The origin of Paraconsistent Logic is closely related with the argument that from the assertion of two mutually contradictory statements any other statement can be deduced, which can be referred to as ex contradict!one sequitur quodlibet (ECSQ). Despite its medieval origin, only in the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this paper is to study what happened before: from Principia Mathematica to that time, when it became (...) well established. The main historical claims that I am going to advance are the following: the first explicit use of ECSQ as the main argument for supporting the necessity of excluding any contradiction from deductive systems is to be found in the first edition (1928) of the book Grundzüge der theoretischen Logik by Hilbert and Ackermann. At the end, I will suggest that the aim of the 20th century usage of ECSQ was to change from the centuries long philosophical discussion about contradictions to a more "technical" one. But with Paraconsistent Logic viewed as a technical solution to this restriction, the philosophical problem revives, but now with an improved understanding of it at one's disposal. (shrink)
Rips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.
It is said that Europe finds itself today in a post-christian situa-tion. Further, there are many who advocate abandoning monotheism in order to get back to prechristian polytheism in the hope that the plurality of gods would favour a democratic tolerance in a pluralistic world. In this article the author firstly asks if European Christians have not gone back to adoring idols and to attempting to distinguish between them in the new forms of devotion to possessiveness, to power and to (...) pleasure. He then goes on to ask about the possibilities of pro-claiming the God of Jesus Christ. The third and the fourth part of the article point out several forms of necessary witness to God in contemporary society, with special reference made to European society in the conclusion. (shrink)
Misuse or misunderstanding of medication information is a common and costly problem in the U.S. The risks of misunderstanding medication information are compounded for the large and growing population of individuals with limited English proficiency that often lacks access to this information in their own language. This paper examines practices related to translation of medication information in the European Union that may serve as a model for future U.S. policy efforts to improve the quality and availability of medication information for (...) individuals with limited English proficiency. (shrink)
Este trabajo se ocupa de algunas ideas éticas del filósofo latinoamericano Andrés Bello (1781-1865), en especial de su “teoría de los sentimientos morales”. En la polémica del siglo XIX entre el llamado racionalismo ético (representado por Théodore Jouffroy) y el utilitarismo (Bentham), Bello adopta una postura intermedia, que pudiera calificarse de “hedonismo moderado” o de “eudemonismo”. Sus puntos de vista sobre la motivación moral o la manera en que la razón y el sentimiento se entrelazan para formar nuestras creencias (...) morales, se revelan como muy próximos a las doctrinas de Aristóteles y de algunos autores contemporáneos. (shrink)
The origin of paraconsistent logic is closely related with the argument, 'from the assertion of two mutually contradictory statements any other statement can be deduced'; this can be referred to as ex contradictione sequitur quodlibet (ECSQ). Despite its medieval origin, only by the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this article is to study what happened earlier: from Principia Mathematica to that time, when it became well (...) established. The two main historical claims that I am going to advance are the following: (1) the first explicit use of ECSQ as the main argument for supporting the necessity of excluding any contradiction from deductive systems is to be found in the first edition of the book Grundz ge der Theoretischen Logik (Hilbert, D. and Ackermann, W. 1928. Grundz ge der Theoretischen Logik . Berlin: Julius Springer Verlag); (2) ukasiewicz's position regarding the logical constraints against contradictions varies considerably from his studies on the principle of (non-) contradiction in Aristotle, published in 1910 and what is stated in his 'authorized lectured notes' on mathematical logic that appeared in 1929. The two texts are: 1) a paper in German ( ukasiewicz, J. 1910. ' ber den Satz des Widerspruchs bei Aristotles'. Bulletin International de l'Acad mie des sciences de Cracovie, Classe d'Histoire et de Philosophie, pp. 15-38) [English translation: ukasiewicz, J. 1971. 'On the principle of contradiction in Aristotle', Review of Metaphysics , XXIV , 485-509]; and 2) a book in Polish. ukasiewicz, J. 1910. O zasadzie sprzecznosci u Aristotelesa Studium krytyczne , Warsaw: Panstwowe Wydawnictwo Naukowe [German translation: ukasiewicz, J. 1993. ber den Satz des Widerspruchs bei Aristotles . Hildesheim: Georg Olms Verlag]. The lecture notes were then published as a book ( ukasiewicz, J. 1958. Elementy Logiki Matematycznej . Warszawa: Panstwowe Wydawnictwo Naukowe [PWN] and then translated into English ( ukasiewicz, J. 1963. Elements of Mathematical Logic. Oxford, New York: Pergamon Press/The Macmillan Company) . The second half of this article will concentrate on ukasiewicz's position on ECSQ. This will lead me to propose that to regard him as a forerunner of paraconsistent logic by virtue of those early writings is accurate only if his book published in Polish is considered but not if the analysis is restricted to the paper originally published in German (as has been the case for the principal reconstructions of the history of paraconsistent logic). Furthermore, I will stress that in the 1929 book he presented one formalization of ECSQ as an axiom for sentential calculus and, also, he used ECSQ to defend the necessity of consistency, apparently independently of Hilbert and Ackermann's book. At the end, I will suggest that the aim of twentieth century usage of ECSQ was to change from the centuries-long philosophical discussion about contradictions to a more 'technical' one. But with paraconsistent logic viewed as a technical solution to this restriction, then, the philosophical problem revives but having now at one's disposal an improved understanding of it. Finally, ukasiewicz's two different positions about ECSQ open an interesting question about the history of paraconsistent logic: do we have to attempt a consistent reconstruction of it, or are we prepared to admit inconsistencies within it? (shrink)
The works of Argentine Arturo Andres Roig not only constitute one of the best developed examples of Latin American philosophy, but is also an important transformation to common philosophical themes. This paper explains three essential points. One is the transformation of the subject and its ro..
El trabajo analiza la obra del filósofo Arturo Andrés Roig, recientemente fallecido, desde la perspectiva del humanismo latinoamericano, corriente de pensamiento crítico de fuerte presencia en América Latina. El núcleo de la propuesta teórica de Roig está dado por la problemática del sujeto o, como ..
Se busca rastrear la imagen que Platón tiene de Heráclito y articularla con la estructura argumentativa del Cratilo, para comprender las necesidades textuales a las que responde la doctrina del flujo perpetuo, es decir, la discusión sobre la corrección (ὀρθότης) del nombre. Gracias a la inclusión del testimonio heraclíteo, resulta posible rastrear la presunta consolidación de la tesis sobre los nombres primarios y los secundarios como el eje de la separación entre dos planos de realidad (uno estable y uno móvil) (...) y de la teoría de las Ideas -es decir, como la base de la epistemología platónica presente en los diálogos de madurez-. The article seeks to trace the image Plato has of Heraclitus and connect it with the argumentative structure of the Cratylus in order to understand the textual needs that give rise to the doctrine of perpetual flux, that is, the discussion regarding the correctness (ὀρθότης) of names. The inclusion of Heraclitus's testimony makes it possible to trace the alleged consolidation of the thesis regarding primary and secondary names as the axis of separation between two levels of reality (one stable, the other, changing) and the theory of Ideas -that is, as the basis of Plato's epistemology as set forth in the late dialogues-. (shrink)
Upshot: This is a book for thoughtful science and mathematics teachers and curriculum developers and educational philosophers. Quale helps us to challenge pernicious received “truths‘ and offers us intriguing perspectives, valuable discourse ventures and practical paedagogic strategies to engage the youth of today who are turning away from science in droves, to their and our cost.