The aim of this essay is to develop a formal reconstruction of Greek arithmetic. The reconstruction is based on textual evidence which comes mainly from Euclid, but also from passages in the texts of Plato and Aristotle. Following Paul Pritchard’s investigation into the meaning of the Greek term arithmos, the reconstruction will be mereological rather than set-theoretical. It is shown that the reconstructed system gives rise to an arithmetic comparable in logical strength to Robinson arithmetic. Our reconstructed Greek arithmetic is (...) then compared to modern developments in the foundations of arithmetic. Finally, it is shown that our reconstruction can help to clarify some issues in Plato’s philosophy of arithmetic, especially the question if Plato’s views can be compared to 19th – 20th century developments in the logical construction of arithmetic. (shrink)

We will explicate Cantor’s principle of set existence using the Gödelian intensional notion of absolute provability and John Burgess’ plural logical concept of set formation. From this Cantorian Comprehension principle we will derive a conditional result about the question whether there are any absolutely unprovable mathematical truths. Finally, we will discuss the philosophical significance of the conditional result.

Alexander's satrapal appointments in Syria have long been a focal point of scholarly dissension, for the relevant passages in the ancient sources are uniformly inconsistent and sometimes disconcertingly corrupt. A running debate continued until 1935, when Oscar Leuze presented a monumental survey of the ancient evidence together with exhaustive refutation of the hypotheses advanced by earlier scholars. Since then the problems of Syria under Alexander have been left virtually undisturbed, which is a pity. In the first place, Leuze's (...) treatment is not impregnable. His massive discussion tends to convince through sheer accumulation of argument rather than by the cogency of its logic, which can often be faulted. (shrink)

Sous le thème de la « méthode », l’auteur se propose de formuler une éthique de la lecture à partir de Gilles Deleuze. L’analyse est fondée sur un dédoublement de la lecture : d’abord la lecture qu’a fait De-leuze de David Hume tel qu’exprimé dans Empirisme et subjectivité (1953) et celle de Henri Bergson dans Le bergsonisme (1966), ensuite par la lecture que l’auteur fait de ces deux livres de Deleuze. Par l’entremise de l’empirisme (Hume) et de l’intuition (Bergson), (...) l’auteur conclut que la lecture que Deleuze a faite est performative en ce sens qu’elle fait ce qu’elle énonce. Une éthique de la lecture correspondante se voudra donc, de même, performative : elle dépassera le donné à tra-vers le délire, s’ouvrira à l’inhumain et au surhumain à travers le vir-tuel. (shrink)