THREE ARGUMENTS IN PLATO’S GORGIAS

The following is a revised version of a document distributed in class on 11/17/04. The arguments that appeared on the original handout as I. and II. appear here as II. and III., respectively. The argument that appears here as I. was projected on the screen in section 3 and printed on the back of the handout in section 7. I have made some alterations to the analyses, and have added references to the sources of conclusions in II. and III.

*Note on step 5: Socrates seems to draw this conclusion from steps 3 and 4, as indicated, but the inference is a non sequitur. The inference would be valid if the following premise were substituted for 4:

Step 5 follows from 3 and 4a, provided that we understand “beneficial” to mean “producing something good.”

**Notes on step 10: The inference from 9 to 10 is rather loose, and I do not know of an economical way to tighten it up. Replacing step 10 with the following sequence of steps will narrow the logical gap, but not close it entirely:

10. The ability of a tyrant to put people to death and so forth, thinking that such actions benefit him when in fact they do not, does not benefit the tyrant.
    
11. Therefore, that ability is not great power. (From 9 and 10)
    
12. Therefore, the tyrant who does those things does not have great power. (From 12)

This still leaves a gap between 11 and 12: the tyrant may, as far as the premises of the argument are concerned, have great power, not because of his ability to put people to death and so forth but because of something else. But presumably Socrates would be making enough of a point by establishing that the ability of a tyrant to do such things does not itself constitute great power, as that was surely the claim that Polus meant to defend.

***Note on steps 4–6: Because of the oddity of the form of Socrates’ reasoning in this passage, in scoring the quizzes I did not count steps 5 and 6. Many students believed that 5 was inferred from 3 as well as 4; but 5 in fact does not depend on 3 in the least. This may be shown by an analogy. Suppose that it is the case that to find suitable clothes at the Big and Tall Men’s Shop, a man must be over six feet tall, or over 200 pounds, or both. Now consider the following argument:

Step 2 is validly inferred from 1 alone: it does not in the least depend on any facts about the Big and Tall Men’s Shop.  Now if we also know that Mr. Wienerman finds suitable clothes at the Big and Tall Men’s Shop, then we can validly draw the further conclusion that Mr. Wienerman is over 200 pounds, just as, in argument II. above, Socrates infers 6 from 3, 4, and 5; but, within that argument, 5 follows directly from 4 alone. What makes the form of the argument confusing is that step 5 is in fact logically superfluous; Socrates could have validly inferred 6 directly from 4; and probably I ought to have omitted 5 from my analysis, rather than following the text as closely as I did.

III. The following is an extensively simplified version of the argument of 476a–479e (pp. 42–49); in fact, one might question whether this is Plato’s argument at all; but it certainly uses some of the claims that Socrates makes (and Polus grants), and argues for the same conclusion as Socrates does: