Necessity or Contingency. The Master Argument

Por • 30 nov, 2017 • Sección: Leyes

Jules Vuillemin


The Master Argument, recorded by Epictetus, indicates that Diodorus had deduced a contradiction from the conjoint assertion of three propositions. Epictetus adds that three solutions of the aporia had been obtained by denying one or another of the propositions advanced while maintaining the other two. The argument, which has to do with necessity and contingency and therefore with freedom, has attracted the attention of logicians above all. In any case there have been many attempts at reconstructing it in logical terms, without excessive worry about historical plausibility and with the foregone conclusion that it was sophistic since it directly imperiled our common sense notion of freedom. On both of these counts I have taken exception to recent tradition. The success of the argument with the Ancients, and with Ancients who were no mean logicians, seemed reason for presuming that the Master Argument is not sophistic and that the contradiction it produces is a real one. On the other side, I looked for a classical text containing the propositions stated by Epictetus and which could have furnished Diodorus with the material for his argument. I believe to have found such a text in Aristotle’s De Caelo. In order to demonstrate the contradiction in the propositions thus restored, I had in my turn to translate them into logical terms. It is unlikely that Diodorus proceeded in such a way. Although the translation I have proposed tries to remain faithful to its models as they have been handed down to us, it inevitably gives them a precision they did not have in themselves. This indulgence in precision amounts to historical inexactitude but seemed necessary nevertheless as it had to do with restoring a reduction to the absurd. There is one distinctive feature of the translation that must be noticed. The propositions figuring in the Master Argument are in- xii / NECESSITY OR CONTINGENCY: THE MASTER ARGUMENT terpreted in terms of temporal modal logic where both the modalities and the statements they govern have chronological indices. This means that the force of the argument comes not from purely logical or modal considerations, but from our experience of time. To bring to its complete end the research undertaken here, I would have had to assign to the Master Argument and to each of the solutions it is susceptible of, an explicit axiomatic system formalized according to a set of rules. For want of competence, of stamina, of time, I have been content to formulate only what was needed to elucidate the argumentation. Justification for the first four chapters is to be found in the Epictetus passage. The remaining chapters extend the debate about the Master Argument to Greek philosophy at large. In this way it is seen that principles are challenged-even logical ones at that-which are not mentioned in the Epictetus passage but which must have played their role in the argument. The reader will judge whether that extension is legitimate or not. As one well imagines, the debate on the issue was continued by the philosophers of the Middle Ages and the Moderns. This was quite generally done in ignorance of the Master Argument itself; but I have had no hesitation in appealing to them where they might be apt to help explain or specify the position of the Ancients.


Jules Vuillemin Necessity or Contingency. The Master Argument, Stanford, CSLI Publications, 1996

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