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)

We show how to interpret intuitionistic propositional logic into a predicative second-order intuitionistic propositional system having only the conditional and the universal second-order quantifier. We comment on this fact. We argue that it supports the legitimacy of using classical logic in a predicative setting, even though the philosophical cast of predicativism is nonrealistic. We also note that the absence of disjunction and existential quantifications allows one to have a process of normalization of proofs that avoids the use of "commuting conversions.".

As public administrations adopt artificial intelligence (AI), we see this transition has the potential to transform public service and public policies, by offering a rapid turnaround on decision making and service delivery. However, a recent series of criticisms have pointed to problematic aspects of mainstreaming AI systems in public administration, noting troubled outcomes in terms of justice and values. The argument supplied here is that any public administration adopting AI systems must consider and address ambiguities and uncertainties surrounding two key (...) dimensions: the algorithms’ results, and how public managers make decisions for and about AI systems’ design. The article is based on bibliographic research in institutional theory perspective that relates the design of AI systems and relevant literature on the decision-making process in public policy. The main finding is to explain why autonomous decision systems continue to reproduce ambiguities and uncertainties when applied in public administration and propose a reflection on AI governance in public administration. This article points to the need for design institutions that immerse themselves in understanding the nuances, details, and potential outcomes of AI governance for public administration. Such institutions would reconcile consequentialist logic with a logic of appropriateness to help navigate and mediate ambiguities and uncertainties. (shrink)

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we obtain (...) a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

We introduce a new typed combinatory calculus with a type constructor that, to each type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, associates the star type σ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^*$$\end{document} of the nonempty finite subsets of elements of type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory (...) calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. (shrink)

Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predicate calculus into a second-order predicative system for which there is no need for commuting conversions. Furthermore, we show that the redex (...) and the conversum of a commuting conversion of the original calculus translate into equivalent derivations by means of a series of bidirectional applications of standard conversions. (shrink)

We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically true. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.

We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov's principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak König's lemma. We discuss some applications, as well as some previous results in the literature.

When is humanitarian intervention legitimate and how should such interventions be conducted? This article sets out eight liberal principles that underlie humanitarian intervention, some of them abstract principles of international ethics and others more concrete principles that apply specifically to humanitarian intervention. It argues that whilst these principles do not determine the legitimacy of particular interventions, they should ?incline? our judgments towards approval or disapproval. The basic principles include the liberal idea that governments are the mere agents of the people, (...) that tyrannical governments forfeit their legal protections, that human rights entail obligations for governments, that justifiable intervention must intend the end of tyranny or anarchy, that the doctrine of double-effect should be respected, that intervention is only warranted in severe cases, that intervention be welcomed by those it is intended to save, and that ideally it is welcomed by the community of democratic states. (shrink)

Teson critiques a recent article by John Rawls in which Rawls extends his acclaimed political theory to include international relations.

Notions of disambiguation supporting a compositional interpretation ofvambiguous expressions and reflecting intuitions about how sentences combinevin discourse are investigated. Expressions are analyzed both inductively byvbreaking them apart, and co-inductively by embedding them within larger contexts.

In the course of ten short sections, we comment on Gödel's seminal dialectica paper of fifty years ago and its aftermath. We start by suggesting that Gödel's use of functionals of finite type is yet another instance of the realistic attitude of Gödel towards mathematics, in tune with his defense of the postulation of ever increasing higher types in foundational studies. We also make some observations concerning Gödel's recasting of intuitionistic arithmetic via the dialectica interpretation, discuss the extra principles that (...) the interpretation validates and comment on extensionality and higher order equality. The latter sections focus on the role of majorizability considerations within the dialectica and related interpretations for extracting computational information from ordinary proofs in mathematics. (shrink)

Esse texto é um resultado parcial e provisório de uma pesquisa de Pós-doutorado em andamento na Scuola Normale Superiore de Pisa/Italia sobre a supervisão do filósofo Roberto Esposito. Observa-se que nessas primeiras décadas do século XXI o pensamento filosófico Italiano, por algumas das razões que tentaremos expor abaixo, tem sido objeto de um grande interesse mundial, tornando-se objeto de inúmeros seminários, livros e artigos. O texto tenta avaliar se existiria algo como uma “filosofia Italiana” para além da pertença nacional daqueles (...) que contribuíram para a sua construção. Pode-se falar em uma Italian Theory? Se a resposta a essa questão for afirmativa, quais seriam as suas especificidades? (shrink)

We give an elementary proof of the strong normalization of the atomic polymorphic calculus Fat.

