Monday, September 14, 2015

Reflections on the Difference, Contradiction, and Motion of all things in Plato's Sophist 246a-259b

the Sophist, Plato’s search for the nature of the sophist, who, in contrast to the philosopher, merely pretends to teach wisdom for wealth and fortune, leads him to examine the nature of appearances, falsehood, and lies, which are, for Plato, altogether defined as that which is neither real nor true. In the middle of the dialogue he presents, as a rhetorical antinomy, the “clash of argument” between the materialist Giants and the idealist Friends of the Gods (Findlay 1978, 12), and enters the fray of this “interminable battle” and “clash of argument” to “shatter and pulverize” each opponent (246a-249d): he argues against the materialists, who identify reality with bodies, for admitting that the body is animated by the soul while the soul is bodiless, and yet failing to recognize that this very admission requires some further universal ground to be shared between material bodies and the immaterial souls beyond the body (247d); and he argues against the idealists, who identify reality with intelligible forms, for admitting that the unchanging being of the souls may know changing becoming through the senses, and yet failing to recognize that this activity of knowing requires both the knowing subject and the known object to be changed in the process. (248c-d)

Plato forthrightly rejects both extreme positions of the stasis of the idealists for annulling becoming (249b) and the extreme dynamism of the materialists for annulling being (249c), and advises, instead, that “only one course is open to the philosopher”: to annul the extreme incompatible while preserving the moderate compatible elements of each opposed position, “like a child begging for ‘both’ at once.” (249d) The unity of these opposites is, however, not merely the sum of the opposed parts. In apparent answer to the part-whole dilemma of the Thaeatetus, which asked whether any complex whole as identical or different from the sum of its parts (203d-204a), he describes this reality as some “third thing over and above these two contraries”, which “is not motion and rest ‘both at once’, but something distinct from them… in virtue of its own nature.” (250c) This ‘third thing’ is thus neither unchangeable, nor changeable; nor both, nor neither; but rather some new mixture that can only emerge from within the confluence of the explosive contradiction of opposites.

Plato names this “guide on the voyage of discourse” (253b) the philosopher’s “science of dialectics.” (253d) He proposes to demonstrate its application by dividing and combining the “most important” Ideas for the purpose of finding the elusive definition of “what is not.” (254b) Since (i) Existence can be combined with both (ii) Rest and (iii) Motion, but neither (ii) Rest nor (iii) Motion may be combined with one another, while each participates in (i) Existence; and since (ii) Rest and (iii) Motion are the same for themselves but different for each other, while neither (ii) Rest nor (iii) Motion is the same as (iv) Sameness and (v) Difference; Plato enumerates at least five Arch-Ideas: (i) Existence; (ii) Rest; (iii) Motion; (iv) Sameness; and (v) Difference. (254d-255e) And just as Plato had previously rejected the extremes of static idealism and dynamic materialism, he now also rejects the extremes of absolute identity and absolute difference: for to avoid the transitivity of predicates and the Parmenidean reduction of all the Arch-Ideas to static Parmenidean Being, Plato denies the strict identity of any of the Arch-Ideas (255a); but to preserve the existence of motion Plato affirms that “motion is [exists] by virtue of partaking of existence.” (255e)

After enumerating the five kinds, or Arch-Ideas, by which reality is specifically divided (254d-255e), Plato first defines the third kind of (iii) Motion as that Arch-Idea which is not (ii) Rest (i.e. (iii) Motion), and yet exists in virtue of partaking in (i) Existence. (255e) Since, moreover, Motion partakes and yet is different from (iv) Sameness, Motion also participates in (v) Difference. Hence, (iii) Motion is defined as the proper opposite of (ii) Rest, which participates in (i) Existence, (iv) Sameness, and (v) Difference. Since Motion participates in (iv) Sameness that is itself the same and (v) Difference that is itself not the same, it is “both the same and not the same.” (256a) Plato explains how, for this equivocation, (iv) Sameness is imparted in the term 'same(ness)' in two different ways: Motion is called 'the same' “in reference to itself” by its participation in (iv) Sameness; but Motion is called 'not the same' when it is co-imparted in “combination with difference”, or with reference to another. The co-impartation of Sameness and Difference in an act of Existence makes Motion an existent in which identity and difference are centered, or as an identity-in-difference.  Plato applies this co-impartation of identity-in-difference to “fearlessly contend that motion is different from existence” even as it “partakes of existence.” (256d)

Plato makes identity-in-difference a universal principle of the science of dialectics when he suggests that it must “be possible for ‘that which is not [viz. different from existence] to be [viz. participative identity with existence] not only in the case of motion but of all other kinds.” (256d) Plato then applies the principle of identity-in-difference to the first Arch-Idea of (i) Existence when he contends that “existence likewise ‘is not’ in as many respects as there are other things.” (257a) There are thus as many negative opposites of existence as there are existing things. This application of the principle of identity-in-difference to Existence, allows Plato to re-conceive the logical function of negation (e.g. not-S) so that it may signify a relative rather than an absolute difference. He explains that “that which is not” does not mean “something contrary to what exists but only something that is different” (257b); and “the prefix ‘not’” does not signify its absolute contrary but rather only “indicates something different from the words that follow.” (258c)

