ABSTRACT A spatial logic is a modal logic of which the models are the mathematical models of space. Successively considering the mathematical models of space that are the incidence geometry and the projective geometry, we will successively establish the language, the semantical basis, the axiomatical presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilogic of incidence geometry, and PRO, the modal multilogic of projective geometry.

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

Este trabajo pretende elucidar los rasgos generales de la metafísica de los megáricos en contra de las interpretaciones tradicionales que les atribuyen la defensa de un monismo numérico o una teoría de las Formas. Con base en los testimonios sobre Euclides y Estilpón de Mégara, intentaré mostrar que la metafísica megárica se caracteriza principalmente por el desarrollo de los conceptos de unidad e identidad de cada cosa consigo misma, lo que conlleva el rechazo de la diferencia y, en consecuencia, de (...) cualquier tipo de cambio. Esta perspectiva no excluye la existencia de múltiples entidades que, sin embargo, no son Formas. Por esta razón, los megáricos no desarrollan un monismo de tipo numérico, sino que su visión es coherente con un monismo de tipo predicativo que impugna la posibilidad de adjudicar atributos múltiples a una misma entidad. This paper purports to clarify the general features of Megarian metaphysics against two traditional interpretations which ascribe to this philosophical group either the defense of a numerical monism or a theory of Forms. Based on the testimonies of Euclid and Stilpo of Megara, I will aim to show that a main characteristic of Megarian metaphysics is the development of the concepts of unity and identity of each thing to itself, which involves a disavowal of difference as a possible property and, consequently, of any kind of change. I also intend to show that, although this standpoint does not exclude the existence of multiple entities, it implies that these entities are not Forms. Consequently, the Megarians do not develop a numerical monism but a predicational one, according to which the adscription of many predicates to the same entity is rejected. (shrink)