The polyvalent logic presupposing an infinite number of values in the interval false-true 0 ≤ x ≤ 1 is a part of bivalent (0-1), Aristotelian logic. Poetic logic is inscribed on a different surface. It remains indebted to Aristotelian logic not in being a part thereof, but insofar as it contains and transgresses that logic. Since poetic unity is constructed in relation to an other as double, the problem of truth (of the 1) does not concern it. The poetic paragram bypasses the one, and its logical space is 0-2, the 1 existing only virtually. (pg 44, Towards a Semiology of Paragrams)Admittedly, I didn't read all of the document. What I read, I didn't understand. I'm taking Kristeva out of context because I don't understand the context. Nevertheless, I got questions:
- How is polyvalent logic "part of" bivalent logic? The inverse (bivalent part of polyvalent) seems more reasonable to me. Yet, polyvalent and bivalent seem to have quite different logical rules.
- Unlike polyvalent logic, Kristiva claims that poetic logic (what's that?!) has a logical space of 0-2. It's therefore still bivalent, but because it doesn't contain 1 (truth) it need not concern itself with truth. Hm... but isn't the "1" merely a symbol to represent "truth"? Couldn't "2" also represent "truth"? Or "0" for that matter? In fact, you could be really crazy and suggest "√-1" to be the symbol for "truth". It wouldn't matter, would it?
I will leave you with another quote from earlier in the document. I find it entirely incomprehensible, though it does appear to contradict the above by saying that paragrammatic numerology (which I think is the same as poetic numerology) is "two" and "all" rather than "0" and "2". I like the "The zero is two which are one" statement, though that is very similar to another phrasing I know (i.e., the doctrine of the trinity - god, son and holy ghost are three that are one.) I'm not sure that the bible is a good source for learning logic, however...
The zero as non-sense does not exist in the paragrammatic network. The zero is two which are one: in other words, the one as indivisible and the zero as nothingness are excluded from the paragram, whose minimal unity is both an (empty) all and an (oppositional) two. We shall examine more closely this paragrammatic numerology, where there is no 'one' or 'zero' but only 'two' and 'all'. Unity is empty, does not count, the one is zero but it signifies: it controls the space of the paragram, it is there to fix the centre, but the paragram does not give it a value, a stable meaning. This 'unity' is not the synthesis of A and B; but it has the value of one because it is all, and at the same time it cannot be distinguished from two, because within this unity come together all the contrasting semes, both opposed to each other and united. At once unity and couple, the oppositional dyad, to apply a spatial expression, is realized in the three dimensions of volume. (pg 37, Towards a Semiology of Paragrams)