Talk:Semiotic square

Is Greimas's square really derived from the Aristotelian square? The example's logical structure is instead that of the Boolean square of opposition.

A	E
I	O

Aristotelian: A & E can't both be true. I & O can't both be false. So there are 8 distinct options for compounding: A, I, E, O, A-or-E, I-&-O, T, & F.

Boolean: A & E can both be true. I & O can both be false. And 16 distinct options are produced for compounding.

The example:

masc.	fem.
~fem.	~masc.

allows the Boolean-style square's full 16-fold of resultant distinct options, not merely the Aristotelian 8. It makes no difference if you arrange it like so,

masc.	~fem.
fem.	~masc.

you still get 16:

Example's semiotic square's options for compoundings:
strictly masc. or strictly fem.	masc. & ~fem. (strictly masc.)	fem. & ~masc. (strictly fem.)	masc. & ~masc. (or {fem. & ~fem.}, etc.) (tautologously false)
masc. or fem. or both (not neuter)	masc.	fem.	masc. & fem. (hermaphrodite)
~fem. or ~masc. or both (not hermaphrodite)	~fem.	~masc.	~masc. & ~fem. (neuter)
masc. or ~masc. (and {fem. or ~fem.}, etc.) (tautologously true)	masc. or ~fem. or both (not strictly fem.)	fem. or ~masc. or both (not strictly masc.)	neuter or hermaphrodite

The Tetrast 15:35, 1 September 2007 (UTC)[reply]

84.100.243.155 (talk) 22:15, 14 June 2009 (UTC)Contribution of Jean-François Monteil I do not say here that the blending of S1 the male principle and S2 the female principle is inconceivable. So, I do not exclude a priori the conjunction S1 AND S2. But then, one cannot identify S1 and S2 with the points : A et E of the logical square. By definition, A et E symbolize facts which are mutually contrary. If you identify S1 the male principle with A and S2 the female principle with E, you forbid yourself to imagine the coexistence in a same subject of the male principle and the female principle, and that a priori. If you hold that a conjunction of the male principle and the female principle is a possibility, which, once more, is quite legitimate, you may no longer identify S1 and S2 with A and E. You must choose: if S1 and S2 are compatible, S1 and S2 must not be identified with A and E. Contrariwise, if S1, it’s A and if S2, it’s E, then S1 and S2 are necessarily incompatible. Let us suppose now that S1 and S2 are identified with A and E and are mutually contrary. We have to consider a triad of three contrary facts and a triad of three subcontrary facts. I define two contrary facts as two facts that are incompatible and can be both excluded. For instance, being male and being female are incompatible facts and both can be excluded in so far as there are entities which are neither male nor female. I define two subcontrary facts as two facts that are compatible and cannot be both excluded. For instance, being non-male and being non-female are quite compatible facts since, as we have just seen, certain entities are neither male nor female. Obviously, if the male principle and the female one cannot coexist in the same subject, being non-male and being non-female cannot be both excluded for the exclusion of the quality non-male is equivalent to the quality male and the exclusion of the quality non-female is equivalent to the quality female.Both triads, which we are going to describe briefly, can be represented in the logical hexagon of Robert Blanché. With its 6 points: A E I O + Y U, the logical hexagon is a more complete and therefore more potent figure than the square with its four points A E I O . If we use the logical hexagon to deal with the question, we have to speak of three contrary facts: S1 being male, S2 being female, ~S1 and ~S2 being neither male nor female. This being neither S1 nor S2 is being A-SEXUAL. It corresponds to the third contrary Y added by Robert Blanché. A word now about the three subcontrary facts. We have non-S1 being non-male, non-S2 being non-female, and last, S1 w S2 that is, being either S1 or S2. This S1 w S2 corresponds to the third subcontrary U added by Robert Blanché’s Structures intellectuelles. If one identifies S1 with A and S2 with E, there are three pairs of contradictory facts to consider:[reply]

     I-	S1 versus non-S1 identified with the pair A versus O.
                 Male versus non-Male
    II-         S2 versus non-S2 identified with the pair E versus I.
                 Female versus non-Female 
    III-   ~S1 and ~S2 versus S1 w S2 identified with the pair Y versus U.
                  Neither Male nor Female versus Either Male or Female

I sum up my remarks about the article of wikipedia: semiotic square. Since the author of the article presupposes that S1 must be identified with A and S2 with E, the value ~S1 and ~S2 being A-SEXUAL, must be opposed to the value S1 w S2 being SEXED and not to a value S1 et S2. The articles de Jean-François Monteil on the logical square and the logical hexagon can be found on a site of the University of Bordeaux : http://erssab.u-bordeaux3.fr and on a personal site: http://www.grammar-and-logic.com/index.php. Jean-François Monteil 14 Juin 09