La interpretación logicista propuesta por Keynes condujo a un modelo en el que la probabilidad se traduce en un grado de creencia racional concebido como una relación entre un cuerpo de conocimiento y una proposición o conjunto de proposiciones. Un análisis detenido del “Treatise on probability” permite concluir: i) que el modelo Keynesiano no sólo es una consecuencia, sino que constituye una extensión de los “Principia mathematica” y los “Problems of philosophy” en la que la aproximación al concepto de probabilidad es perfectamente asimilable a la aproximación de Russell y Whitehead a la matemática y ii) que, más allá de la naturaleza innegablemente metafísica, la representación numérica de la probabilidad logicista comprende un número muy restringido de casos, debido a la calidad de heurístico del principio de indiferencia.

It is the purpose of this article to set forth the initial ideas and implications of a mathematical theory first expounded in the RAND Corporation Research Memorandum RM900. In that paper, and in the abstract [3], we refer to the theory as a theory of behavior; and this is a more adequate description. For, not only does the theory purpose to locate the concept of probability properly in the context of reality; it also provides a truer precisement of the concept of human motivation-what in the literature of economics and econometrics is designated by the word «utility»; and it implies an inherent discreteness attending all real behavior, in agreement with the quantum theory of physics.

In what follows, we present, in a rather rough and preliminary way, some general remarks on a quite delicate issue: semantics. To some extent, as will be clear anyway as we proceed, we are here concerned with formulating and spelling out some questions, problems and ideas on this topic, rather than considering their possible solutions. Our basic aim thus consists in just pointing out to some problems that, as far as we see, deserve to be considered and examined — a project, in fact, for a series of works. This explains, or so we hope, the rather concise style adopted throughout the piece.

Perhaps the most significant, if not the most important, achievements in chemistry and physics are the Periodic Table of the Elements in Chemistry and the Standard Model of Elementary Particles in Physics. A comparable achievement in mathematics is the Periodic Table of Geometric Numbers discussed here. In 1878 William Kingdon Clifford discovered the defining rules for what he called geometric algebras. We show how these algebras, and their coordinate isomorphic geometric matrix algebras, fall into a natural periodic table, sidelining the superfluous definitions based upon tensor algebras and quadratic forms.

April 25, 2003, marked the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov, the twentieth century’s foremost contributor to the mathematical and philosophical foundations of probability. The year 2003 was also the 70th anniversary of the publication of Kolmogorov’s Grundbegriffe der Wahrscheinlichkeitsrechnung. Kolmogorov’s Grundbegriffe put probability’s modern mathematical formalism in place. It also provided a philosophy of probability – an explanation of how the formalism can be connected to the world of experience. In this article, we examine the sources of these two aspects of the Grundbegriffe – the work of the earlier scholars whose ideas Kolmogorov synthesized.

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.

In this survey paper we give an historical and at the same time thematical overview of the development of ring geometry from its origin to the current state of the art. A comprehensive up-to-date list of literature is added with articles that treat ring geometry within the scope of incidence geometry.

The first seeds of mathematical intuitionism germinated in Europe over a century ago in the constructive tendencies of Borel, Baire, Lebesque, Poincaré, Kronecker and others. The flowering was the work of one man, Luitzen Egbertus Jan Brouwer, who taught mathematics at the University of Amsterdam from 1909 until 1951. By proving powerful theorems on topological invariants and fixed points of continuous mappings, Brouwer quickly build a mathematical reputation strong enough to support his revolutionary ideas about the nature of mathematical activity. These ideas influenced Hilbert and Gödel and established intuitionistic logic and mathematics as subjects worthy of independent study. Our aim is to describe the development of Brouwer’s intuitionism, from his rejection of the classical law of excluded middle to his controversial theory of the continuum, with fundamental consequences for logic and mathematics.

With a series of important papers in the 1960s, Jaakko Hintikka initiated a surge of interest in Kant’s philosophy of mathematics, developing an interpretation which has in some ways defined the field. Because I can’t do justice to all of the details of Hintikka’s view here, I propose to stand back and consider the broader context. In a later paper revisiting the topic, Hintikka complained that subsequent discussions of his interpretation of Kant paid no attention to “the overall picture of Kant’s thinking about mathematics in its historical setting or to my view of the role of Kant’s theory of space, time, and mathematics (including the whole of his transcendental aesthetics) within the structure of his philosophical system”

Este artículo presenta una reconstrucción de las principales tesis del pensamiento de Lambert y sus contribuciones a la formación de la filosofía teórica de Kant. Para ello, el artículo se divide en tres partes. En un primer momento, se desarrolla una consideración del intento de Lambert de garantizar la ilusión (Schein) en el campo de la fenomenología (Körperwelt) y de instituir el dominio de la verdad metafísica (Intellectualwelt). En un segundo momento, se considera el primer paso de Kant en su alejamiento de la propuesta de Lambert, que se presenta en la tesis de la Disertación Inaugural de que los campos sensibles e intelectuales de los conocimientos se basan en dos facultades distintas y intransmutables. Por último, se trata del paso final de Kant en su alejamiento de la propuesta de Lambert, esto es, de la justificación de los fenómenos en Duisburg Nachlaβ en un dominio objetivo y no ilusorio, debido a la determinación de la facultad de entendimiento.