This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence.

Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional logic -results traditionally credited to Bernays (1918) and Post (1921). These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its soundness and completeness: a sentence is provable if and only if valid. By 1917, strongly influenced by PM, Hilbert accepted the theory of types and logicism -a surprising shift. But by 1922 he abandoned the axiom of reducibility and then drew back from logicism, returning to his 1905 approach of trying to prove the consistency of number theory syntactically.

The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory (with particular attention to Carnap and Tarski), Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though he would shortly abandon that viewpoint and promote first-order logic as all of logic. Quine’s class-theoretic systems NF and ML, and his farewell to logicism, are examined. The last section attempts to summarize the motives why set theory was preferred to other systems, and first orderlogic won its position as the paradigm logic system after the great War.

Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal (symbolic, mathematical) logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical means. As a result formallogic was taken over by mathematics in the beginning of the 20th century as is shown by sketching the German example.

In this paper, Tarskis notion of Logical Consequence is viewed as a special case of the more general notion of being a theorem of an axiomatic theory. As was recognized by Tarski, the material adequacy of his definition depends on having the distinction between logical and non logical constants right, but we find Tarskis analysis persuasive even if we dont agree on what constants are logical. This accords with the view put forward in this paper that Tarski indeed captures the more inclusive notion of theoremhood in an axiomatic theory. The approach to logical consequence via axiomatic theories leads us to grant centrality to inference schemas rather than to full-fledged arguments and to view the logically valid schemas as a subclass of generally valid schemas.

Nonreductive naturalism holds that we can preserve the (scientifically valued) metaphysical truth of physicalism while averting the methodological mistakes of reductionism. Acceptable scientificexplanation need not (in some cases cannot and in many cases, should not) be formulated in the language of physical science. Persuasive arguments about the properties of phenomenal consciousnesspurport to show that physicalism is false, namely that phenomenal experience is a nonphysical fact. I examine two recent, comprehensive efforts to naturalize phenomenal consciousness and argue thatnonreductive naturalism yields a dilemma of reductionism or panpsychism.

Este artículo presenta un alnplio panorama histórico de las conexiones existentes entre ramas de las matematícas y tipos de lógica durante el periodo 1800-1914. Se observan dos corrientes principales,bastante diferentes entre sí: la lógica algebraica, que hunde sus raíces en la logique yen las algebras de la época revolucionaria francesa y culmina, a través de Boole y De Morgan, en los sistemas de Peirce y de Schröder; y la lógica matematíca, que tiene una fuente de inspiraeión en el analisis matemático de Cauchy y de Weierstrass y culmina, a través de las inieiativas de Peano y de la teoria de conjuntos deCantor, en la obra de Russell. Se extraen algunas conclusiones generales, con referencias relativas a la situaeión posterior a 1914.This article contains a broad historical survey of the connections made between branches of mathematics and types of logic during the period 1800-1914. Two principal streams are noted, rather different from each other: algebraic logic, rooted in French Revolutionary logique and algebras and culminating, via Boole and De Morgan, in the systems of Peirce and Schröder; and mathematical logic, inspired by the mathematical analysis of Cauchy and Weierstrass and culminating, via the initiatives of Peano and the set theory of Cantor, in the work of Russell. Some general conclusions are drawn, with examples given of the state of affairs after 1914.

This paper points out several difficulties to understand Putnam’s views in his recent “Dewey Lectures”, which involve a certain move away from his “internal realism”. The main goal is to set into relief tensions in Putnam’s thinking probably provoked by his philosophical development. Two such tensions are touched upon. In the first place, Putnam wants to reject an account of phenomenal consciousness (sensory experience in particular) he had subscribed to during his realist times, which he calls “Cartesianism cum Materialism”, CM. He puts forward what he takes to be an alternative, apparently based on the traditional Chisholmian “Theory of Appearing”. The paper suggest firstly that, in view of the facts to be accounted for, a theory along those lines cannot count as a real alternative to CM. In the second part, the paper develops an analogous tension between the views on truth Putnam seems to be willing to defend in the Dewey Lectures, and previous criticisms of the semantic conception of truth by hirn that heclaims still to be willing to subscribe.

Cherchant à refonder l’édifice euclidien, Leibniz a formulé une Caractéristique géométrique qui annonce les concepts géneraux de la théorie des ensembles. Dans ce cadre, il a pu en particulier formaliser sa conception du continu. L’intérêt du Pacidius Philalethi (1676) est de montrer qu’en choisissant la conception intensionnelle du continu -position qu’il ne dementira jamais- il sélectionne parmi les images duales celle dont se déduit le changement qualitatif, base d’une philosophie naturelle qui soutiendra encore la dynamique ultérieure. Une tâche se dessine maintenant, soit déduire la nécessité d’un mouvement universei et infiniment varié à partir de ses conditions topologiques.We know that Leibniz intended to bring new foundations to the euclidean geometry and he has according to this view formulate a Characteristica geometrica which announces few general concepts of set theory. Parlicularly he tried to formalise his conception of continuity. Before the main interest of the Pacidius Philalethi (1676) is here: showing us that Leibniz when he chooses an intensional conception of continuity he chooses in the same time the dual image from which be can deduce the qualitative variation. We reckon again these conception at the grounds of his later philosophy of nature. But now we have to follow Leibniz demostrating how universal and infinite variations flow from its topological conditions.

EI tratamiento que hace Descartes deI ‘yo pienso-existo’, lejos de todo proceder inferencial, nos muestra la condición propia de un pensamiento que es “res cogitans”: mi ‘asistir a’ como condición originaria de la fuerza de realidad que soy. Así, el conocimiento que tengo de mí como pensamiento es prejudicativo: no necesita afirmación alguna, sino que expresa prevolitivamente el ser-siendo, o acto, que soy como pensamiento, y que no se extiende a mi cuerpo. The treatment Deseartes does of ‘I think - I exist’ far from any inference, shows the conditioning which is proper of a “res cogitans” thought: my ‘attendance to’ as the originary conditioning of the strength of reality which I am. Thus, the Knowledge I have of myself as thought is prejudicative: it needs no affirmation but it expresses prevolitionally the ‘to be-being’, or act, that I am as thought and which does not extend to my body.

En este artículo me propongo analizar el punto de partida epistemológico de un reciente libro de Philip Kitcher (The Advancement of Science) a través de su discusión con las concepciónes ‘escépticas’. Podemos distinguir entre dos tipos de escepticismo en Ia trama deI libro de Kitcher: uno débil y otro radical. Intentamos difinir el tipo de realismo que Kitcher defiende, para finalmente mostrar que tal tipo de realismo es posible para Kitcher en Ia medida que no toma en cuenta el escepticismo en su versión radical. En efecto, Kitcher sólo se enfrenta al escepticismo débil. Y es precisamente debido a esta restricción que es capaz de mantenerse al margen de una alternativa que sigue siendo crucial: realismo fuerte o realismo “de espíritu kantiano”.The purpose of this article is to carry out an analysis of the epistemologic standpoint on a recent book by Philip Kitcher (The Advancement of Science) by discussing the sceptic ideas which are dealt with there. We can discriminate between two kinds of scepticism appearing on Kitcher’s book: a weak and a radical one. Then we work towards a definition of the kind of realism held by this author and, finally, we try to show that such a viewpoint as Kitcher’s is possible to hold provided that we do not take the radical scepticism into account for that question. Kitcher only objects by means of the weak scepticism. And it is precisely because of that restriction that he is capable of not giving a definition of a crucial alternative: strong realism or realism in “Kantian spirit”.