Triad: Critique of Dualism, Support of Monism in Plato
by Joseph A. Newton, III
12 June 1992
PHI 390 - James F. Hill, Ph.D.
Valdosta State University
Plato has been read as holding to a dualistic ontology that
separates into two worlds the intelligible and the sensible by a
seemingly unbridgeable gulf. This unbridgeability causes the
greatest difficulty, for how can entities in ontologically
separate worlds interact? This difficulty has typically led to
solutions which deny ontological dualism and opt instead for a
monism or a pluralism of idealism or of materialism. I shall
contend, however, that a dualistic interpretation of Plato's
philosophy is a misreading, that, in fact, Plato himself crit-
icizes dualistic ontology, and further that Plato's dialectician
employs a triadic method in which contraries are held together in
the pursuit of a unitary whole.
There is ample textual evidence of Plato's criticism of
dualistic ontology. A dualistic conception of the theory of forms
is entertained by young Socrates in Parmenides. This inadequate
formulation is explicitly criticized by Parmenides in what soon
came to be known as the Third Man Argument. But Parmenides does
not thereby dismiss the forms, rather, he affirms them and hints
at the possibility of a triadic formulation of the theory.
After listening to Zeno's treatises, young Socrates attempts
to solve Zeno's paradox by postulating a dualistic distinction
between real (intelligible) and apparent (sensible) and that the
paradox is the result of a confusion of absolute ideas with
concrete things which participate in those ideas. Then Parmenides
examines Socrates' doctrine of the independence of ideas from
concrete things:
"... when there is a number of things which
seem to you to be great, you may think, as you
look at them all, that there is one and the
same idea in them, and hence you think the
great is one" (132a, Fowler).
Following out the consequences of this hypothesis of the
independence of ideas, Parmenides shows that the problem of
relating ideas to material things will require indefinitely higher
ideas to relate the ideal and the material:
"That is, another idea of greatness will
appear, in addition to absolute greatness and
the objects which partake of it; and another
again in addition to these, by reason of which
they are all great; and each of your ideas
will no longer be one, but their number will be
infinite" (132b, Fowler).
This problem later came to be known as the "Third Man Argument."
But the purpose of this criticism is not to destroy the theory of
forms, for Parmenides asserts:
"... if anyone, with his mind fixed on all
these objections and others like them, denies
the existence of ideas of things, and does not
assume an idea under which each individual
thing is classed, he will be quite at a loss,
since he denies that the idea of each thing is
always the same, and in this way he will
utterly destroy the power of carrying on
discussion" (135c, Fowler).
The purpose of the criticism is to correct the dualistic
conception of forms and their participants as Parmenides attempts
to help Socrates solve his problem by suggesting that "could
there be some other third kind of participation" (131a, Fowler)
and encouraging him by affirming that "we must seek some other
method of participation" (133a).
But young Socrates is unable to solve his dilemma because he
has been unprepared and uninitiated as Parmenides explains,
"... for you try too soon, before you are
properly trained, to define the beautiful, the
just, the good and all the other ideas" (135d,
Fowler).
The final portion of the dialogue is then a demonstration of
the proper method of framing hypotheses, a method which evinces a
triadic structure. The function of the dialogue as a critique of
dualism can been seen working again in some of the other
dialogues.
In Republic Book VII, Plato implicitly criticizes dualism
when he corrects a previously accepted progression of science
through numbers, geometry, and astronomy by inserting the study of
three-dimensional objects after geometry and before astronomy.
Astronomy based merely upon geometry is incomplete and begins upon
arbitrary starting points instead of being grounded in a first
principle.
Subsequent to the parable of the cave, Socrates and Glaucon
discuss the proper education of the guardians by the state. Their
discussion focuses on constructing the proper sequence of studies
that will effect the "conversion and turning about of the soul"
(521c, Shorey). They have proceeded first from the study of
numbers, second to that of geometry, and third to astronomy when
Socrates realizes their mistake, "'After plane surfaces,' said I,
'we went on to solids in revolution before studying them in
themselves'" (528b). Socrates makes this mistake purposively, in
order to illustrate the current state of education, as he
explains:
"For, while the next thing in order is the
study of the third dimension or solids, I
passed it over because of our absurd neglect
to investigate it, and mentioned next after
geometry astronomy, which deals with the move-
ment of solids" (528d).
This "absurd neglect" is exemplified by "the so-called arts and
sciences whose assumptions are arbitrary starting points" (511d).
