Thursday, June 01, 2006

A Flawed Semiotic Square?

Adrian Miles, "Singin' in the Rain: Greimas"
Department of Communication Studies HyperText Project (2001)

Some time back (9/8/05), I posted an entry titled "Who said that literary theorists can't be logical!"

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...


At 10:48 PM, Anonymous Anonymous said...

This looks like a diagram from Jung on the Psychology of the Transference to me: it maps the operation of psychological incest. No, guess that is something else.
Guess I can't say I know what this is exactly.

At 1:27 AM, Blogger Saur♥Kraut said...

OUCH. my head hurts...

At 4:20 AM, Blogger Horace Jeffery Hodges said...

Eshuneutics and Saur, whatever it is and whyever it hurts, it's all my fault for confusing subcontraries with contraries.

I promise to be good from now on...

Jeffery Hodges

* * *

At 1:14 PM, Blogger Daniel said...

Ive been trying to wrap my mind around the ever-allusive semiotic square all evening. here is what i think the deal is. the bottom two entities are not contraries according to your definition of contrary, i.e. "mutually exclusive but not mutually exhaustive," because they are not mutually exclusive. black/white works the same way. purple is both non-black and non-white. i think its only the top two that are contraries...? so, my guess is that the semiotic squares that have the bottom two are "contrary" are defunct!? this would not be surprising considering the scholarly habits of most literary theorists.

another thing ive noticed about this is that the "complimentarity" seems to only run one way, but the web sites that have explained the S.C. to me so far have made no mention of it. everything that is in S1 is also included in -S2, but there are things in -S2 which arent in S1. maybe im just running around in circles, i still fail to see how this thing doesnt just state the obvious in an overly-complicated manner.

At 1:17 PM, Blogger Daniel said...

i meant S.S., not S.C.

At 2:06 PM, Blogger Horace Jeffery Hodges said...

Herr Richter, you're probably a better judge than I of the Semiotic Square. You're certainly right that the bottom two entities are not contraries.

A few hours after posting the entry, I realized my error. The bottom two entities are subcontraries.

I added an update to explain:

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"

Perhaps the update didn't post on some cached sites -- if that's where you were reading.

I don't know that the Semiotic Square is very useful. I found it interesting because it implied a desire among some literary theorists to be logical.

The theorists might not quite have succeeded in that, however, for my cyberbuddy Bill Vallicella noted the following in an email:

"One quibble I have is that the author speaks of a seme as a minimal unit of sense and then identifies that with a proposition. Surely that is a mistake: if so, then the constitutents of propositions would lack sense. There also seems to be some blurring of the distinction between predicates and propositions."

So, yes, there are some problems with the Semiotic Square even if correctly judged.

Jeffery Hodges

* * *

At 7:37 AM, Blogger Daniel said...

ahh alright that explains it.

Sprechen Sie Deutsch? Ich sprechen Deutsch nicht :)

At 8:36 AM, Blogger Horace Jeffery Hodges said...

Ich habe sechs Jahre in Deutschland gelebt, aber mein Deutsch ist leider manchmal nicht grammatisch.

Jeffery Hodges

* * *

At 1:06 AM, Blogger Daniel said...

Aber Ich sprichen Deutch nicht!


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