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.


Bibliography

         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.