Socratics - Megaric School - Euclid

The head of the Megarian school, Euclid, was nevertheless linked to Plato, since he received Plato and the other disciples of Socrates at Megara when they left Athens after the death of the master; and Plato, by presenting his Theaetetus as a conversation of Socrates, collected by Euclid, undoubtedly wanted to bear witness to the bonds of friendship that lasted long after the tragic event. (2) It is no less true that his doctrine, as far as can be guessed from a few lines of Diogenes Laertius, is at the antipodes of that of Plato. For the latter, let us recall, all thought, all intellectual life was impossible, unless one admitted a system of ideas at once united among themselves and yet distinct. Now when Euclid says that “the Good is one thing, though it be called by different names: science, god, intelligence, and other names,” when he suppresses the opposites of the Good, by asserting that they do not exist, it seems that his intention is to resist every attempt to unite the concepts otherwise than by declaring them identical, or to distinguish them otherwise than by excluding one from the other. Science, god, intelligence, these are precisely the terms that, in the Timaeus for example, Plato seeks to distinguish between themselves and to distinguish from the supreme Good, while uniting them and hierarchizing them. Euclid, by identifying them and denying their opposite, makes impossible any dialectical speculation of the kind of those in the Timaeus or the Philebus; diversity is only in names and is no longer in things. We also know how familiar and indispensable reasoning by comparison is to Plato; Euclid denies its possibility and does not want to know a similar that is neither identical nor different; either the terms of comparison are similar to things, and then it is better to use things; or they are different, and the conclusion is not valid (3).

The famous sophisms that Diogenes Laertius attributes to Euclid’s successor, Eubulides of Miletus (4), seem to target logic more specifically of Aristotle, and also, in the form in which Cicero presents them in the Academics, Stoic logic. The principle of contradiction states that one cannot say both yes and no on the same question; sophisms show us cases where, by virtue of this principle, one is forced to say both yes and no, where, consequently, thought denies itself. Such is the sophism of the liar: “If you say that you lie and if you tell the truth, you lie”, where one agrees both that one lies and that one does not lie; in the name of logic, the Megaric forces his adversary to confess that he wears horns, since one possesses what one has not lost and that one has not lost horns; he forces him to recognize that he does not know his own father, by presenting him to him under a veil; he makes him agree that Electra knows and does not know the same things, since, when she meets him still unknown, she knows that Orestes is her brother, but she does not know that he is Orestes. He silences him by asking him how many grains of wheat it takes to make a heap (sorites fallacy), or how much hair one must have lost to be bald (5). All these logical jokes lead to the impossibility of choosing between yes and no, and therefore of discussing with the help of defined concepts. They must have had great success; Stilpo of Megara, a contemporary of Theophrastus, is said to have attracted to his courses the disciples of the Peripatetics and those of the Cyrenaics. We know two parts of his teaching quite well, which touched on the philosophy of the concept: first the criticism of ideas (6). The method of this triticum is that which Diogenes Laertius indicates as that of Euclid in his refutations; he attacked the demonstrations not by criticizing the premises, but by showing the absurdity of the conclusion; in the same way Stilpon, assuming the existence of ideas, deduces absurd consequences: the ideal man is not such and such, for example speaking or non-speaking; consequently we have no right to say that the man who speaks is man; he does not correspond to the concept. The ideal vegetable is eternal; what you show me is therefore not a vegetable, since it did not exist a thousand years ago. Or else, if you want to say that such an individual man corresponds well to the concept of man, it will be necessary, if this man is for example in Megara, to say that there is no man in Athens, since the property of the concept is to be unique. As for the scope of this criticism, we see that it targets no less the concept of Aristotle than the idea of Plato; let us only recall the efforts that Aristotle made to respond to criticisms of the same kind.

References

2. Diogenes Laertius, Lives of the Philosophers, II, 106; Plato, Theaetetus, 142 a-143 c.
3. Diogenes Laertius, II, 106 and 107.
4. II, 108; cf. 111.
5. Cicero, Early Academics, II, 96: Diogenes Laertius, Lives, VII, 187; Lucian, The Lives of Vencanus, 22; Early Academics, II, 92.