Theoria: An International Journal for Theory, History and Foundations of Science

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”.

Armstrong (1983) poses two requirements that law-statements must satisfy in order to support the corresponding counterfactuals. He also argues that law-statements can not satisfy one of these requirements if they merely express regularities, although both requirements are satisfied if law-statements are interpreted as expressing relations between universals. I try to show that Armstrong’s argument can be raised against Armstrong’s own solution by adding three premisses to it: the inference thesis, the contingency thesis and a principle whose rationality I also argue for. Finally, I offer a more reasonable alternative condition for nomic counterfactual supporting which is satisfied by law-statements if they are interpreted as expressing relations between universals, but not so if we interpret them as mere regularities.

En este artículo pretendo analizar ciertos elementos de la tematica correspondiente a la noción de parte temporal. En la primera parte estudio dicha noción y describo las tesis principales con las que los partidarios de la teoría de partes temporales se comprometen al respecto, En la segunda parte expongo algunas críticas contra la existencia de partes temporales presentadas por los partidarios de continuantes e intento mostrar que o bien estas críticas parten de ciertas confusiones que las hacen insatisfactorias o bien son perfectamente salvables desde el marco tetradimensionalista. Me centro especialmente en las criticas de J.J. Thomson, P. Geach, D. Mellor y S. Haslanger, que hacen referencia a las cuestiones acerca deI supuesto carácter instantaneo de las partes temporales, su existencia ex nihilo, la analogía espacio-temporal y la causalidad humeana.In this paper some answers to certain arguments against temporal parts are presented. The first part explores the very notion of temporal part and tries to describe the main tenets that friends of temporal parts hold. The second one develops sonze criticisms that friends of continuants have expoused against those entities and argues that most of these criticisms mischaracterize the problems at issue. The discussion focuses on J.J. Thomson’s, P. Geach’s, D. Mellor’s and S. Haslanger’s arguments about the impossibility of procesualism to escape from some problematic commitents like instantaneous parts, ex nihilo existences, time-space analogies and humean causes. Nevertheless I will try to show that some of this consequences do not folIow and that some other are seen not to be as threatening as they might first have appeared.

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.

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.

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.

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.