I have been reading Albert Camus’ The myth of Sisyphus. His central question is whether life is worth living even if it is absurd. In order to answer that question he first demonstrates why life indeed is absurd. Absurdity for Camus is a result of the conflict, and tension between two factors: (1) Human nostalgia which describes the human condition which is a desire for unity, a single principle explaining and making intelligible the whole of reality. (2) The fact that reality is actually unreasonable and unintelligible. The absurd arises because of the irreconcilable tension between these two facts. As humans we deeply and intrinsically want what reality lacks and thus the absurd condition is born.
In order to advance his thesis Camus must show that the world is unintelligible and inreasonable. One way he attempts to do this is by showing that reason is impotent because of paradoxes it is immediately confronted by when it reflects on truth claims.
A central passage that I have been grappling with where Camus explains his point is the following:

“The mind’s first step is to distinguish what is true from what is false. However, as soon as thought reflects on itself, what it first discovers is a contradiction. Useless to strive to be convincing in this case. Over the centuries no one has furnished a clearer and more elegant demonstration of the business than Aristotle: “The often ridiculed consequence of these opinions is that they destroy themselves. For by asserting that all is true we assert the truth of the contrary assertion and consequently the falsity of our own thesis (for the contrary assertion does not admit that it can be true). And if one says that all is false, that assertion is itself false. If we declare that solely the assertion opposed to ours is false or else that solely ours is not false, we are nevertheless forced to admit an infinite number of true or false judgments. For the one who expresses a true assertion proclaims simultaneously that it is true, and so on ad infinitum.”

The conclusion that Camus wants to arrive at is that human reason has failed to make reality intelligible. As he says, “to understand is, above all, to unify” and reason he says, has been found completely incompetent of understanding reality. It has been unable of finding the single absolute principle that unifies the whole of reality.

Now it is not clear to me why Camus would say that when thought reflects on itself it discovers a contradiction. Does the contradiction arise in trying to define what thought is? Or does it arise in trying to distinguish what is true from what is false? The examples Camus uses do not seem related to this point and in no way demonstrate that there is a contradiction when “thought reflects on itself”.
Firstly, I agree completely with him that saying “all propositions are true” leads to an incoherence because then you affirm that even propositions contrary to yours are also true. Similarly claiming “all propositions are false” leads to an incoherence because even that proposition must itself be false. Thus far I am following him but then the next illustration has left me scratching my head – either I do not understand the gravity of what Camus wants to convey or he has exaggerated the point and tries to draw too much from it.
If we claim “propositions contrary to this proposition are false” Camus says we are then forced to admit an infinite number of judgments.

For example if we claim some proposition P such as “The earth is round” we are also claiming in addition (P is true). If we claim “P is true” then we are claiming as well that “(P is true), is true” and so on to infinity.

If this is how we are to interpret Camus it would be a fairly trivial argument to hang such a significant conclusion such as that the mind contradicts itself and cannot come to know what is true. One response is that to claim some proposition P, is shorthand for saying that P is true.
Another possible response is that these are different sentences expressing identical propositions. However even if the paradoxes hold clearly they have not prevented Camus himself from asserting a number of propositions which he takes to be true and has felt the need to convey them in the most eloquent of fashions. Clearly then the inspite of the paradoxes we might face when make truth claims – the mind is still able to navigate its way through that maze and arrive at some truth.

Thus the first argument that Camus advances to demonstrate that reality is unintelligible, and incapable of being grasped by reason I find unpersuasive. Have I misinterpreted Camus here?