Andrei Kolmogorov’s Grundbegriffe der Wahrscheinlichkeits-rechnung 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.

El presente artículo examina la concepción del sujeto en el pensamiento de Jean Paul Sartre. Dicho examen se lleva a cabo, por motivos históricos y conceptuales, apelando directa e indirectamente a la filosofía de Heidegger, Husserl, et.al., siendo éste último el bastión, alterno a Sartre mismo, más importante para el desarrollo del presente texto. Así, dicho análisis del concepto de sujeto, y de sus implicaciones y conceptualizaciones fenomenológicas, se lleva a cabo a través del estudio de varias formas de conciencia: la conciencia del objeto, referida a algo distinto de sí misma, y la conciencia de sí, que, al mismo tiempo, se dice de dos formas distintas, a saber: 1. Como conciencia refleja, no reflexiva; y 2.

Some interpretations of quantum mechanics use notions of possible states and possible trajectories. I investigate how this modal approach correlates with several metaphysical conceptions of a transition from potential to actual existence. The comparison is based on a discussion in contemporary analytical metaphysics of modality. I also consider an analogy between Leibniz’s theory of the possibilities striving towards existence, wave mechanics of Schrodinger, and Feynman path integral.

Este artículo ofrece razones iniciales para interpretar en forma dia-léctica las “pruebas de la existencia divina” que Descartes ofrece en sus Meditaciones III y V. Primero indico algunos precedentes entre los comentaristas contemporáneos y señalo cómo esa manera de abordar los problemas fundamentales arranca en los clásicos griegos. Después muestro cómo un procedimiento dialéctico podría resolver un conjunto de problemas que, en principio, incluye el tradicional “círculo cartesiano”. Por último, intento mostrar que no es impensable atribuirle a Descartes una argumentación metafísica del tipo indicado; para ello, esgrimo un pequeño conjunto de argumentos textuales. Mi conclusión es que este tipo de interpretaciones merecen explorarse con mayor esmero.

Counterfactual definiteness is shown from analysis of Bell’s Theorem to be the factor separating classical from quantum theories. From this, it is shown that, by replacing it with ‘counterfactual semi-definiteness’, the definiteness of possible options available after a measurement event, some apt analysis of possible states can be kept. While not as solid as that forbidden by the EPR paradox and Bell’s Theorem, it allows us to start investigating the physical implementation of possible states in a way that has rarely been done. Working from this, the idea of counterfactuality, and interaction between counterfactual possibilities, is developed further.

Legendre’s Conjecture is one of the most elegant open problems in Number Theory, which states that there is a prime between consecutive two perfect squares. In this note, we prove the conjecture holds true and also discuss the related results.

Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of universal algebra, such as theories of symmetric operads, non-symmetric operads, generalised operads, PROPs, PROs, and monads. These variants of universal algebra are called notions of algebraic theory. In this paper, we develop a unified framework for them. The key observation is that each notion of algebraic theory can be identified with a monoidal category, in such a way that algebraic theories correspond to monoid objects therein.

En este artículo presentaremos primero dos discusiones muy puntuales que confrontan a Badiou con Nancy y Lacan en torno al vacío y al infinito. Mostraremos después cómo pensamos que se articula el concepto, tanto en filosofía como en psicoanálisis, a la luz de dichas complejidades y de las imbricadas relaciones entre los diversos dispositivos de pensamiento que ellas implican.

We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that comprehension is compression, i.e., explaining many facts using few theoretical assumptions, and that a theory may be viewed as a computer program for calculating observations. This provides motivation for defining the complexity of something to be the size of the simplest theory for it, in other words, the size of the smallest program for calculating it. This is the central idea of algorithmic information theory (AIT), a field of theoretical computer science.

The broad concept of an individual’s welfare is actually a cluster of related specific concepts that bear a “family resemblance” to one another. One might care about how a policy will affect people both in terms of their subjective preferences and also in terms of some notion of their objective interests. This paper provides a framework for evaluation of policies in terms of welfare criteria that combine these two considerations. Sufficient conditions are provided for such a criterion to imply the same ranking of social states as does Pareto’s unanimity criterion. Sufficiency is proved via study of a community of agents with interdependent ordinal preferences.