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)

This book explores the notion of endangerment which stands at the heart of a network of concepts, values and practices dealing with objects considered threatened by extinction, and with the procedures aimed at preserving them. It looks at some of the fundamental ways in which this process involves science, but also more than science: not only data and knowledge and institutions, but also affects and values. With a focus on endangerment sensibility, it encapsulates tensions between the normative and the utilitarian, (...) the natural and the cultural. (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.".

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)

Inertia is enshrined in Newton’s first law of motion, a body at rest or in uniform motion remains in that state unless a force is applied to it. Now, consider (1). (1) Pat stopped the car before it hit the tree. Can we conclude from (1) that the car struck the tree? Not without further information such as that supplied in (2). (2) But the bus behind kept going. A post-condition for Pat stopping the car is that the car be (...) at rest. To satisfy a pre-condition for the car hitting the tree (namely, that the car not be at rest), inertia requires that some intervening force act on the car (as hinted, for example, by (2)). In the absence of such a force, (1) would appear to suggest that Pat prevented a collision between car and tree. Exactly what bit of physics are we importing into natural language interpretation here? Oversimplified, Newton’s first law of motion says: no change without force. Identifying force with cause, we come to the slogan no temporality without cause, capturing in a phrase the proposal from Steedman 2000 that.. (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.

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)

Reichenbach's event, reference and speech times are interpreted semantically by stringing and superposing sets of temporal formulae, structured within regular languages. Notions of continuation branches and of inertia, bound (in a precise sense) by reference time, are developed and applied to the progressive and the perfect.

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

El propósito de este artículo es presentar, en forma sucinta, los principales elementos de la concepción budista del universo, entendido como la realidad toda, no en sus comienzos, tal como ella aparece en los textos más antiguos, ni en el curso de su evolución histórica, mostrando sus diferentes etapas, sino en la forma en que esta concepción asumió cuando ella fue fijada de una vez para siempre algunos siglos después de la muerte o – como prefieren los budistas - el (...) Parinirvana de Buda.Infi.. (shrink)

El presente trabajo muestra la imposibilidad de separar el ideal de la igualdad revelado por la crítica de Rousseau, y que constituye la base moral de un nuevo estado de derecho poblado de individuos, de la constitución de la idea de libertad como valor político y del individualismo que se erige sobre ésta- En otras palabras, quizás, el ideal de sociedad pensado por Rousseau no era realizable, pero lo que efectivamente se realizó no habría sido posible sin sus ideales.

In 1913, the future psychologist and epistemologist Jean Piaget (1896-1980), then a seventeen-year-old naturalist, gave a talk criticizing 'the notion of the species according to the Mendelian school'. In it, he confounded Mendelism and mutationism, and misunderstood both. He attributed an environmental nature to the 'factors' postulated by Mendel's laws for inherited characteristics, and thought that mutations resulted from the appearance of a new environmental factor. Such misinterpretations are closely related to Piaget's assimilation of the Bergsonian critique of 'mechanistic' science (...) into his work in malacological taxonomy. (shrink)

Schubert’s proposal ([Sch00]) that sentences not only describe but also characterize situations is worked out in the context of Linear Temporal Logic (LTL), a well-known propositional logic with linear future operators (e.g. [HR04]). The resulting formalism LTL∗∗ illustrates an approach that diverges from Schubert’s FOL∗∗ in technical details but shares many (if not all) its motivations.

Morality is a normative system of guidance that figures into practical reason by telling people what to do in various situations. The problem, however, is that morality has inherent gaps that often render it inefficacious. First, it may be indeterminate due to the high level of generality in which its principles are formulated. Second, moral terms such as ‘good’ and ‘right’ may be so vague that they fail to specify the requisite behavior. And third, its subjective aspect, which is a (...) product of personal experience, generates moral disagreement and thereby creates coordination problems that frustrate society’s collective moral aims. The objective of this article is to advance the thesis that morality must sometimes depend on law as a supplementary source of practical reason, a dependence which can be explained in terms of three essential features of law: its institutional character, its claim to authority, and its status as a second-order exclusionary reason for action. It shall then be explained how these three features enable law to make difficult decisions on behalf of individuals, define objective standards of conduct, and solve coordination problems, respectively, and in doing so, manage to fill in the gaps of morality mentioned above. Hence, it will be argued that law is also a normative system that helps people achieve their moral aims, notwithstanding the fact that it guides human behavior through a different logic and mode of operation from those of morality. (shrink)

judgments of acceptability A basic choice point is whether the conjunction of two propositions each separately acceptable must be deemed acceptable Concepts of acceptability closed under conjunction are analyzed within Keisler s weak logic for generalized quanti ers or more speci cally lter quanti ers In a di erent direction the notion of a lter is generalized so as to allow sets with probability non in nitesimally below to be acceptable..

