A Flawed Semiotic Square?
In that piece, I quoted from Shlomith Rimmon-Kenan's Narrative Fiction: Contemporary Poetics (London and New York: Methuen & Co. Ldt., 1983; [cf. new 2002 edition]):
Whereas the two pairs of opposites in Lévi-Strauss's homology are of the same kind, Greimas puts into place two kinds of opposed semes (the 'seme' being the minimal unit of sense): contradictories and contraries. Contradictories (A v. not-A) are created when one seme (or -- in logic -- one proposition) negates the other, so that they cannot both be true and they cannot both be false. They are mutually exclusive and exhaustive (e.g. 'white' v. 'non-white'). Contraries, on the other hand (A v. B), are mutually exclusive but not exhaustive (e.g. 'white' v. 'black'). They cannot both be true, though they might both be false (Copi 1961, pp. 142-3). (Rimmon-Kenan, 12)I then noted that for those who had an interest in this sort of thing, Routledge has a new edition (2002) available.The "Copi'' referred to is Irving M. Copi's Introduction to Logic (available since 2004 in edition number twelve).
I now want to focus on what Rimmon-Kenan then adds after the material quoted above:
Replacing 'A' and 'B' by 'S1' and 'S2' (the 'S' standing for 'seme'), Greimas presents the 'semiotic square' thus: (Rimmon-Kenan, 12)Here, Rimmon-Kenan introduces a diagram similar to the image at the top of this entry (and accessible here). Note that the supralinear strokes above the lower S1 and lower S2 indicate non-S1 and non-S2, respectively. You will also need to alter the above image slightly in your mind's eye. The positions non-S2 and non-S1 have two horizontal arrows exactly like those two between S1 and S2. Additionally, between S1 and non-S2 and between S2 and non-S1, there are vertical arrows pointing up. Finally, ignore the words "presuppostion" and "contradiction."
Rimmon-Kenan then goes on to state:
In the universe of the French novelist Bernanos, for example, S1 and S2 are 'life' and 'death', and the square takes the following form: (Rimmon-Kenan, 12)
Rimmon-Kenan then re-labels the square, with S1 and S2 as "life" and "death," respectively, and non-S2 and non-S1 as "non-death" and "non-life," respectively. Now, in terms of Copi's logic, S1 (life) and non-S1 (non-life) as well as S2 (death) and non-S2 (non-death) are contradictories, which means that "they cannot both be true and they cannot both be false .... [but] are mutually exclusive and exhaustive." In terms of the same logic, S1 (life) and S2 (death) along with non-S2 (non-death) and non-S1 (non-life) are contraries, which means that "[t]hey cannot both be true, though they might both be false," and they "are mutually exclusive but not exhaustive" (Rimmon-Kenan, 12).
But if non-S2 (non-death) and non-S1 (non-life) are contraries, then they should be mutually exclusive categories, which I don't quite understand. Take a stone of non-organic origin, for instance. It's certainly non-life, so it fits nicely into non-S1 (non-life). But it's also non-death since it was never a living thing, so it fits nicely into non-S2 (non-death). This means that non-S2 (non-death) and non-S1 (non-life) are not mutually exclusive and thus cannot be contraries.
My question: Where am I going wrong in all this? Is the semiotic square flawed , or does the problem lie with my reasoning?
Perhaps my cyber-buddy Maverick Philosopher aka Bill Vallicella could enlighten me ... or anyone else out there.
UPDATE: Now, I see where I went wrong. The categories non-S2 (non-death) and non-S1 (non-life) are not contraries; they are subcontraries. Subcontraries "cannot both be false together, but they could both be true" (see here).
The square wasn't flawed; my thinking was. Sometimes (i.e,. often), my brain shortcircuits, but the connections do finally get made...