El presente artículo es un reconocimiento y un homenaje a L'Höpital, de cuya muerte se ha cumplido recientemente el tercer centenario. En él se estudia la correspondencia L'Höpital-Leibniz para analizar el recientemente creado por Leibiz cálculo diferencial e integral y su ontología subyacente, así como la publicación del primer manual sobre la materia escrito por L'Höpital.

The dream of Leibniz and that of Frege, to create a lingua characteristica in order to demonstrate conceptual thought, incorporates in a wider process, the division and tension between the distinct Spheres which the human sub-species have been creating. Spheres which remain hidden by natural language, essentially spoken language. For the creation and demonstration of the Conceptual Sphere the establishing of a language of characteres has become indispensable, essentially written language. Is a consequence a tension is established between Natural language-Formal (...) language with their corresponding reductionist tendences. (shrink)

En 1931 Gödel publica su Teorema de incompletud. Resultado clave en Lógica matemática, se interpretó como una limitación de los formalismos, un fracaso del Programa de Hilbert. Sin embargo, el método de aritmetización, la recursividad han propiciado una visión positiva y la creación de nuevas teorias - Teorías de la Complejidad, de Información algorítmica... -. Con ellas, nuevas demostraciones del teorema y, consecuentes, nuevas discusiones en Filosofía de la Matemática. En especial, desde la Teoría de la Complejidad. Además de incompleta, (...) la Matemática se ve por algunos como aleatoria y experimental. En este ensayo se pretende explicitar los supuestos de estas interpretaciones. Discusión que conduce, en principio, a su rechazo, dejando abierta la problemática sobre el aspecto epistemológico dei razonamiento matemático. (shrink)

The pascalian use of indivisibles is here considered in the context of the theological and mathematical debates of the time, by distinguishing it clearly from this of Cavalieri. The combinatory and geometrical approaches are closely linked in Pascal’s work. His use of indivisibles has a heuristic, inventive character and not only a demonstrative one. Ontologically speaking, it stems out from the acceptance of actual infinite. The use of the symmetry axiom of Archimedes is the basis of the pascalian use of (...) the infinitesimals, which has, in other respects, some close connexions with the Leibnizian conception of infinitesimals. (shrink)

May 2020 marked the 25th anniversary of the death of Miguel Sánchez-Mazas, founder of Theoria. An International Journal of Theory, History and Foundations of Science, and regarded as the person who brought mathematical logic to Spain. Here we present some of his biographical features and a summary of his contributions, from his early work in the 1950s - introducing contemporary advances in logic and philosophy of science in a philosophically backward milieu dominated by the scholasticism of that era in Spain (...) - to the development of a project of Lebnizian lineage aimed at producing an arithmetic calculation that would elude some of the difficulties confronting Leibniz’s calculus. (shrink)

Obras escogidas/M. Sánchez-Mazas. - v.1.

Gennaro Chtjerchia, Dynamics of meaning: anaphora, presupposition, and the the of grammar. Chicago and London: The University of Chicago Press, 1995.xv+ 270 pp, £59.95, £31.95 G. Pr...

The standard representation of the Central Dogma (CD) of Molecular Biology conspicuously ignores metabolism. However, both the metabolites and the biochemical fluxes behind any biological phenomenon are encrypted in the DNA sequence. Metabolism constrains and even changes the information flow when the DNA‐encoded instructions conflict with the homeostasis of the biochemical network. Inspection of adaptive virulence programs and emergence of xenobiotic‐biodegradation pathways in environmental bacteria suggest that their main evolutionary drive is the expansion of their metabolic networks towards new chemical (...) landscapes rather than perpetuation and spreading of their DNA sequences. Faulty enzymatic reactions on suboptimal substrates often produce reactive oxygen species (ROS), a process that fosters DNA diversification and ultimately couples catabolism of the new chemicals to growth. All this calls for a revision of the CD in which metabolism (rather than DNA) has the leading role. (shrink)

En los últimos cursos que impartió en el Collège de France, entre 1980 y 1984, Michel Foucault dio un protagonismo creciente en sus investigaciones al cinismo antiguo. Su estudio histórico de la ética antigua, orientado primero hacia la experiencia moral de los placeres, y luego al tema del cuidado de sí y de las prácticas ascéticas a través de las cuales se constituye la subjetividad en el marco de una estética de la existencia, termina con el ejemplo de los cínicos (...) a causa del fallecimiento de Foucault en junio de 1984. No obstante, los cínicos parecen representar al final de esos análisis un momento privilegiado, en cierto modo una culminación. El presente artículo pretende indagar en las razones de ese privilegio sobre la hipótesis de que, en los cínicos, Foucault encuentra respuesta al problema del aspecto voluntario de las resistencias al poder. (shrink)

The emphasis of systems and synthetic biology on quantitative understanding of biological objects and their eventual re-design has raised the question of whether description and construction standards that are commonplace in electric and mechanical engineering are applicable to live systems. The tuning of genetic devices to deliver a given activity is generally context-dependent, thereby undermining the re-usability of parts, and predictability of function, necessary for manufacturing new biological objects. Tolerance and allowance are key aspects of standardization that need to be (...) brought to biological design. These should endow functional building blocks with a pre-specified level of confidence for bespoke biosystems engineering. However, in the absence of more fundamental knowledge, fine-tuning necessarily relies on evolutionary/combinatorial gravitation toward a fixed objective. (shrink)

Recesión de D. Blanco Fernández, Principios de filosofía política, Editorial Síntesis, Madrid, 2000.