We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between shaky arguments and overarching claims.

Postulo que es posible un realismo no estándar, un realismo que se coloque más allá de la representación y la predicción, centrándose en la experimentación. Y reconozco como ejemplo el realismo «materialista» del nuevo experimentalismo de Ian Hacking y de la teoría del cierre categoríal de Gustavo Bueno, ampliamente desarrollados en el último capítulo de la tesis. Estos dos filósofos marcan un nuevo rumbo en filosofía de la ciencia: «los filósofos de la ciencia se han limitado a pensar la ciencia como representación o predicción, pero de lo que se trata es de pensarla como transformación (construcción e intervención)». En cualquier caso, de cara al futuro, no cabe sino reconocer que la mayor o menor potencia de una teoría de la ciencia se va a medir por su capacidad para estar al tanto del funcionamiento de las ciencias modernas, como la física cuántica o la física del caos

In the theory of conditional sets, many classical theorems from áreas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or optimization. The frequent experience that such theorems can be proved by ‘conditionalizations’ of the classical proofs suggests that a general transfer principle is in the background, and that formulating and proving such a transfer principle would yield a wealth of useful further conditional versions of classical results, in addition to providing a uniform approach to the results already known. In this paper, we formulate and prove such a transfer principle based on second order arithmetic, which, by the results of reverse mathematics, suffices for the bulk of classical mathematics, including real analysis, measure theory and countable algebra, and excluding only more remote realms like category theory, set theoretical topology or uncountable set theory, see eg the introduction of Simpson

Since long, the origins of modern science have been a topic of debates and controversies between continuist and discontinuistic historical approaches. Despite their differences, these approaches shared the emphasis on scientific methodology. But in the last decades of the twentieth century, historians and philosophers of science proposed critical approaches to methodology which radically altered the debate on the origins of modern science. Two historians, Steffen Ducheyne and Marco Sgarbi have recently offered a reappraisal of the traditional continuist theses, with respect to the influence of British Aristotelianism on Newton and early modern Empiricist philosophers.

We investigate relationships between versions of derivability conditions for provability predicates. We show several implications and non-implications between the conditions, and we discuss unprovability of consistency statements induced by derivability conditions. Among other things, we improve Buchholz’s schematic proof of provable Σ1-completeness.

Putting Natural Time into Science Roger White, Wolfgang Banzhaf This contribution argues that the notion of time used in the scientific modeling of reality deprives time of its real nature. Difficulties from logic paradoxes to mathematical incompleteness and numerical uncertainty ensue. How can the emergence of novelty in the Universe be explained? How can the creativity of the evolutionary process leading to ever more complex forms of life be captured in our models of reality? These questions are deeply related to our understanding of time. We argue here for a computational framework of modeling that seems to us the only currently known type of modeling available in Science able to capture aspects of the nature of time required to better model and understand real phenomena.

We investigate relationships between versions of derivability conditions for provability predicates. We show several implications and non-implications between the conditions, and we discuss unprovability of consistency statements induced by derivability conditions. Among other things, we improve Buchholz’s schematic proof of provable Σ1-completeness.

Se presentan algunos de los hitos históricamente relevantes y llevados a cabo o instigados, de manera esencial, por matemáticos en la creación, avance y desarrollo de la cosmología como disciplina científica. Asimismo, se detalla la estrecha relación entre las matemáticas y la cosmología, a través de la geometrización de ésta llevada a cabo por Einstein con su teoría de la relatividad general y la colaboración posterior de ilustres matemáticos del siglo XX.

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Los–Tarski and the Chang–Los–Suszko preservation theorems follow.

De acuerdo con los principales enfoques al respecto (Sexto, Diógenes Laercio, Galeno, B.Mates, Long, Bochenski, Lukasiewicz) la lógica (dialéctica) de los estoicos es principalmente un sistema deductivo, lo que, en términos actuales, ha sido visto como un sistema de lógica proposicional. La obra de Crísipo acerca de los cinco argumentos indemostrables constituye la principal base de dicho sistema. En este artículo se examina la naturaleza de dichos cinco indemostrables así como el llamando teorema de Antipatro y los esquemas básicos de inferencia, o zemas. Por otra parte y en particular, sostengo que dichos argumentos indemostrables tienen otro importante rol para la filosofía y la historia de la lógica, cual es el de constituirse en una justificaciónde la deducción, un problema central en el presente. Se analiza, primero, la justificación por los indemostrablesy por el principio de condicionalización y, segundo, la justificación cognitiva de la lógica implícita en un sistema estoico.