Glaucon articulates Socrates' criticism:
"And though it is true that those who contem-
plate them are compelled to use their under-
standing and not their senses, yet because
they do not go back to the beginning in the
study of them but start from assumptions you
do not think they possess true intelligence
about them although the things themselves are
intelligibles when apprehended in conjunction
with a first principle. And I think you call
the mental habit of the geometers and their
like mind or understanding and not reason be-
cause you regard understanding as something
intermediate between opinion and reason" (511d).
Thus, the basis of a proper education grounded in a first
principle cannot be reduced to principles of two-dimensional
studies of numbers and geometry alone but must go beyond these to
encompass the study of three-dimensional objects in themselves.
Socrates purposively jumps from geometry to astronomy to criticize
the deficiency of contemporary, dualistic education, perhaps
exemplified by the Sophists whom Socrates criticizes for only
pretending to have wisdom, and to suggest that the study
of the third dimension is ignored by artisans and scientists, such
as astronomers, who build their specialized knowledge on top of
studies of no more than two dimensions: numbers and geometry.
Robert E. Wood compares the two-dimensional superficies, flat
projections on a plane, with the three-dimensional stereometry,
capable of imaging the depth dimension of the soul, which is in
this sense a solid (502,508). This same pattern of self-criticism
of dualistic thinking in another dialogue Plato puts in the mouth
of someone who should know: an astronomer.
In Timaeus, the astronomer begins his cosmology with the
distinction between two kinds of being: that which is always the
same and that which is always in a process of becoming. However,
in a second, subsequent cosmological account, Timaeus corrects his
earlier classification of being and adds to his scheme a third
kind of being, the receptacle, before proceeding with a
description of the creation of the universe out of triangles.
At the beginning of his cosmological account, Timaeus begins
by making a distinction between two kinds of being:
"Now first of all we must, in my judgement,
make the following distinction. What is that
which is Existent always and has no Becoming?
And what is that which is Becoming always and
never is Existent?" (28a, Bury)
Being is accepted as a duality, incorporating being and becoming.
However, after the first account of the framing of the world soul
by the demiurge, Timaeus begins a second account with a trichotomy
of being:
"We must, however, in beginning our fresh
account of the Universe make more distinctions
than we did before; for whereas then we distin-
guished two Forms, we must now declare another
third kind. For our former exposition those
two were sufficient, one of them being assumed
as a Model Form, intelligible and uniformly
existent, and the second as the model's Copy,
subject to becoming and visible. A third kind
we did not at that time distinguish, consider-
ing that those two were sufficient; but now
the argument seems to compel us to try to
reveal by words a Form that is baffling and
obscure. What essential property, then, are
we to conceive it to possess? This in parti-
cular, -- that it should be the receptacle,
and as it were the nurse, of all Becoming"
(Bury, 49A).
This introduction of the receptacle as a third kind of being thus
corrects the earlier dichotomy with a trichotomy. Again Plato
employs a literary pattern in which a discoursant criticizes his
own dualistic thought as inadequate. In the Republic,
Socrates cannot proceed directly from plane geometry to astronomy.
In Timaeus, the philosopher-astronomer recounting a cosmology
recognizes that dualistic ontology is not sufficient for a
complete explanation grounded to a first principle. A third kind
of being is required.
Going beyond a criticism of dualism, Plato's theory evinces a
triadic structure that promises to ground itself in a first
principle. Perhaps in no other dialogue is the triad more
textually explicit than in Timaeus. Not only does the triad
manifest in the fundamentally triangular structure of the
universe, it also appears in the action of the demiurge framing
the world-soul as well as in the conception of space, the
receptacle, the third kind of being.
In the second cosmological account given by Timaeus, a
previously dualistic ontology is improved with the addition of a
third kind of being. Timaeus explains:
"Wherefore we must also acknowledge that one
kind of being is the form which is always the
same, uncreated and indestructable, never
receiving anything into itself from without,
nor itself going out to any other, but invis-
ible and imperceptable by any sense, and of
which the contemplation is granted to intelli-
gence only. And there is another nature of
the same name with it, and like to it,
perceived by sense, created, always in motion,
becoming in place and again vanishing out of
place, which is apprehended by opinion jointly
with sense. And there is a third nature,
which is space and is eternal, and admits not
of destruction and provides a home for all
created things, and is apprehended, when all
sense is absent, by a kind of spurious reason,
and is hardly real -- which we beholding as in
a dream, say of all existence that it must of
necessity be in some place and occupy a space,
but that what is neither in heaven nor in
earth has no existence" (52a-b, Jowett).
