Dialectica 

About: Dialectica is an academic journal published by Wiley-Blackwell. The journal publishes majorly in the area(s): Argument & Physicalism. It has an ISSN identifier of 0012-2017. Over the lifetime, 1430 publications have been published receiving 15354 citations.

More about metaphor

Abstract: Summary An elaboration and defense of the “interaction view of metaphor” introduced in the author's earlier study, “Metaphor” (1962). Special attention is paid to the explication of the metaphors used in the earlier account. The topics discussed include: selection of the “targets” of the theory; classification of metaphors; how metaphorical statements work; relations between metaphors and similes; metaphorical thought; criteria of recognition; the “creative” aspects of metaphors; the ontological status of metaphors. Metaphors are found to be more closely connected with background models than has previously been recognized.

Structural Realism: The Best of Both Worlds?*

Abstract: Summary The main argument for scientific realism is that our present theories in science are so successful empirically that they can’t have got that way by chance - instead they must somehow have latched onto the blueprint of the universe. The main argument against scientific realism is that there have been enormously successful theories which were once accepted but are now regarded as false. The central question addressed in this paper is whether there is some reasonable way to have the best of both worlds: to give the argument from scientific revolutions its full weight and yet still adopt some sort of realist attitude towards presently accepted theories in physics and elsewhere. I argue that there is such a way - through strucfurul realism, a position adopted by PoincarC, and here elaborated and defended. Resume L’argument principal en faveur du realisme scientifique, c’est que nos theories scientifiques actuelles sont empiriquement si efficaces que cela ne peut pas Etre di3 au hasard - on doit en quelque sorte avoir decouvert les plans de I’univers. L’argument principal contre le realisme scientifique, c’est qu’il y a eu des theories scientifiques massivement efficaces qui ont ete autrefois tenues pour vraies mais sont considerkes aujourd’hui comme fausses. La principale question traitee dans ce papier, c’est s’il y a un moyen raisonnable de prendre le meilleur des deux mondes: de donner tout son poids a l’argument tire des revolutions scientifiques et d’adopter pourtant une sorte d’attitude realiste a I’egard des theories actuellement acceptkes en physique ou ailleurs. Je rnontre qu’une telle voie existe: le realisme sfrucfurel, une position adoptke par Poincare, que je defends et dkveloppe ici. Zusammenfassung Das Hauptargument fur wissenschaftlichen Realismus ist, dass unsere gegenwartigen Theorien in der Wissenschaft empirisch so erfolgreich sind, dass sie nicht zuftilligerweise so geworden sein kdnnen - statt dessen miissen sie irgendwie mit dem Plan des Universums Ubereinstimmen. Das Hauptargument gegen den wissenschaftlichen Realismus ist, dass es ausgesprochen erfolgreiche Theorien gegeben hat, die einmal akzeptiert gewesen waren, aber jetzt als falsch betrachtet werden. Die in diesem Papier behandelte Kernfrage lautet, ob es einen verniinftigen Weg gibt, aus beiden Weltcn das Beste zu haben: dem Argument vom Vorhandensein wissenschaftlicher Revolutionen sein volles Gewicht zu geben und dennoch eine Art von realistischer Einstellung gegeniiber den heute in der Physik und anderswo akzeptierten Theorien einzunehmen. Ich argumentiere, dass es einen solchen Weg gibt - durch den von Poincart iibernommenen strukturellen Realismus, der hier ausgearbeitet und verteidigt wird.

Über eine bisher noch nicht benützte erweiterung Des finiten standpunktes

Abstract: Zusammenfassung P. Bernays hat darauf hingewiesen, dass man, um die Widerspruchs freiheit der klassischen Zahlentheorie zu beweisen, den Hilbertschen flniter Standpunkt dadurch erweitern muss, dass man neben den auf Symbole sich beziehenden kombinatorischen Begriffen gewisse abstrakte Begriffe zulasst, Die abstrakten Begriffe, die bisher fur diesen Zweck verwendet wurden, sinc die der konstruktiven Ordinalzahltheorie und die der intuitionistischer. Logik. Es wird gezeigt, dass man statt deesen den Begriff einer berechenbaren Funktion endlichen einfachen Typs uber den naturlichen Zahler benutzen kann, wobei keine anderen Konstruktionsverfahren fur solche Funktionen notig sind, als einfache Rekursion nach einer Zahlvariablen und Einsetzung von Funktionen ineinander (mit trivialen Funktionen als Ausgangspunkt). Abstract P. Bernays has pointed out that, in order to prove the consistency of classical number theory, it is necessary to extend Hilbert's finitary stand-point by admitting certain abstract concepts in addition to the combinatorial concepts referring to symbols. The abstract concepts that so far have been used for this purpose are those of the constructive theory of ordinals and those of intuitionistic logic. It is shown that the concept of a computable function of finite simple type over the integers can be used instead, where no other procedures of constructing such functions are necessary except simple recursion by an integral variable and substitution of functions in each other (starting with trivial functions).

Adjointness in Foundations

Abstract: In this article we see how already in 1967 category theory had made explicit a number of conceptual advances that were entering into the everyday practice of mathematics. For example, local Galois connections (in algebraic geometry, model theory, linear algebra, etc.) are globalized into functors, such as Spec, carrying much more information. Also, “theories” (even when presented symbolically) are viewed explicitly as categories; so are the background universes of sets that serve as the recipients for models. (Models themselves are functors, hence preserve the fundamental operation of substitution/composition in terms of which the other logical operations can be characterized as local adjoints.) My 1963 observation (referred to by Eilenberg and Kelly in La Jolla, 1965), that cartesian closed categories serve as a common abstraction of type theory and propositional logic, permits an invariant algebraic treatment of the essential problem of proof theory, though most of the later work by proof theorists still relies on presentation-dependent formulations. This article sums up a stage of the development of the relationship between category theory and proof theory. (For more details see Proceedings of the AMS Symposium on Pure Mathematics XVII (1970), pp. 1–14, and Marcel Dekker, Lecture Notes in Pure and Applied Mathematics, no. 180 (1996), pp. 181–189.) The main problem addressed by proof theory arises from the existential quantifier in “there exists a proof. . . ”. The strategy to interpret proofs themselves as structures had been discussed by Kreisel; however, the influential “realizers” of Kleene are not yet the usual mathematical sort of structures. Inspired by Lauchli’s 1967 success in finding a completeness theorem for Heyting predicate calculus lurking in the category of ordinary permutations, I presented, at the 1967 AMS Los Angeles Symposium on Set Theory, a common functorization of several geometrical structures, including such proof-theoretic structures. As Hyperdoctrines, those structures are described in the Proceedings of the