Analiza i Egzystencja (Jun 2006)
Rekonstrukcje rozumowania Diodora Kronosa w ontologii czasu punktowego (RECONSTRUCTIONS OF DIODOR CRONOS' REASONING IN POINT ONTOLOGY OF TIME)
The basic purpose of the paper is to present the famous and historical reasoning of ancient logician Diodor Cronos in a framework of the point ontology of time (POT). Diodor created his argument to prove that his definitions of alethic modalities in temporal terms are correct. We do not know details of it, especially we do not know the body of the reasoning. Instead of this we have premises and conclusion of the argument. If we want to know anything of assumptions concerning the concept of time involved in the reasoning, we have to reconstruct Diodor's proof. POT is the most popular and old kind of representation of time. In fact it is far from perfection but it allows us in a very elegant and easy way to model different sorts of time (branching, linear, dense etc.). Using some historical aspects of the reasoning and logic of temporal realization the author shows the reconstruction according the idea of Nicholas Rescher. The proof gives an answer what kinds of properties of time the reasoning needs in order to be conclusive. It turns out that the minimal requirements are linearity and non-ending, i.e. the lack of the latest moment of time. In the paper rhe author refers to other reconstructions that do not need, for example, linearity and enable us to allow the time to be branched in the future. It means that different approaches to the formal tools and Diodor's premises give different answer to the main question.