However, even the first account realizes the need for a triadic
ontology and describes the demiurge compounding a third,
intermediary kind of being:
"Midway between the Being which is indivisible
and remains the always the same and the Being
which is transient and divisible in bodies, He
blended a third form of Being compounded out
of the twain, that is to say, out of the Same
and Other; and in like manner He compounded it
midway between that one of them which is
divisible in bodies. And He took the three of
them and blent them all together into one
form, by forcing the Other into union with the
Same, in spite of its being naturally diffi-
cult to mix. And when with the aid of Being
He had mixed them, and had made of them one
out of three, straightway He began to distri-
bute the whole thereof into so many portions as
was meet; and each portion was a mixture of
the Same, of the Other, and of Being" (35a-b,
Bury).
Presumably, the ontology of this first account remains dualistic
and imports what it needs by the action of the demiurge. The
second account does not employ a demiurge, perhaps because this
third is shifted from a creative action of a god into third kind
of being.
Why is a third kind of being necessary? Timaeus affirms that
two things cannot be combined without a third:
"Wherefore also God in the beginning of creat-
ion made the body of the universe to consist
of fire and earth. But two things cannot be
rightly put together without a third; there
must be some bond of union between them. And
the fairest bond is that which makes the most
complete fusion of itself and the things which
it combines, and proportion is best adapted to
effect such a union" (31c, Jowett).
Thus two things cannot be joined without a third thing to effect
the joining. The most perfect bond is that of harmonic
proportion, a method that folds itself into the union. But how
does such a bonding method effect such perfection of union?
Timaeus gives a mathematical explication of how harmonic
proportion is applied to unify things into a one:
"For whenever in any three numbers, whether
cube or square, there is a mean, which is to
the last term what the first term is to it,
and again, when the mean is to the first term
as the last term is to the mean -- then the
mean becoming first and last, and the first
and last both becoming means, they will all of
them of necessity come to be the same, and
having become the same with one another will
be all one" (32a, Jowett).
This passage describes how two or more things can be truly
harmonized into one thing by the action of a third. The
emplacement of the third into relation with the two is such that
it presupposes and anticipates a unity. That is, the placement of
the third is guided by a commitment to principles of ethics and
aesthetics: the good, the beautiful, the one. This action is
exemplified by the demiurge in his creation and framing of the
world-soul as well as by the philosopher attempting to find a
unifying explanation of multiplicities of phenomena.
The significance of a two-level application of a ratio is
explained further by Timaeus:
"If the universal frame had been created a sur-
face only and having no depth, a single mean
would have sufficed to bind together itself
and the other terms, but now, as the world
must be solid, and solid bodies are always
compacted not by one mean but by two, God
placed water and air in the mean between fire
and earth, and made them to have the same pro-
portion so far as was possible - as fire is
to air so is air to water, and as air is to
water so is water to earth - and thus he bound
and put together a tangible heaven" (32b,
Jowett).
The process of the application of division by a certain ratio and
its reapplication to those results provides two means and thus
three dimensions with which to explain the experience of space in
the physical, phenomenal world. It is not enough to explain a
visual field with only two dimensions of width and length because
this leaves out explanation of the experience of depth in space.
Similarly, it is not enough to explain what is known with only two
dimensions of intelligibility and sensibility because meaning, the
relation of the knower to the knowledge of the known, would be
ignored. Plato specifically states that the knower cannot be left
out of the relation between intelligibles and sensibles when he
states:
"And the motions which are naturally akin to
the divine principle within us are the
thoughts and revolutions of the universe.
These each man should follow, and by learning
the harmonies and revolutions of the universe,
should correct the courses of the head which
were corrupted at our birth, and should
assimilate the thinking being to the thought,
renewing his original nature, so that having
assimilated them he may attain to that best
life which the gods have set before mankind,
both for the present and the future" (90c-d,
Jowett).
Bury translates differently: "making the part that thinks like
unto the object of its thought, in accordance with its original
nature ..." This anticipates and specifically answers to the
charges against modern thought brought by postmodernists,
deconstructionists, and others such as the conflict theorists of
the Frankfurt school of sociology. Modern thought has been
criticized by these for its lack of self-awareness and the
resulting tyranny of cultural absolutisms. But perhaps Plato's
method of methods can anticipate this problem and provide for its
solution. Here in Plato we can see the inspiration for Peirce's
triadic formulation of semiotic and his criticism of Saussure's
dualistic semantics.
The problem of dualism in Plato manifests when an attempt is
made to understand how an object participates in its form. One
solution is that provided in Timaeus' second cosmological account,
which posits a triadic ontology in which space provides the home
for all created objects. Another solution is that of the
introduction of the application of harmonic proportion, provided
in Timaeus' first cosmology by the demiurge. This demiurgic
introduction of harmony from without will be analogous to the case
of the philosopher in his approach to knowledge by the employment
of the dialectic.
