First, a quick restatement of Socrates’ argument found on 474-475 in Gorgias:

         Good and admirable are not the same. Bad and shameful are not the same.

         Whatever is admirable is admirable because it causes pleasure or benefit, or both.

         Whatever is shameful is shameful because it causes pain or is bad to some degree, or both.

         Whenever one of two shameful things is more shameful than the other, it will be so because it surpasses the other either in pain or in badness, or in both.

         Suppose a person performs an unjust act against another, causing the latter to suffer. Let A be the performance of this unjust act. Let B be the suffering of this             unjust act.

         Which is worse: A or B?

         First, we posit that A is more shameful than B.

         If A is more shameful than B, it must be because A surpasses B in pain or badness, or both.

         Does A surpass B in pain? Clearly not.

         Therefore A surpasses B in badness.

         And since A surpasses B in badness, it is worse.

In sum, to perform an unjust act against another is worse than to be the object of suffering of that unjust act.

Isn’t Socrates equivocating? Perpetrating an injustice is “worse” in badness (it is a bad act) and “better” in pain (it does not cause the actor any pain) than suffering the same injustice, which is “worse” in pain (it hurts) and “better” in badness (it is not shameful to be the object of an unjust act), but is “worse in badness” worse overall? His point is not proven here. A diagram:

B and P are incommensurate.

The key phrase that Socrates states is:

“Because [doing an unjust act] surpasses [being the object of an unjust act] in badness, doing what’s unjust would be worse than suffering it.”

The bolded “worse” above discounts or does not count the pain as a bad, which is an error that no one in the dialogue seems to catch.

All Socrates has shown is that doing an unjust act is bad, which is already known.

Although there are many possible arguments, Socrates does not claim that pain is not bad, and the question at the outset is whether the pain is worse, which implies that pain has some degree of disutility.

Who’s the sophist now, Socrates?

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