En este artículo me propongo revisar en qué medida cabría atribuir a Wittgenstein la responsabilidad de haber propiciado un «giro retórico» con sus inquisiciones filosóficas, correlativo al giro más general, en el mismo sentido, que, según recientemente se ha venido reconociendo, habría sufrido nuestra cultura en los últimos tiempos. Dado que cabe leer la obra de Wittgenstein como si una de sus más pujantes preocupaciones consistiese en dilucidar qué debemos entender hoy por racionalidad, el mentado «giro retórico», de haberse cumplido (...) en él, podría leerse como algo que atañe cardinalmente a tal cuestión. Explicaremos primeramente, pues, en qué consiste efectuar un giro retórico en la filosofía acerca de la racionalidad; para trasladarnos posteriormente a sopesar la presencia de tal giro en Wittgenstein (y de Wittgenstein en tal giro). (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...) with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

As a philosophy of mathematics, strict finitism has been traditionally concerned with the notion of feasibility, defended mostly by appealing to the physicality of mathematical practice. This has led the strict finitists to influence and be influenced by the field of computational complexity theory, under the widely held belief that this branch of mathematics is concerned with the study of what is “feasible in practice”. In this paper, I survey these ideas and contend that, contrary to popular belief, complexity theory (...) is not what the ultrafinitists think it is, and that it does not provide a theoretical framework in which to formalize their ideas —at least not while defending the material grounds for feasibility. I conclude that the subject matter of complexity theory is not proving physical resource bounds in computation, but rather proving the absence of exploitable properties in a search space. (shrink)