Socrates and Callicles from Gorgias Callicles believes that all pleasures are good (the good = the pleasant). Socrates will prove that there are two kinds of pleasure, good and bad, and therefore that not all pleasures are good. The argument proceeds according to a basic rule of dialectic which is that words which are absolute opposites (p and -p) function in such a way that anything which is true of one is false of its opposite (your enemy's enemy is your friend). Thus, if one exists, its opposite cannot exist. Not at the same time at least. They are antithetical. Another dialectical rule to keep in mind is that a noun and its adjectival form have the same truth value. If gold is valuable, then anything golden is similarly valuable.
Socrates: Is the opposite of fortunate unfortunate?
Callicles: Yes.
Socrates: Then a person cannot be both fortunate and unfortunate at once (according
to the rule of
noncontradiction a thing cannot both be and not be simultaneously, x cannot
equal both p and -p at once).
Callicles: Yes.
Socrates: Now, with the opposites health and sickness, can one be both healthy
and sick at once?
Callicles: No.
Socrates: So one becomes healthy at the moment one ceases to be sick?
Callicles: Yes.
Socrates: Now, consider good and happiness and their opposites, evil and misery.
Are these not also
absolute opposites such that the moment one becomes one, one ceases to be the
other?
Callicles: Yes.
Socrates: You cannot be both at once?
Callicles: No.
Socrates: Now then, if we find that any pair of things can be possessed together,
then they cannot be good
and evil. Do you agree. Think carefully before you answer. [1]
Callicles: I agree.
Socrates: All right. Is thirst painful?
Callicles: Yes.
Socrates: Then if one is thirsty, one is in pain?.
Callicles: Yes.
Socrates: And when one drinks, does the pain go away all at once or gradually?
Callicles: Gradually.
Socrates: So there is a time when one is still drinking but yet not entirely
free of pain?
Callicles: Yes.
Socrates: So for a time at least one is both drinking and still thirsty, that
is experiencing pleasure and yet
still in pain?
Callicles: Yes.
Socrates: Therefore, pleasure does not equal good [Anything which is always
good is never bad. Pain is
bad. Pleasure can be painful, which means pleasure can be bad; therefore, pleasure
is not always good] .
[1] Now here is an example of the difference between
dialectic and strict logic. Strictly speaking the most one can say is that apparently
opposite terms exist in a different relation to each other than do absolutely
opposite terms. Put another way, the test for absolute opposition is that one
cannot have or be both x and - x at once. The corollary must also therefore
be true; if one can have--or be--x and y at once, then x and y are not like
x and -x. And therefore, just because x ~ y does not mean that y = -x which
is the substitution Socrates would have Callicles admit to. In effect, Socrates
manages to trip Callicles up by switching the discussion from positive terms
to double negative terms. While he cannot extricate himself from the difficulties
Socrates has put him in, Callicles does not submit either. He gets indignant
not because he has been proven wrong (in a demonstrative sense), but because
he has not successfully maintained what he nevertheless still believes is right.
He has lost, but he has not been convinced.