Finite-state methods are applied to determine the consequences of events, represented as strings of sets of fluents. Developed to flesh out events used in natural language semantics, the approach supports reasoning about action in AI, including the frame problem and inertia. Representational and inferential aspects of the approach are explored, centering on conciseness of language, context update and constraint application with bias.

Dynamic and proof-conditional approaches to discourse (exemplified by Discourse Representation Theory and Type-Theoretical Grammar, respectively) are related through translations and transitions labeled by first-order formulas with anaphoric twists. Type-theoretic contexts are defined relative to a signature and instantiated modeltheoretically, subject to change.

Every model of IΔ0 is the tally part of a model of the stringlanguage theory Th-FO . We show how to “smoothly” introduce in Th-FO the binary length function, whereby it is possible to make exponential assumptions in models of Th-FO. These considerations entail that every model of IΔ0 + ¬exp is a proper initial segment of a model of Th-FO and that a modicum of bounded collection is true in these models.

Events and situations are represented by strings of temporally ordered observations, on the basis of which the events and situations are recognized. Allen’s basic interval relations are derived from superposing strings that mark interval boundaries, and Kamp’s event structures are constructed as projective limits of strings. Observations are generalized to temporal propositions, leading to event-types that classify event-instances. Working with sets of strings built from temporal propositions, we obtain natural notions of bounded entailment from set inclusions. These inclusions are decidable (...) if the sets are accepted by finite automata. (shrink)

Situations serving as partial worlds as well as events in natural language semantics are constructed from a type-theoretic interpretation of firstorder formulae and (after a type reduction) temporal formulae. Limitations of the Russell-Wiener-Kamp derivation of time from events are discussed and overcome to give a more widely applicable account of temporal granularity. Finite situations are formulated as strings of observations, conceptualized to persist inertially (in the absence of forces).

Let be the fragment of elementary Peano arithmetic in which induction is restricted to -formulas. More than three decades ago, Parsons showed that the provably total functions of are exactly the primitive recursive functions. In this paper, we observe that Parsons' result is a consequence of Herbrand's theorem concerning the -consequences of universal theories. We give a self-contained proof requiring only basic knowledge of mathematical logic.

This paper first illustrates what kind of ethical issues arise from the new information, communication and automation technology. It then argues that we may embrace the popular idea that technology is ethically neutral or even ambivalent without having to close our eyes to those issues and in fact, that the ethical neutrality of technology makes them all the more urgent. Finally, it suggests that the widely ignored fact of normal responsible behaviour offers a new and fruitful starting point for any (...) future thinking about such issues. (shrink)

Numerical probabilities are eliminated in favor of qualitative notions, with an eye to isolating what it is about probabilities that is essential to judgements of acceptability. A basic choice point is whether the conjunction of two propositions, each acceptable, must be deemed acceptable. Concepts of acceptability closed under conjunction are analyzed within Keisler's weak logic for generalized quantifiers — or more specifically, filter quantifiers. In a different direction, the notion of a filter is generalized so as to allow sets with (...) probability non-infinitesimally below 1 to be acceptable. (shrink)

