[lit-ideas] Re: Le Pesanteur et la Grace
- From: Robert.Paul@xxxxxxxxxxxxxxxxxx (Robert Paul)
- To: lit-ideas@xxxxxxxxxxxxx
- Date: 06 Aug 2004 21:15:11 PDT
JL writes, in response to Erin Holder's temporary bafflement regarding Weil's
transparent utterance, "The demonstrable correlation of opposites is an image
of the transcendental correlation of contradictories," that what Weil may have
in mind is Aristotle's Square of Opposition? (Affirmo, Nego):
A E
I O
Consider 'red', 'blue', and 'non-blue'. If x is blue, then x is not red. If
x is blue, then x is not non-blue. That x is not blue if x is red is a
_demonstrable_ correlation (it can be demonstrated). What this is an 'image' of
is
the _trascendental_ (and thus non-demonstrable by 'deductive' logic)
correlation of 'blue' and 'non-blue'
*The traditional square of opposition has the shape JL says it has, but only at
the corners, so to speak. What is missing from his sketch is how the
propositions which are represented here by the letters A, E, I, and O, are
logically related. Traditionally, A = a universal affirmative proposition (All
whales are fish); E = a universal negative proposition (No whales are fish); I =
a particular affirmative (Some whales are fish); and O = a particular denial
(Some whales are not fish). It's clear that although both A and E cannot be true
together, they do not contradict one another in the sense that if either is true
the other can't be. E happens to be true, and its being true makes A false; yet
the law of the excluded middle 'Either all whales are fish or none are' doesn't
force us to choose between them.
*Thus, I and E and O and A are the only true contradictories: neither pair can
be true together. To show that not all whales are fish it's sufficient to show
that some fish aren't. And so on. What this has to do with 'correlation' and
negation escapes me. How many things are said to be red or not red here? If we
latch onto the lower left proposition 'Some...are...' then we mind have
'Something ('at least one thing,' as logicians say) is red. Where do we go from
here and how are we helped to go there by the square of opposition? Beats me.
This is something the S of O can't handle unless there is an offstage
demonstration that for all x, if x is blue, x is not red, and even then it's
impossible to see where, on a diagram which uses _as such a diagram must_ the
same subject and predicate throughout, a proposition with a different subject
and predicate would go. (The truth of 'All cats are mammals' doesn't bear on the
truth of 'All whales are mammals' e.g.), so there is no place for propositions
about red things and blue things in the same illustratration.
'Opposite' is a word Weil might have thought about for more than five minutes if
she wanted to say something intelligible about 'contradictories' and how they
are or are not 'correlated,' either transcendentally, or on the High Street.
Robert Paul
Mutton College
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