This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

Jaakko Hintikka, in a series of talks in Brazil in 2008, defended that IF logic and paraconsistent logic are, in a sense, very similar. Having sketched the proposal of a new paraconsistent system, he maintains that several achievements of IF logic could be reproducible in paraconsistent logic. One of the major difficulties, left as a challenge, would be to formulate some truth conditions for this new paraconsistent first-order language in order to make IF logic and paraconsistent logic more inter-related. My (...) proposal is that this would demand an innovative game-theoretical semantic approach to paraconsistentism, but also that the syntax of the paraconsistent “Logics of Formal Inconsistency” can model the internal logic of Socratic elenchi. I aim to discuss these, and other points posed by Hintikka, as challenges and opportunities for paraconsistentism, paraconsistent logics and IF logics, as well as to raise some criticisms on Hintikka’s view about paraconsistency. (shrink)

La exposición y crítica de las doctrinas antiguas tiene un lugar importante en los escritos de Aristóteles. Sin embargo, ciertas dudas se han vuelto corrientes acerca de la confiabilidad de sus descripciones. Más aún, se ha sostenido que Aristóteles deforma la comprensión histórica a través de la introducción de conceptos y términos propios. En este libro se aborda el problema a través de un análisis de las críticas que Aristóteles dirige a la teoría platónica de las Ideas, que permite explicar (...) la constitución y desarrollo de importantes conceptos aristotélicos a partir de la confrontación dialéctica con las doctrinas de su maestro. En efecto, las dificultades genuinas que Aristóteles descubre en el platonismo constituyen el motor para gestar nuevos conceptos, que no son ajenos, sino que surgen como implicaciones del examen crítico. Así, la imposición de términos propios no debe interpretarse como distorsión, sino como el modo que Aristóteles adopta para exhibir su particular solución a los problemas que los filósofos anteriores dejaron sin solución. (shrink)

Essence and causes in and through the movements in Nature. From Aristotle and in dialogue with Alicia Juarrero: According to Aristotle there is an intrinsic relation between ordinary language, logic and ontology, which is a key element for the knowledge of reality. Such a relation is applied by the Stagirite in the sphere of nature as support for the analysis made by the incipient natural sciences of his time. Thus, Aristotle provided a unitary conception of nature and the sciences which (...) study it. His contributions are still relevant for the study of nature. This paper tries to show the present validity of the Aristotelian thought, provided it is understood in the appropriate way. This attempt is made by means of confronting Aristotle’s ideas with those of a contemporary proposal, namely Juarrero’s, which has nevertheless a similar intention. (shrink)

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aris... (shrink)

(1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is valid, it is not useful. This conclusion, (3), is unacceptable. Since the argument is valid, we must reject at least one premise. So, should we reject (1) or (2)? This puzzle is usually known as the ‘scandal of deduction’. Analytic philosophers have tried to reject (1) (...) but have assumed premise (2). I argue here that Aristotle would deny (2). Aristotle thinks that at least some deductive arguments are useful, even though they present no new conclusions. Thus, Aristotle’s view contrasts with analytic philosophers of logic, who assume that all useful deductive arguments present novel conclusions. I don’t claim that Aristotle ‘solves’ the problem: it was never posed in Aristotle’s time. Rather, I suggest that Aristotle does not face the problem because he assumes deductions can be useful, without presenting novel conclusions. Aristotle’s view of deduction tames the scandal. (shrink)

Sweet Analytics, ‘tis thou hast ravish'd me,Bene disserere est finis logices.Is to dispute well logic's chiefest end?Affords this art no greater miracle?(Christopher Marlow, Doctor Faustus, Act 1,...

A few days before his death my husband requested me to write a few words of thanks on the publication of this collection of articles. He had already prepared the greater part of the volume for the press and had also decided on the title Science a Road to Wisdom. His original selection was somewhat more comprehensive, which is still partly reflected in the Preface. Knowing how much he wished to see this collection published, I respectfully and lovingly fulfil his (...) request, thanking Else M. Barth and J. J. A. Mooij for their extensive and expert care in putting the final touches to the volume. ADDITION TO THE TRANSLATION Finally, I wish to thank Peter G. E. Wesly for his willingness to undertake the translation of the book into English. c. P. C. BETH-PASTOOR IX PREFACE In this republication of a number of philosophical studies I have refrained from including articles of a specialized nature on symbolic logic and the methodology of the exact sciences. There was no cause to include my contributions towards the didactics of mathematics and physics, nor did I consider it appropriate to reprint pieces of a predominantly polemical nature. I decided, however, that a very modest selection from my purely historical work would not be out of place. (shrink)

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..

This is a translation of an article published in the journal Argeiaki Ge, which was asked from me by the scientific journal Journal of Classical Studies Matica Srpska. The Argive Hapocration was a philosopher and commentator from the second century A.D. His origin is not disputed by any source. However, there is still a potential possibility that he might have descended from a different Argos: namely that which is in Amfilochia, Orestiko or that in Cyprus. Yet, the absence of any (...) additional geographical designation in his name in ancient sources is likely to disprove such claims. Simply mentioning ‘Argos’ can only indicate the most notable of the cities with this name, namely the Argive Argos. As will be revealed later in this paper, the close relationship between Hapocration with the Atticus family may well support his Argive origin. I support that it is obvious to assume that there is a close affinity of philosophical activity in Phlius and in Argos which remains to be investigated in more detail in the future. The research of written and archaeological sources can flourish further still. I hope that in the near future there will be evidence enough for a fuller presentation of philosophical activity in ancient Argos. (shrink)