Este artigo objetiva pensar o debate envolvendo a questão da literalidade na obra de Gilles Deleuze, mormente naquela escrita em parceria com Félix Guattari, a partir de um recuo pelo pensamento do filósofo Henri Bergson. Apresentada como um modo singular de operar com a escrita, a literalidade deleuze-guattariana exigiria que determinadas formulações, mormente aquelas de teor imagético fossem lidas ao pé da letra (a la lettre) ao invés de interpretadas como metáforas. Tendo adentrado em nosso país por meio do dossiê (...) Entre Deleuze e a Educação, publicado em 2005 no periódico Educação & Sociedade, a questão da literalidade fomentou uma discussão acalorada, nomeadamente no campo educacional – dado o fato de um dos participantes, François Zourabichvili, propor uma pretensa teoria de ensino deleuzeana a partir dessa noção. Longe de querer encerrar tal debate, almejamos pensá-lo sob a égide do pensamento bergsoniano, a fim de propor um escape do binarismo estabelecido. (shrink)

O texto tem como objetivo apresentar a categoria de “biopolítica afirmativa” de Roberto Esposito. Para tanto, na primeira parte discute-se rapidamente o que se convencionou chamar de “a diferença italiana”. O segundo tópico do texto discute o significado de comunidade a partir do seu étimo originário munus. Na seção seguinte aborda-se o “dispositivo imunitário” onipresente em nossas sociedades. A partir dessas considerações pode-se, na última parte, discutir o problema central proposto, isto é, a biopolítica afirmativa.

Explicitness has usually been approached from two points of view, labelled by Kirsh the structural and the process view, that hold opposite assumptions to determine when information is explicit. In this paper, we offer an intermediate view that retains intuitions from both of them. We establish three conditions for explicit information that preserve a structural requirement, and a notion of explicitness as a continuous dimension. A problem with the former accounts was their disconnection with psychological work on the issue. We (...) review studies by Karmiloff-Smith, and Shanks and St. John to show that the proposed conditions have psychological grounds. Finally, we examine the problem of explicit rules in connectionist systems in the light of our framework. (shrink)

El artículo analiza, el papel que juega la epistemología en la formación profesional y disciplinaria de las ciencias sociales en el nuevo contexto de educación superior, en donde, aparece con fuerza la idea de una formación basada en competencias, a través de la cual se exige una articulación de los..

Em um artigo influente publicado em meados dos anos 80, Jacques Brunschwig defendeu a ideia de que o debate dialético, para Aristóteles, não resultaria em vencedores e derrotados. Sua defesa é baseada no debate dialético como sendo um trabalho comum entre questionador e respondedor (cláusula koinon ergon [cf. Tópicos VIII.11 161a20-21]) e como um tipo de teste de consistência de uma dada proposição (cláusula dia tēn thesis [cf. Tópicos VIII.4 159a20]). Apesar dos muitos méritos do artigo, penso que o argumento (...) de Brunschwig não considera adequadamente aspectos importantes do debate dialético no que concerne à performance dos debatedores, especialmente acerca dos recursos que o questionador deve usar. Ao não considerarmos esses aspectos, temos dificuldades para interpretar passagens em que Aristóteles recomenda o uso de táticas para enganar o respondedor. Meu objetivo nesse artigo será oferecer uma explicação diferente das cláusulas dia tēn thesis e koinon ergon, de modo que isso implicará uma conclusão segundo a qual o debate dialético honesto pode envolver vencedores e derrotados e manter a observância das duas cláusulas. Palavras-chave: Dialética; Aristóteles; Debate. Winners and losers in Aristotle’s dialectical debate. Abstract: In the mid-eighties Jacques Brunschwig published an influential paper of whose main claim consists in a defence of the Aristotelian conception of dialectical debate as a game without winners and losers. His claim is based on the dialectical debate as being a common work between answerer and questioner (koinon ergon clause [cf. Topics VIII.11 161a20-21]) and as a kind of test of the consistency of a given proposition (dia tēn thesis clause [cf. Topics VIII.4 159a20]). Despite its many merits, I think Brunschwig’s argument overlooks important aspects of the dialectical debate concerning the debaters’ performance, especially the resources that should be used by the questioner. By overlooking these aspects, we end up with several troubles to interpret passages in which Aristotle recommends deceptive tactics in the debate. My objective in this paper is to give a different account the dia tēn thesis and the koinon ergon clauses, which will imply a conclusion by which fair dialectical debates can still have winners and losers and observe both clauses. Key-words: Dialectics; Aristotle; Debate. Ganadores y perdedores en el debate dialéctico según Aristóteles. Resumen: En un influyente artículo publicado a mediados de los años 1980, Jacques Brunschwig defendió la idea de que el debate dialéctico, para Aristóteles, no resultaría en ganadores y perdedores. Su defensa se basa en el debate dialéctico como trabajo común entre el que pregunta y el que responde (cláusula koinon ergon [cf. Tópicos VIII.11 161a20-21]) y como una especie de prueba de la consistencia de una proposición dada (cláusula dia tēn thesis [cf. Tópicos VIII.4 159a20]). A pesar de los muchos méritos del artículo, creo que el argumento de Brunschwig no considera adecuadamente aspectos importantes del debate dialéctico con respecto a la actuación de los debatientes, especialmente con respecto a los recursos que debe utilizar el interrogador. Al no considerar estos aspectos, nos resulta difícil interpretar pasajes en los que Aristóteles recomienda el uso de tácticas para engañar al que responde. Mi objetivo en este artículo será ofrecer una explicación diferente de las cláusulas dia tēn thesis y koinon ergon, de modo que esto implique una conclusión de que el debate dialéctico honesto puede involucrar a ganadores y perdedores y mantener la observancia de las dos cláusulas. Palabras-clave: Dialéctica; Aristóteles; Debate. 1 Pesquisa desenvolvida no âmbito do Edital Universal Nº28/2018 financiada pelo CNPq sob o número 433825/2018-9. Data de registro: 01/08/2023 Data de aceite: 24/04/2024. (shrink)

