We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al. [‘Why Surplus Structure is Not Superfluous.’ Br. J. Phi. Sci. Forthcoming.] We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.

We present a full formalization in Martin-Löf’s Constructive Type Theory of the Standardization Theorem for the Lambda Calculus using first-order syntax with one sort of names for both free and bound variables and Stoughton’s multiple substitution. Our formalization is based on a proof by Ryo Kashima, in which a notion of beta-reducibility with a standard sequence is captured by an inductive relation. The proof uses only structural induction over the syntax and the relations defined, which is possible due to the specific formulation of substitution that we employ. The whole development has been machine-checked using the system Agda.

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas.

Philosophers frequently struggle with the relation of metaphysics to the everyday world, with its practical value, and with its relation to empirical science. This paper distinguishes several different models of the relation between philosophical ontology and applied (scientific) ontology that have been advanced in the history of philosophy. Adoption of a strong participation model for the philosophical ontologist in science is urged, and requirements and consequences of the participation model are explored.

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.

Un pueblo o raza tiene su origen o logos en el mito, la razón, el ser. No es posible de otro modo. En Argentina, considera el autor, no es posible filosofar por carecer de estos referentes onto-antropológicos. Sin embargo, para poder construir, “crear” (pensar cristiano) o “causar dinámicamente” (pensar griego), el status existencial de la filosofía Argentina en América Latina, se debería instituir el ontismo y evadir los positivismos, pues se debería considerar “la realidad del mundo de acuerdo a sus determinantes intrínsecos..:” En esa perspectiva, la posibilidad de filosofar en Argentina partiría de varios pensadores como Heidegger, Hegel y Wiggenstein, que fundan su reflexión filosófica en una crítica de la racionalidad a partir de una indagación originaria (fenomenológica, idealista y lingüística) acera del Ser.

I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact—in sum, real application of the theory in actual scientific practice.

Cuando hablamos de la Historia de la ciencia como una disciplina integrada en el ámbito de las ciencias humanas, lo decimos en el sentido que esta oposición: ciencias humanas / Ciencias naturales, adquiere en la teoría del Cierre Categorial de Gustavo Bueno, que aparece escuetamente expuesta en el artículo de Alberto Hidalgo de este mismo diccionario, y al que apelamos para su comprensión más cabal. Gustavo Bueno (1924) basa su distinción en el principio gnoseológico fundamental de su teoría, según la cual el grado de cientificidad de una disciplina estará en función del proceso de la «neutralización de las operaciones»,

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.

We looked at a method for estimating the complexity measure of game tree size (the number of legal games). It seems effective for a number of children’s games such as Tic-Tac-Toe, Connect Four and Othello.