Paradox

A FOOTNOTE TO “PLATO” 101because of Plato’s powerful build as a wrestler.But was Plato’s original name even more apt? Someoneis well named if the predicate corresponding to his namedescribes him. Professor Sober is well named because he issober. Professor Grim is ill named because he is not grim.Aristocles means well-named. So the issue is whether Well-Named is well named.We would run into a dilemma if Plato had instead beennamed Ill-Named (Geach 1948). Either Ill-Named is wellnamed or ill named. If Ill-Named is ill named, then thepredicate corresponding to his name accurately describeshim. So if he is ill named, then he is well named. But if Ill-Named is well named, then the predicate corresponding tohis name does not apply to him.The ill-named dilemma is a version of the liar paradox:L: Statement L is false. If L is true, then since it says that it isfalse, it must be false. But if statement L is false, then thingsare just as L says—in which case L is true after all. L isparadoxical because there is no consistent assignment oftruth-values to it.The opposite problem makes the truth-teller sentenceparadoxical: R: Statement R is true. R is paradoxical becausewe can consistently assign either truth-value to R. Since thereis no further basis for assigning a truth-value, R would be trueor false without anything making it true or false.Most logicians react by saying that R is neither true norfalse. This is based on the feeling that the sentence is empty.But if R is neither true nor false, then R seems to falsely claimto be true.“Well-Named is well named” is a version of the truthtellerparadox. We can consistently say that “Well-Namedis well named” is true and we can consistently say that it is