Cicero's Liar Paradox

As a follow up to my previous post and a quick exercise, I will briefly consider a more classic formulation of the Liar's Paradox. This one come from Cicero's Academica (2.30), though he attributes it to Chrysippus. Cicero (an Academic Sceptic) is responding to Lucullus (follower of Antiochus who practically became a Stoic). Here he casts doubt on the validity of logical inference.

Cicero puts its thus: Si dicis te mentiri verumque dicis, mentiris; dicis autem te mentiri verumque dicis; mentiris igitur. Translation: "If you say that you are lying and are speaking truly, you lie; but you do say that you are lying and are speaking truly; therefore you lie."

The following is valid, though not really a syllogism as such because it doesn't give us new knowledge (since the minor premise is the same as the conclusion): Si mentiris, mentiris; mentiris autem; mentiris igitur. If you are lying, you are lying; you are lying; therefore you are lying. Cicero states this later as if it was equivalent to the paradox stated above. It is not however.

Lets take the first premise of the paradox:  "If you say that you are lying and are speaking truly, you lie." What are you saying that you are lying about? If about another proposition and you were in fact lying, then you would indeed be speaking truly. But of course there is no paradox here. You would not be claiming that you were lying about this proposition. The idea is that the liar is lying about his own statement about his lying. 

But if you say you are lying about the very statement you are making (sc. that you are lying), your statement is actually meaningless. In order to be lying about something, you have to be lying about something. If you say that your are lying, what are you lying about? If the answer is that you are lying, then again it can be asked what that lying is about. If that is about lying and that is about lying and so on, we have an infinite regress. The statement "I am lying" only makes apparent sense. But if it just about itself, it doesn't make sense.

Secondly, since every proposition implies its own truth, if I say "I am lying" then I am affirming the truth of my lying. But at the same time I am affirming the falsity of my lying because I am lying. Therefore, the statement is incoherent and absurd. This doesn't mean that it is both true and false. But rather that it is neither. It is absurd. If you both affirm and deny the same thing, you aren't making sense. Likewise a pseudo-proposition that affirms and denies the same thing doesn't actually make any claim. Therefore, it is not a proposition. A proposition affirms an identity between two beings or denies such an identity. If I try to both of these things, then I end up doing neither. I have cancelled myself out. Therefore, I have made my statement absurd. I have deprived it of intelligible value.