THE LIAR PARADOX

     In his letter to Titus Paul refers to a famous saying of a Cretan poet who is supposed to have said “All Cretans are always liars.” This is referred to by logicians as the “Cretan paradox” because it appears that if it is true, it is at the same time false because it is true. That is to say, if all Cretans are always liars, then this statement itself is false. It would seem that there is no way for a Cretan person to utter a true statement about all Cretans always being liars without perjuring himself. Ironically, Paul says that this poet was right!

    I would like to apply this paradox to the issue of determinism vs. indeterminism. If the statement “All statements are strictly a function of bio-physical functions” is claimed to be true, then it itself cannot make a claim to be true. In other words, if this statement is true its claim should apply to itself and that means it too is a function of bio-physical functions and cannot make a claim to being true. Either it is false or seemingly meaningless. The notions of truth and falsehood simply do not apply to this statement and presumably, therefore, to any other statements.

Such statements involving self-reference are truly problematic. It would seem that the possibility of being “true” depends upon the possibility of also being “false” – or meaningless. I would argue that the possibility of a given statement being true is logically dependent on the possibility of it also being false. Thus, normal truth claims (and falsehood claims) entail a commitment to the freedom of action and thought. It is, then, self-contradictory for someone to utter (and thus believe) statements involving the truth claim that all statements (including this one) are entirely a function of bio-physical interactions. Such claims are logically self-contradictory.

It would seem that this reasoning would lay to rest forever the debate between freewill and determinism. The notion of complete determinism logically eliminates the possibility of this or any statement being true. In order for there to be meaningful truth claims there has to be the live possibility of truth and error. Otherwise, our statements are reduced to sounds and air exiting our lips. If all Cretans are always liars, the ideas of lying and telling the truth have no meaning. This seemingly silly riddle of self-reference carries with it serious consequences for certain logical and linguistic issues. If what we say is meant to matter, then what we say cannot be merely a function of neurons and biodynamics, including our talk about neurons and biodynamics.