El pasado 8 de junio 2020, Fernando Soler Escalona, estudiante de nuestra Facultad, obtuvo el grado académico de Doctor en Teología, con una tesis sobre El sentido teológico de las metáforas de comer y beber en la obra de Orí-genes, redactada bajo la supervisión de Samuel Fernández, Profesor Titular de Patrología. La defensa fue inusual: la pandemia de COVID-19 obligó a realizarla por videoconferencia, para mantener el aislamiento físico entre los participantes. En la espera de la publicación integral de (...) la tesis, reproducimos a continuación la presentación que el Doctorando hizo de sus investigaciones durante la defensa. (shrink)

The geographical Utopias that present a New World, from classical Antiquity and the Middle Ages to the exploration and conquest of American territories by Spain, give a two-fold vision of the myth of gold. On the one hand, the legendary lands in which were found the wealth and power generated by the coveted metal—El Dorado, El Paititi, the City of the Caesars—establish the direction of a venture toward the unknown, and a geography of the imaginary marked the ubiquitous sign of (...) the mythical gold. But at the same time, America permitted the felicitous re-encounter in its territory of the Golden Age that had been lost in the Old World. The first steps of Western man toward the American adventure wavered contradictorily between these extremes, in that gold was at the same time “booty and marvel.”. (shrink)

The paper explains the application of a Social Innovation Based Transformative Learning pedagogical approach in an undergraduate, final year business ethics course taught at an Australian university. Using social innovation as an enabling process to extend students’ cognitive, behavioural and managerial competencies in an integrated manner, the paper describes how the SIBTL approach helps ethics teachers to promote students’ ethical action.

We introduce a class of models of the bounded arithmetic theoryPV n . These models, which are generated by their tally part, have a curious feature: they have end-extensions or satisfyB∑ n b only in case they are closed under exponentiation. As an application, we show that if then the polynomial hierarchy does not collapse.

This article discusses the concept of constituent power and its application to the situation in Chile after the 18th October 2019. In particular, it discusses the relation between constituted and constituent powers, with a view to understanding the significance of the 15 November Agreement that opened the way for the ongoing constituent process.