The puthujjana takes his existence for granted

You will find this contradiction illustrated in the passage from Camus in NIBBĀNA [a], but it is more concisely presented in the later part of the Mahā Nidāna Suttanta (D. 15: ii,66-8), where the Buddha says that a man who identifies his 'self' with feeling should be asked which kind of feeling, pleasant, unpleasant, or neutral, he regards as his 'self'. The man cannot identify his 'self' with all three kinds of feeling at once, since only one of the three kinds is present at a time: if he does make this identification, therefore, he must do it with the three different kinds of feeling in succession. His 'self', of course, he takes for granted as self-identical—'A is A'—that is to say as the same 'self' on each occasion. This he proceeds to identify in turn with the three different feelings: B, C, and D. A is therefore both B and C (not to mention D); and C, being different from B, is not B: so A is both B and not B—a violation of the Law of Contradiction. But whether or not it is with feeling that the puthujjana is identifying his 'self', he is always identifying it with something—and it is a different something on each occasion. The puthujjana takes his existence for granted—cogito ergo sum (which, as Sartre says, is apodictic reflexive evidence of the thinker's existence)—and is in a perpetual state of contradiction.

So we have the following situation. Assuming the validity of the Laws of Thought, the thinker discovers that the whole of his thinking depends upon an irreducible violation of the Laws of Thought, namely the contradictory existence of the thinker. And this itself is a contradiction. If he tolerates this contradiction he denies the validity of the Laws of Thought whose validity he assumed when he established the contradiction in the first place; there is therefore no contradiction for him to tolerate, and consequently he is not denying the Laws of Thought; the contradiction therefore exists and he tolerates it.... Or he may refuse to tolerate the contradiction; but if he does so, it is in the name of the Law of Contradiction that he does so, and refusal to tolerate the contradiction requires him to deny the validity of the Laws of Thought by which the contradiction was originally established; he has therefore no reason to refuse to tolerate the contradiction, which, if the Laws of Thought are invalid, is inoffensive; he therefore does not deny the validity of the Laws of Thought, and the contradiction is offensive and he refuses to tolerate it.... Or perhaps he neither tolerates the contradiction nor refuses to tolerate it, in which case he violates the Law of Excluded Middle.... Most certainly the problem exists!

How is it dealt with? (i) The rationalist, by remaining on the level of reason and refusing to look at his premises, asserts the validity of the Laws of Thought, and successfully blinds himself to the standing violation of the Laws of Thought—his own existence. (ii) The mystic endorses the standing violation of the Laws of Thought by asserting their invalidity on principle. This obliges him to attribute their apparent validity to blindness or ignorance and to assert a Reality behind appearances that is to be reached by developing a mode of thinking based on the three Laws: 'A is not A'; 'A is both B and not B'; 'A is neither B nor not B'. (iii) The existentialist says: 

'Contradiction is the truth, which is a contradiction, and therefore the truth. This is the situation, and I don't like it; but I can see no way out of it'. To maintain this equivocal attitude for a long time is exhausting, and existentialists tend to seek relief in either rationalism or mysticism; but since they find it easier to endorse their personal existence than to ignore it they are more inclined to be mystical than rational.

Obviously, of these three attitudes, the first two evade the problem either by arbitrarily denying its existence or by arbitrarily denying the Laws of Thought upon which it depends. Only the third attitude asserts the Laws of Thought and asserts the existence of the problem. Though the puthujjana does not see the solution of the problem, he ought at least to see that to evade the problem (either by denying its existence or by denying the Laws of Thought on which it depends) is not to solve it. 

He will therefore choose to endure the discomfort of the third attitude until help comes from outside in the form of the Buddha's Teaching, or he himself finds the way out by becoming a Buddha.

Nanavira Thera