Analogous to the framing of the world soul by the demiurge is
the framing of an hypothesis by the Eleatic philosopher in
Parmenides. A third way of participation in the forms, neither by
whole or part nor by imitation, is demonstrated by the
philosopher's action of holding together of contraries in his
pursuit of truth of the one ultimate reality of being.
After the criticism of the untrained philosopher for a
dualistic conception of forms and participants in Parmenides,
Socrates, Zeno, and the others implore Parmenides to demonstrate
the Eleatic method of philosophy which takes an hypothesis and
traces out the consequences of both its truth and falsity.
Parmenides proceeds with a discussion of the hypothesis that "one
is" and its opposite "one is not." Thus the principle of
dichotomy or the method of division by contraries is demonstrated
(Fowler, 196).
Reiner Schürmann describes Parmenides method of framing an
hypothesis as a "unitary usage of contraries" in which the
philosopher "learns how to hold contraries together" (12-13).
Schürmann states,
"Now, if the One holds together differing
forces, then it anchors every human law on the
solid evidence that what is, is; but it also
anchors there its contrary opposite. It is
difficult not to conclude from such 'holding
together,' synechia, that henological legiti-
mation of positive laws ties these laws back
to an ultimate ground and unties them by the
same movement" (13).
These contraries are not contradictories, they are
antinomies. Thus they do not exclude each other (as do the ideas
of being and non-being) but rather imply or call out each other.
This process of framing an hypothesis is three-fold: a unity is
grasped, divided, and re-unified. The process is guided by the
principle of unity and the philosopher's search for a unitary
whole, a synthesis of theses and antitheses. Thus the value of
unity as good precedes, is presupposed by, and is implied in the
method.
Dualistic ontology receives a triadic critique in Plato.
Explanation of participation between two kinds of being becomes
difficult. Plato's solution is either to expand ontology to a
three-fold being or to employ a demiurge or a dialectician. A
triadic ontology posits unchanging-being, becoming, and
receptacle-for-becoming with their respective entities forms,
objects, and space. While this implies a Parmenidean graduated
reality where only being is real and becoming is illusion, it
promises the penetration of sensibles and the recognition of
intelligibles through dialectic. Dialectic is logic at the
service of beauty (aesthetics) and of good (ethics) insofar as it
employs harmonic proportion and seeks a unitary whole. Dialectic
is the movement of becoming towards being, of eros towards the
good. The problem then becomes how to be able to relate the many
into the one. Peirce informs us of what Plato surely knew, that a
minimum of three relations are required to build all higher
relations. Thus Plato employs a triadic scheme to save a monistic
realism from dualistic ignomy.
Hamilton, Edith and Huntington Cairns, ed. The Collected
Dialogues of Plato: Including the Letters. Princeton, NJ:
Bollingen Series LXXI: Princeton U. Pr., 1989 [1961].
Plato. Parmenides. Francis Macdonald Cornford, trans. The
Collected Dialogues of Plato: Including the Letters.
Hamilton, Edith and Huntington Cairns, ed. Princeton, NJ:
Bollingen Series LXXI: Princeton U. Pr., 1989 [1961].
-----. Parmenides. H. N. Fowler, trans., intro. Plato in Twelve
Volumes: Cratylus, Parmenides, Greater Hippias, Lesser
Hippias. vol 4. Cambridge, MA: Harvard U. Pr., 1975 [1929].
-----. Republic. Paul Shorey, trans. The Collected Dialogues of
Plato: Including the Letters. Hamilton, Edith and Huntington
Cairns, ed. Princeton, NJ: Bolligen Series LXXI: Princeton
U. Pr., 1989 [1961].
-----. Timaeus. R. G. Bury, trans., intro. Plato in Twelve
Volumes: Timaeus, Critias, Cleitophon, Menexenus, Epistles.
vol 9. Cambridge, MA: Harvard U. Pr., 1975 [1929].
-----. Timaeus. Benjamin Jowett, trans. The Collected Dialogues
of Plato: Including the Letters. Hamilton, Edith and
Huntington Cairns, ed. Princeton, NJ: Bollingen Series LXXI:
Princeton U. Pr., 1989 [1961].
Schürmann, Reiner. "Tragic Differing: The Law of the One and the
Law of Contraries in Parmenides." Graduate Faculty
Philosophy Journal . 13: 1 (1989), 3-20.
Wood, Robert E. "Image, Structure and Content: On A Passage in
Plato's Republic." Review of Metaphysics. 40: 2 (March 1987),
495-514.
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