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PARADOX
a tenet contrary to received opinion; a statement that
is seemingly contradictory or opposed to common sense and yet
perhaps is true; a self- contradictory statement that at first
seems true; an argument that apparently derives
self-contradictory conclusions by valid deduction from acceptable
premises. (Webster's) A paradox is not the same as a
contradiction. "The shirt is blue; the shirt is not blue," and
"It is raining; it is not raining," are examples of
contradictions. A paradox occurs when one makes an assumption
and, following a logical argument, arrives at the converse. A
paradox will always result when one formulates a set that
contains itself. Below are several examples:
l. Suppose there is a small town that consists only of men.
There are two kinds of men in this town--those who shave
themselves and those who are shaved by the barber. Who shaves
the barber? If he shaves himself, then he is shaved by the
barber. But if he is shaved by the barber, then he shaves
himself. If the barber is assumed to be in one set, he appears
in the other. This situation occurs because the barber both
appears in the set and is used to define the set.
2. A person from the island of Crete asserts, "All Cretans
are liars." We can conclude that if he is telling the truth,
then he is lying. But if he is lying, then he is telling the
truth. Once again an element of the set is referring to the set.
3. Consider a businessman accused of accepting a bribe. He
claims, "I did not take the bribe." There are two possible
interpretations of this statement. Either he is a knowledgeable
observer making a correct statement, or he is a knowledgeable
observer lying to avoid going to jail. The businessman is both
the observer and the person being observed. We have no way of
knowing which role he is playing.
As the third example indicates, paradox leads to
"undecidability". When two equally correct interpretations are
possible, in the absence of further information, no decision
other than a random choice is possible. (Umpleby)
From the Greek para + dokein, "to think more", conventionally, an argument that apparently derives self-contradictory conclusions by valid deductions from acceptable premises (Webster's). More generally, any description or situation that is compelling enough to lead an observer into a vicious cycle involving mutually exclusive interpretations, indications or acts, force him to step out of or transcend the cycle and to construct a logically more powerful (see ordinality) cognitive system within which the vicious cycle has disappeared. E.g., "This sentence is false" is false when it is assumed to be true and true when it is assumed to be false. The resolution of this vicious cycle requires a logic that accepts self-reference which the prepositional calculus does not. Paradoxes appear not only in logic but also in interpersonal communication, e.g., double-bind, in social organization and might be the stimulus for morphogenesis. (Krippendorff)
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