In the 1760s, the international debate on the solution to determining longitude at sea is at its acme. Two solutions emerge, the mechanical and the astronomical ones. The Portuguese mathematician and astronomer José Monteiro da Rocha (1734–1819) is well aware of that debate. For him, Harrison’s No. 4 marine timekeeper cannot be seen as a solution. The desirable solution could only be astronomical. In a manuscript from c. 1765, which unfortunately he fails to publish, Monteiro da Rocha is very critical (...) of Lacaille's lunar-distance method (1759) and proposes another one. In this paper, we intend to analyse Monteiro da Rocha’s criticisms and proposals, trying to understand how this manuscript fits into the international longitude debate and the Portuguese scientific scenario at the time. Concurrently, we will re-examine the classical historiography around the English vs. French priority proposal of the lunar-distance method, purging it from its mythologies to shift it towards a more open, less linear history. (shrink)

The manifesto of a new philosophy of technology.

The present essay is devoted to analyzing Reinhold’s contribution to one of the most relevant questions in German idealism, namely, the possibility of an absolute principle of all philosophy, as a task left open by Kant’s critical enterprise. The main aim is to assess the extent to which Reinhold is the first to propose this philosophical problem as a question of language, and in doing so the possibility of an absolutely apodictic philosophical language, as it would be later resumed and (...) developed by Fichte and other authors. Keywords: Reinhold, language, philosophy, principle, consciousness. (shrink)

Emergentes não raras vezes nas Lições de Antropologia de Kant, os termos “Einbildungskraft”, “Einbildungsfähigkeit” e “Imagination” são comummente tomados – e, prova maior disto mesmo, traduzidos – como um só. O presente artigo propõe-se pôr em causa e demonstrar a incorrecção desta abordagem. Bem pelo contrário, estamos em crer que, no âmbito da antropologia kantiana, em primeiro lugar, “faculdade de imaginação” e “capacidade de imaginação” não são uma e a mesma coisa, antes significam diferentes estratos, diferentes dimensões conceptuais na compreensão (...) do processo de representação humana; em segundo lugar, também “faculdade de imaginação”, enquanto “Einbildungskraft”, não é o mesmo que o seu correspondente na “Imagination”, antes duas dimensões de um e o mesmo problema antropológico, o problema por excelência do acto de representar, que surge entre o mundo e o designar humano. Tais distinções, que, assim o cremos, requerem uma compreensão mas também uma tradução mais criteriosa do que até aqui, trazem a uma mais distinta luz o modo como Kant estrutura e ordena as diferentes fases do processo da imaginação humana, e salienta aquelas que, para o filósofo, são as diferentes potencialidades desta última.__. (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)

En este artículo presentamos las principales corrientes de la Filosofía Experimental y atendemos a una de las críticas más severas a la que se ha sometido este reciente programa de renovación metodológica. Según Antti Kauppinen la Filosofía Experimental está condenada al fracaso porque no puede obtener mediante sus métodos el tipo de intuiciones que interesan a los filósofos –las intuiciones robustas del hablante competente. Aun aceptando parte de las críticas de Kauppinen, en este artículo sostenemos, en primer lugar, que la (...) supuesta incapacidad de la Filosofía Experimental para acceder a las intuiciones robustas de los hablantes tiene que ver en gran medida con los métodos experimentales empleados hasta ahora por los filósofos experimentales. En segundo lugar, defendemos que el proyecto de reforma llevado a cabo desde la Filosofía Experimental resultará viable solo si se adoptan una serie de consejos metodológicos procedentes de la economía experimental. Únicamente entonces podrán los experimentalistas responder con éxito a la objeción de Kauppinen. (shrink)

En el marco del V Congreso Internacional «La actualidad de Michel Foucault» celebrado en la Universidad Complutense de Madrid entre el 6 y el 8 de marzo de 2018, sostuvimos una interesante conversación con Daniel Lorenzini, investigador del pensamiento ético y político de Michel Foucault y editor de varios de sus cursos y conferencias publicadas en los últimos años en Francia. Discutimos sobre el estado actual de los archivos de Foucault adquiridos por la Biblioteca Nacional de Francia (BnF), algunos de (...) los diversos proyectos editoriales que se derivan del trabajo de archivo y análisis de los manuscritos del filósofo, la reciente e inesperada publicación de Les aveux de la chair y su relación con el proyecto de la Historia de la sexualidad tal como fue planteado en 1976, la relación de Foucault con Nietzsche respecto a sus lecturas de la subjetivación y el vínculo, no siempre evidente, entre ética y política a la luz de sus investigaciones sobre el filósofo francés. (shrink)

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