Translation copyright 2001 Neil W. Bernstein; all rights reserved. 

That Bias’s syllogism concerning marriage cannot be considered a convertible argument (1).

  1. Certain people think that the following response of Bias, a wise and noble man, is convertible like the argument of Protagoras that I discussed in the preceding entry.
  2. When someone asked Bias whether he should marry or live a celibate life, Bias said: “In truth, you’ll marry either a pretty woman or an ugly one. If she’s pretty, you’ll have public property; if she’s ugly, you’ll have a punishment. Neither choice is desirable; therefore, do not marry.”
  3. Some people, however, reverse this argument as follows: “If I marry a pretty woman, I won’t have a punishment; if I marry an ugly woman, I won’t have public property; therefore, I should marry.”
  4. But this does not seem at all like a convertible argument, because the reversal is weak and awkward. 
  5. Indeed, Bias argued that the man should not marry because of the inconvenience he would necessarily have to endure in either case.
  6. The person reversing the argument, however, does not defend himself from a present inconvenience but says that he lacks another one that is absent.
  7. It is enough to support Bias’s statement that the man who marries must suffer from one of two inconveniences; having common property or a punishment.
  8. But when someone happened to mention Bias’s syllogism, whose first protasis is “in truth, you’ll marry either a pretty woman or an ugly one”, my teacher Favorinus (2) said that this statement was neither valid nor properly disjunctive. It was not necessary for one of the two possibilities it distinguished to be true, which is required in a disjunctive preamble.
  9. For the statement appears to distinguish ugly and pretty women, the extremes of physical appearance.
  10. “There is, however,” Favorinus said, “a third possibility between these two types distinguished by this statement, though Bias did not have this idea or possibility in mind.”
  11. “There is a certain middle standard of beauty between the most lovely woman and the most hideous, free from the danger of superlative attraction and the distaste for excessive deformity.”
  12. “Quintus Ennius described this kind of woman in his play Melanippa (3), using the perfectly elegant word ‘average’ [stata]. This kind of woman would neither be public property nor a punishment.”
  13. Favorinus wisely called this moderate and modest kind of beauty “wifely”. Moreover, Ennius in the tragedy mentioned above says that virtually all women of ‘average’ beauty keep perfect chastity.


  1. Bias of Priene was one of the seven sages of the Greek world; cf. Diogenes Laertius, Lives of the Philosophers 1.81. Gellius introduces convertible arguments in the preceding entry (“On convertible arguments, called antistrephon in Greek and reciproca in Latin,” Gell. 5.10). He defines the convertible argument as “one that can be turned backwards and used against the person who presented it” (Gell. 5.10.3).
  2. To illustrate the convertible argument Gellius uses the conflict between Protagoras, a famous teacher of rhetoric, and his student Euathlus. At the beginning of his rhetorical training Euathlus paid Protagoras half of his considerable tuition and agreed to pay the remainder when he won his first legal case. When Euathlus subsequently refused to take on cases, however, Protagoras suspected that his former student was trying to avoid paying the remainder of his tuition and took him to court. Protagoras argued that, no matter how the jurors decided, his student would have to pay him. If the jurors were to decide in Protagoras’s favor, then Euathlus would have to follow their verdict and pay Protagoras; but if they were to decide in Euathlus’s favor, then the student would have won his first case and owe Protagoras. Euathlus argued the reverse: that if the jurors were to decide in his favor he would follow their verdict and pay Protagoras nothing; but if they were to decide in Protagoras’s favor he would have lost his first case and thereby owe his teacher nothing. Faced with this dilemma, the jurors refused to offer a verdict.
  3. For the relationship between Gellius and his teacher Favorinus, cf. Holford-Strevens 1988: ch. 6.
  4. Enn. scen. 294 Vahlen, adapted from Euripides’ Melanippe the Wise. Melanippe gave birth to twin sons after being raped by Poseidon; cattle raised her children after she tried to expose them. When her father Aeolus discovered the children, he exposed them and imprisoned Melanippe.

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