This paper focuses on Aristotle’s discussion of PNC in Metaphysics Gamma and argues that the argument operates at three different levels: ontological, doxastic, and semantic through the invocation of three philosophical personae: the first one can only state what is otherwise unprovable, the second one can only confirm that we should trust PNC, the third one denies PNC and must be silenced. Aristotle cannot prove what is beyond proof. This situation results in a fundamental ambiguity in the figure of the (...) philosopher. The Metaphysics is written from the standpoint of an investigative thinker who admits her puzzlement before a question that will forever remain open and imagines another philosopher who has achieved a god-like insight into the first principles of all things. The path from the first figure to the second one, however, remains an enigmatic leap. (shrink)

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

En su defensa del Principio de no-contradicción, Aristóteles discute con varios interlocutores, desde los presocráticos hasta el sofista Protágoras, este último ampliamente conocido en la Antigüedad por trastocar el concepto de verdad con su doctrina del “homo mensura”, declarando así la imposibilidad del discurso falso. Consideramos que una lectura atenta del Libro Γ que rescate la figura del abderita puede mostrar cómo la crítica del sofista es clave para la constitución del pensamiento aristotélico en torno al problema de la verdad. (...) En la primera sección expondré algunas consideraciones sobre el PNC que son relevantes para entender las motivaciones detrás de las críticas aristotélicas al sofista. A continuación, analizaré dos de los argumentos aristotélicos contra los adversarios que discuten de mala fe: por una parte, la “refutación” de Metaph. Γ. 4 y, por otra parte, el “argumento de las apariencias contrarias” de Metaph. Γ. 5. Mi hipótesis es que algunos elementos teóricos esbozados en Γ. 4 permiten reconstruir una crítica aristotélica seria contra Protágoras en Γ. 5. Finalmente expondré una síntesis del camino recorrido y ofreceré algunas conclusiones. (shrink)