On the shoulders of Hipparchus. A reappraisal of ancient Greek combinatorics
The author reconsiders anew an astonishing passage of Plutarch's De Stoicorum repugnatiis where Chrysippus (276--204 B.C.) formulated the problem of the number of conjunctions produced by means of ten assertibles. He has been criticized and refuted by Hipparchus (276--204 B.C.) who proved that his error in calculation is enormous.. Much later in 1870 the German mathematician Ernst Schröder (1841--1902) solved the same problem in his paper Vier combinatorische Probleme [ Z. Math. Phys. 15, 361--376 (1870; JFM 02.0108.04)]{} enumerating the number of brackets in a string of ten elements. It is absolutely plain that the whole issue of ancient Greek combinatorics must be reconsidered from an entirely different perspective, taking also into account that comparatively refined techniques are required to compute the above numbers. The author tries to reconstruct the way Hipparchus numbers were arrived at, trying to convince the reader that the time has come for a reappraisal of ancient Greek combinatorics. The followers fixed their attention more to the manner of speech than to the things spoken about used to term ``conjunction'' for all propositions compounded by means of the conjunctive connections whether they are consequents of one another or incompatibles. Combinatorics had been developed to some extent before him, and the real point had been to formulate a well-defined problem out of Chrysippus claim. A very interesting problem is thus emerging of the interactions between Stoic dialecticians and mathematicians. Synthesis of two independent mainstreams interested in combinatorial results, the geometrical side stemming from Apollonius refined research, and the dialectical side, going back to Aristotle's logical works receiving a decisive spur from the Stoics researches a selection in the course of the textual tradition has been so strong as to convince some of us that the Greek took no interest in these matters.
scientific article; zbMATH DE number 1983516