Parsons, Terence, "The Traditional Square of Opposition", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.),
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**Contrary**- All S are P, No S is P All s is P is contrary to the claim NO S is P.

**Subcontrary**Some S are P, Some S are not P

**Contradiction**- All S are P, Some S are not P, Some S are P, No S are P

**Super alteration[**- Every S is P, implies Some S are P No S is P, implies Some S are not P

**Sub alteration**- All S are P, Some S are P No S are P, Some S are not P

Summary

Universal statements are contraries: 'every man is just' and 'no man is just' cannot be true together, although one may be true and the other false, and also both may be false (if at least one man is just, and at least one man is not just).

Particular statements are subcontraries. 'Some man is just' and 'some man is not just' cannot be false together

The particular statement of one quality is the subaltern of the universal statement of that same quality, which is the superaltern of the particular statement, because in Aristotelian semantics 'every A is B' implies 'some A is B' and 'no A is B' implies 'some A is not B'. Note that modern formal interpretations of English sentences interpret 'every A is B' as 'for any x, x is A implies x is B', which does not imply 'some x is A'. This is a matter of semantic interpretation, however, and does not mean, as is sometimes claimed, that Aristotelian logic is 'wrong'.

The universal affirmative and the particular negative are contradictories. If some A is not B, not every A is B. Conversely, though this is not the case in modern semantics, it was thought that if every A is not B, some A is not B. This interpretation has caused difficulties (see below). While Aristotle's Greek does not represent the particular negative as 'some A is not B', but as 'not every A is B', someone in his commentary on the Peri hermaneias, renders the particular negative as 'quoddam A non est B', literally 'a certain A is not a B', and in all medieval writing on logic it is customary to represent the particular proposition in this way.

These relationships became the basis of a diagram originating with Boethius and used by medieval logicians to classify the logical relationships. The propositions are placed in the four corners of a square, and the relations represented as lines drawn between them, whence the name 'The Square of Opposition'.

We know that Lacan tried to undercut Aristotle’s square of opposition, which he used to develop his four formulae of sexuation:

ReplyDeletehttp://www.swingtradesystems.com/lacan/lacan-and-aristotle.html

He claims his own logical square undermines the universals of both qualities by the ‘existence without essence’ of his own reworked particular negative proposition

So can we conclude his is not Aristotelian?

https://www.slideshare.net/mobile/JayneilEnriquez/square-of-opposition-12628218

ReplyDeleteI would consider myself a student and ask you what you think?

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