Gardner’s Method for Syllogistic

Abstract

Martin Gardner introduced, in the 1950s, a method by digraphs for classical proposition allogic. He proposed, as an open problem, the adaptation of the method for syllogistic. In this paper I answer in the affirmative to Gardner’s question. The resulting method reinforces theses presented in previous works, namely that the validity of syllogisms follows from applications of only two rules, and because it reveals a much smaller number of valid syllogistic forms than suggested by the division in figures and moods, this division is artificial. Furthermore, it highlights the very different nature of two types of components of syllogisms(propositions of existence and rules for passing from a proposition of existence to another), whose distinction has been spontaneously acknowledged in its use by philosophers and jurists. Finally, it demonstrates that BRAMANTIP, amood of the fourth figure should be considered a weakened valid syllogism.