How to find a proof? Leibniz's anagogical analysis illuminated by Kolmogorov's interpretation of logical constants.

Wagner de Campos Sanz (Faculdade de Filosofia, Universidade Federal de Goias, Goiania, GO, Brazil)
09/10/2015 - 11:00
Dipartimento di Matematica e Fisica, Università Roma Tre Largo S. Leonardo Murialdo 1, Roma Palazzina C, III piano, Aula 311

It has long been a difficult task to explain what should be understood by the concept of analysis in the tradition starting with Pappus of Alexandria. Leibniz has himself devoted many lines to the subject. We here focus on a two pages written in which he exemplifies how the analysis of a mathematical proposition in need of proof should proceed. Although we have reasons to believe that his particular example is faulty, we can nonetheless extract a general description of what should be the process of anagogical analysis, provided we stick to some logical concepts Kolmogorov had advanced as an interpretation for logical constants. As we'll see, the concept of hypotheses (or problem) has an important role in the development of the process.