[lit-ideas] "Omnis Determinatio Est Negatio"
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 11 Aug 2004 10:19:12 EDT
Was: Plato's Heteron
In a message dated 8/11/2004 12:53:06 AM Eastern Standard Time,
Robert.Paul@xxxxxxxxxxxxxxxxxx writes:
In early Greek thought this would have been mysterious. In fact, in the
traditional formal logic, there was no negation of entire propositions.
We write 'It is not the case that [for all x, if x is F, x is G'] where x is
a
thing and F and G are properties or predicates (is a dog, and is a
marsupial,
respectively, perhaps).
Kant would have had to write 'All dogs are non-marsupials,' or 'No dogs are
marsupials.'
I don't think that either of these notations could appear in the Sophist,
where
it is being and non-being, not negation that is under investigation.
----
I beg to disagree. Plato seems to have mentioned the equivalent in Greek
for something like 'not' (ou, me). As the passages cited in my "Plato's
Diaphoron", it seems that some of his examples _are_ meant to illustrate the
general
use of 'not'. He failed to see that 'ou' and 'me' fulfils _more_ functions
than he thought they did.
Plato writes: "When we are told THE NEGATIVE signifies THE OPPOSITE, we
shall not admit it; we shall admit only that the particle â??notâ?? [ou or me]
indicates something different from the words to which it is prefixed, or
rather
from the things (pragmaton) denoted by the words which follow the negation."
Plato, Sophist -- cited by David Wiggins (286n11), and J. Dunn 1999:9 as â??a
hint
â?? of a definition of â??notâ?? in terms of â??incompatibleâ??. The
Strangerâ??s
proof (in Soph. 257b) that negation cannot be _reduced_ to pure [polar]
opposition hinges on the fact that the Greek expression "me mega" -- literally
â??not big
â?? -- can _not_ be read as a CONTRARY affirmation. That which is NOT BIG [me
mega] need not therefore be SMALL." [and Aristotelians need not apply].
Plato's Stranger argues explicitly that NEGATION isn't THE CONTRARY ("to
enantion"), but "the other" ("to heteron"). The Platonic concept of NEGATION
as a
mark of DIFFERENCE assimilates [it] NEITHER TO CONTRARIETY NOR TO
CONTRADICTORY
[antithesis]. The Parmenidean swamp of not-being can be skirted if we take
NEGATION to represent, not "not-being," and not [polar] oppositeness (or
contrariety) -- but simply otherness or difference. For Plato, the 'fact'
A is not B
["Dogs are not marsupials", to use Kant's and R. Paul's example] is
unpacked into the corresponding 'positive' ['affirmative'] fact:
"A is other than B."
["Dogs are _other_ [animals] than (from?) marsupials"]. If there is no
positive [affirmative] fact, we have been redeposited into the nightmare realm
of
Parmenides (Cf. R. Gale 1976, E. Toms, and J. F. Pelletier for extended
discussion). Platoâ??s track with negation did attract the attention of Cook
Wilson:
â??[His] contribution to the theory of negation
... was pointing out that "not-being" _often_
*means* 'relative' [and not 'absolute'] not-being,
something that is which _has_ a being of its own,
but not some _other_ kind of being [â?¦] This is the
familiar modern doctrine Omnis Determinatio
Est Negatioâ?? (Wilson 248).
More recently, Wiggins: "[Plato thinks] we are in a position to _explain_
negation [in a way not patently open to Parmenidean objection] ... â??notâ??
(me
or ou), adjoined to a predicate G [e.g. "dog"], signifies being "other than G"
(357B-D). In other words if and only if
~(Theaetetus)G
then, provided we concentrate ... on the kind of case when the predicates
"F" and "G" belong to the same range â?? we infer
There is an F such that {((F)Î?(G)) & (Theaetetus)O[F]}
-- where â??Î?â?? stands for difference (Gk. 'diaphoron') â?? or what might be
meant by the same thing:
(Theaetetus) O[some F such that (F) Î? (G)]
"When we say
"x is not big,"
-- but cf. "a dog is not a marsupial" -- then do we seem to express
(deloun) "small" any more than "middling-sized" by the predicate (rhema)
â??not bigâ???
Plato, 257D. Theaetetusâ??s reply is "kai pos" â?? how could we *mean* 'small'
rather than 'middling-size'? â?? which [one may] take to mean that â??not
bigâ??
_no more_ *means* â??middling sizeâ?? than it *means* â??smallâ??. What 'x is
not
big' *actually* means (rather than otherwise â??implicateâ??] is
"X is OTHER THAN BIGâ??.
R. Paul writes:
>Trying to understand the pre-Socratic and Platonic
>concepts of 'negation' (if there really even is such
>a thing) in terms of the modern negation sign will add
>nothing but confusion to a topic that's already confusing
>enough. ... One of the problems there is how one can
>speak falsely; and no conception of negation as it
>is now understood, sheds light on this.
Wiggins agrees in part, while noting he was only trying...
â??I do not [â?¦] believe that Plato came near to solving the problem of
negation, or that he reached any satisfactory understanding of what problem
this
problem really is. The little clarity we now have about the nature of the
problem of negation does not lead me to think that Platoâ??s notion of other
is of
fundamental importance in solving itâ?? (302).
Cheers,
JL
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