Hemeroteca de la sección ‘Educacion’

Church’s Theorem and the Analytic-Synthetic distinction in Mathematics

Por • 13 ago, 2018 • Category: Educacion

” Kant’s classification of mathematical truth as synthetic a priori has given rise to a very considerable literature on the subject. We will limit ourselves here to discussing a recent attempt to vindicate Kant in terms of certain results in contemporary first order logic. In a series of letures delivered at Oxford in the early sixties, J. Hintikka has proposed formal explications of the Kantian distinction between analytic and synthetic truths and arguments. Entitled “An Analysis of Analyticity”, “Are Logical Truths Tautologies? “, “Kant Vindicated”, and “Kant and the Tradition of Analysis”, these lectures now form a central part of Hintikka’s book Logic, Language Games and Infom1ation : Kantian Themes in the Philosophy of Logic(Oxford, 1973); henceforth references to Hintikka’s presentation will simply be given by the appropriate page number in the book. We shall first give an overview of Hintikka’s arguments, then examine then criticallly, and finally argue for Church’s Theorem as a superior formal vindication of Kant’s position.

L’Implication Matérielle et L’Implication Logique

Por • 6 ago, 2018 • Category: Educacion

La logique classique n’a réussi à systématiser, d’une manière satisfaisante, ni un groupe suffisamment vaste de propositions logiquement vraies, ni un ensemble suffisamment étendu de procédés d’inférence pouvant être appliqués au cours d’un raisonnement déductif. Cet échec est dû au fait qu’on se sert, dans la logique classique, de l’opérateur de l’implication matérielle, lequel ne correspond que d’une façon approximative à l’expression {< si, alors >}.

Levels of spacetime emergence in quantum gravity

Por • 21 jul, 2018 • Category: Educacion

We explore the issue of spacetime emergence in quantum gravity, by articulating several levels at which this can be intended. These levels correspond to the reconstruction moves that are needed to recover the classical and continuum notion of space and time, which are progressively lost in a progressively deeper sense in the more fundamental quantum gravity description. They can also be understood as successive steps in a process of widening of the perspective, revealing new details and new questions at each step. Each level carries indeed new technical issues and opportunities, and raises new conceptual issues. This deepens the scope of the debate on the nature of spacetime, both philosophically and physically.

Kolmogorov and Mathematical Logic

Por • 7 jul, 2018 • Category: Educacion

There are human beings whose intellectual power exceeds that of ordinary men. In my life, in my personal experience, there were three such men, and one of them was Andrei Nikolaevich Kolmogorov. I was lucky enough to be his immediate pupil. He invited me to be his pupil at the third year of my being student at the Moscow University. This talk is my tribute, my homage to my great teacher. Andrei Nikolaevich Kolmogorov was born on April 25, 1903. He graduated from Moscow University in 1925, finished his post-graduate education at the same University in 1929, and since then without any interruption worked at Moscow University till his death on October 20, 1987, at the age 84-. Kolmogorov was not only one of the greatest mathematicians ofthe twentieth century. By the width of his scientific interests and results he reminds one of the titans of the Renaissance. Indeed, he made prominent contributions to various fields from the theory of shooting to the theory of versification, from hydrodynamics to set theory. In this talk I should like to expound his contributions to mathematical logic.

A marriage of category theory and set theory: a finitely axiomatized nonclassical first-order theory implying ZF

Por • 4 jul, 2018 • Category: Educacion

The main purpose of this paper is to introduce a finitely axiomatized theory that might be applicable as a foundational theory for mathematics. For that matter, some twenty axioms in a formal language are introduced, which are to hold in a universe consisting of a class of objects, each of which is a set, and a class of arrows, each of which is a function on a set. One of the axioms is nonclassical: it states that, given a family of ur-functions – i.e. functions on a singleton – with disjunct domains, there exists a uniquely determined sum function on the union of these domains. This ‘sum function axiom’ is so powerful that it allows to derive ZF from a finite axiom scheme.

Arturo Pérez-Reverte: Ahora le toca a la lengua española

Por • 30 jun, 2018 • Category: Educacion

No me había dado cuenta hasta que hace unos días, mientras lamentaba las incorrecciones ortográficas de una cuenta oficial en Twitter de un ministerio, leí un mensaje que acababan de enviarme y que me causó el efecto de un rayo. De pronto, con un fogonazo de lucidez aterradora, fui consciente de algo en lo que no había reparado hasta ese momento. El mensaje decía, literalmente: «Las reglas ortográficas son un recurso elitista para mantener al pueblo a distancia, llamarlo inculto y situarse por encima de él».

Lógica y Filosofía en Whitehead

Por • 25 jun, 2018 • Category: Educacion

Alfred North Whitehead, figura destacada entre los pioneros y grandes maestros de la Lógica Matemática, es también un filósofo importante, quizás uno de los más notables de nuestro siglo. Quienes hemos estudiado su obra en profundidad sabemos que no existe una separación neta y tajante entre su Lógica y su Filosofía. Whitehead no es un autor que se haya dedicado primero a las Matemáticas y a la Lógica y luego las haya abandonado sin más para volcarse en especulaciones filosóficas.En realidad, se revela como un auténtico fIlósofo desdelos comienzosde su actividad intelectual. Justamente por ello, nos parece de máximo interés precisarlas relaciones entre Lógicay Filosofía en Whitehead, ver de qué manera interviene la Lógicaen su Filosofía y determinar hasta qué punto el lógico pesa sobre el filósofo o el lógico y el fIlósofo van a la par.

Current Trends and Open Problems in Arithmetic Dynamics

Por • 20 jun, 2018 • Category: Educacion

Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from p-adic analogues of theorems and conjectures in classical complex dynamics. In this article we survey some of the motivating problems and some of the recent progress in the field of arithmetic dynamics.

Teoría de los requisitos en Leibniz

Por • 4 jun, 2018 • Category: Educacion

La noción de requisito, heredada de la tradición escolástica, desempeña un papel fundamental en la epistemología y en la ontología de Leibniz. Analizamos aquí la teoría de los requisitos elaborada por Leibniz en los dos períodos: 1669-1679; y 1679-1689. En el primero, la noción de requisito va ligada a las nociones de razón y causa. La estructuración de estas nociones permite a Leibniz tomar distancia respecto de las teorías, cartesiana y spinoziana sobre la causa y sobre Dios como causa sui. En el segundo período, Leibniz reformula su teoría de los requisitos para encajarla en su teoría de la definición real, y poder así distanciarse del método cartesiano de las ideas, y del nominalismo de Hobbes.

Geometry and Physics: An Overview

Por • 30 may, 2018 • Category: Educacion

We present some episodes from the history of interactions between geometry and physics over the past century