[lit-ideas] Plato's Diaphoron
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 10 Aug 2004 22:16:49 EDT
Plato on negation, otherness, and diairesis
In "Re: Plato, "Thesis/Antithesis", M. Chase writes:
>Plato *never* uses the two terms [thesis and antithesis] together.
>This one consideration, in my view, renders all Mr. Speranza's ...
>citations from Wiggins,
>Dunn, et al. quite otiose.
Good you add, "in your view". I was only trying to be illustrative, and note
that Plato is aiming at solving the _more general_ problem of 'negation' (or
"not") -- for how can you understand the very word 'antithesis' if it's not
in terms of 'not'?).
Plato indeed did have a thing with negation -- he seems to have failed to
understand it, and his attempt to improve on Parmenides's try at defining 'not'
in terms of 'falsity' -- and using 'otherness' instead -- does not seem to
succeed. And if he only used 'antithesis' once, he possibly used 'apophasis'
(Latin _negatio_) more than once?
I append below some of the other quotes by Plato on, er, 'negatio' -- note
that if Brann is right about 'diairesis', then there's more of a Platonic
influence in Aristotle than is standardly believed.
Cheers,
JL
---
(cf. Julius Moravcsik, â??Logic Before Aristotleâ??).
" It is very difficult to see how without involving oneself in a
contradiction one can really affirm that it is possible to say or think
anything false
(236E) [â?¦] For [1] such an affirmation involves positing that being of that
which is not (to me on einai)."
This relates to "theologia negativa", as was being discussed.
"It is quite undeniable that one who says what is not something says nothing
at all (ton [â?¦] me ti legonta pantapasi meden legein, 237C12)â?¦ Sophist.
237E3-6, tr. by Benjamin Jowett. Cited by Wiggins, p. 269.
"When we say not-being, we speak, I think, not of something that is the
OPPOSITE of being, but only of something different [â?¦]. 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."
Cited by Wiggins (286n11), and Dunn 1999:9 as â??a hintâ?? of a definition of
â??
notâ?? in terms of â??incompatibleâ??.
"The Strangerâ??s proof (Sophist 257b) that negation cannot be reduced to pure
not-being (or opposition) hinges on the fact that the Greek expression me
mega (literally â??not bigâ??, â??not greatâ??) cannot be read as a CONTRARY
affirmation: that which is NOT BIG need not therefore be SMALL."
"Through the Stranger, Plato argues explicitly that negation is not THE
CONTRARY (to enantion), but The Other (to heteron). The Platonic concept of
negation as a mark of difference assimilates 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, not oppositeness (contrariety), but simply otherness
or difference."
"For Platoâ??s Stranger, the putative fact that
A is not B
is unpacked into the corresponding positive fact that
A is other than (different from, or dissimilar to) B.
"But if there is no positive fact, we have been redeposited into the
nightmare realm of Parmenides (Cf. Gale 1976, Toms, and Pelletier for extended
discussion). Platoâ??s track with negation attracted the attention of
logicians and
philosophers since. Thus in Statement and Inference, Cook Wilson writes:
â??Platoâ??s contribution to the theory of negation in the Sophist was
pointing
out that not-being often means relative 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 Determination Est Negatioâ?? (Wilson 248).
A recent revisition is by Wiggins:
â??We are now, Plato thinks, in a position to explain negation in a way not
patently open to Parmenidean objection. The word â??notâ?? (me or ou),
adjoined to
a predicate G, signifies being other than G (357B-D). In other words if and
only if
~(Theaetetus)G
then, provided we concentrate, as Plato seems to, on the kind of case when F
and G belong to the same range â?? we infer
There is an F such that {((F) Î? (G) ) & (Theaetetus) O[F]}â??
-- where â??Î?â?? stands for difference (Greek diaphoron) â?? or what might be
meant by the same thing, â??(Theaetetus) O[some F such that (F) Î? (G)]â??.
"When we say that some object is not big, 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 it actually means (rather than otherwise â??implicateâ??] is
-- â??OTHER THAN BIGâ??.
So [the false sentence] says things which are not as things which are (ta me
onta ara hos onta legei) â?? [i.e. it says] things which are, but different
things which are from the things which are respecting Theaetetus (onton de ge
onta hetera peri sou). For I think we declared that there are many things
which are respective each individual, and that there are many things which are
not [respecting him or it] (Polla men gar ephamen onta peri hekaston einai
pou,
polla de ouk onta). Plato, Sophist 263B12.
Wiggins concludes:
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). (cf. Brann: â??A grand and
deliberate form of distinction making is the â??way of divisionâ?? (diairesis)
found
first in Platonic dialoguesâ??.
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