Positive and negative terms (e.g. S & not-S) are thus no longer conceived as symmetrically opposed contraries. Rather, once negation has been re-conceived as relative difference, the negative term may now signify an asymmetrical opposition, in which a negative opposite is different in meaning from but also related back by participation to its positive opposite. This asymmetrical opposition of contraries allows Plato to re-conceive of the contrary differences that produce contradiction (e.g. S & not-S) on the model of participative difference, in which subordinate contraries are differentiated from even as they participate in superordinate contraries. Contradiction no longer simply annuls one or both of the contraries, but, for Plato’s dialectic, also promises to preserve both of the contraries in a participative identity-in-difference. Since, moreover, “the sum of all things is both at once - all that is unchangeable and all that is in change” (250d), this participative identity-in-difference is also a dynamic self-moving concept that comes to rest only in and through itself.

Since (iv) Sameness is only the same in relation to itself, or to itself, while (v) Difference is only difference in relation to another, or to-another, this identy-in-difference co-impartation of Sameness and Difference in Existence makes Motion both related to-itself and to-another. Since both Sameness relation to-itself and Different relation to-another are centered in the identity-in-difference act of existence, Motion is also only related to itself through its relation to another, and, vice versa, also only related to another through its relation to itself. Hence Motion is related to itself through relation to another through relation to itself, and vice versa, ad infinitum. Yet Plato also hints that this pivoting oscillation of relationality to-itself and to-another, like the framing false opposition of Idealism and Materialism (248a-249d), may be exceeded by a “third thing over above these two... in virtue of its own [essential] nature” (250b-c) and which, by their mutual participation, can be nothing other than the Arch-Idea of (i) Existence itself.

How does Existence exceed the pivoting oscillation of Motion, and Rest, Sameness and Difference, and relationality to-itself and to-another? This may only be possible if Plato's dualistic (and also tetradic) formulae are rejected in favor of triadic formulae, by which the false opposition of every binary-pair may be exceeded, anulled, and resolved. The second scholarch of the Old Academy, Xenocrates (c.339-314 BC), first rendered Platonism in the triadic formulae of the One, the Dyad, and the Triad; and this scheme was carried to perfection by the last ancient Platonist, Proclus (c. AD 412-485). Plato could not make his system comprehensively triadic so long as Existence was conceived as merely one among many extrinsically-related and substantival Arch-Ideas, for the extrinsic relationality of Existence made it impotent to move, exceed, and anull the various other Ideas, and especially the Arch-Ideas of Rest and Motion, Sameness and Difference. This triadicization of philosophy can, rather, only be accomplished once, as Plato seems to suggest, Existence is reconceived as the intrinsically related ground in which all other Ideas participate in themselves and are imparted in others.

For this purpose, we must now re-platonize Plato by reading the triadicism of Proclus into the Sophist. From the Phaedo (100c) and the Republic (596a), we learned that every universal Idea is the perfect paradigm of a predicate-property, which is imperfectly imparted into their particular instances, and which each participate in the universal Idea to the degree that they realize its perfection. Hence, the universal Ideas virtually possess all the diminishing degrees of the possible realization of particular instances. Since the first Arch-Idea of Existence must also virtually possess all the other Ideas, Existence must also be Rest, Motion, Same, and Different. And since Existence possesses Motion, it must, in some sense, be set in motion. It is not merely the self-standing substance of Aristotle, nor merely an eternal and static Ideas of the Phaedo and Republic, but a self-moving Idea that unfolds by division and enfolds by combination all reality reflected within itself.

Plato suggests this absolutization of Motion when he extends its distinctive difference, i.e.  identity-in-difference, to “all the other kinds.” (256e) Everything other than Existence is minimally different, i.e. non-identical and the proper negative opposite of Sameness, only insofar as it is “different from Existence” and “a thing that 'is not'” and “are not”, even though, by participation in Existence, they also “are” and exist. (256e) Since, moreover, everything that is not Existence is different from Existence and an impartation of Difference, all things are negatively differentiated. Everything at all is thus negative in some way simply because all things are different, and difference implies negation, not only horizontally from one another, but also vertically from Sameness and Existence itself.

This absolutization of the negativity of Difference may be dynamized into motion whenever the negativity of Difference coincides by co-impartation with the positivity of Sameness: for example, supposing that the Demiurge, which is self-moving and reflecting Existence, first thinks the imparticipation of Difference into that which is other-than itself (e.g. for Xenocrates, the self-oppositing Dyad), and finally thinks the Sameness of the differentia, whereby that which is other-than itself is reflected back so that both the Difference and the Sameness may again participate in Existence, then Existence sets itself into motion by first thinking by unfolding its own self-difference and then reflecting by enfolding this self-difference back into its own self-participation, and Sameness and Difference coincide in the completely reflective self-relation (e.g. for Xenocrates, the self-relating Triad) of the unfolding Difference and enfolding Sameness. Since this triadic self-relation is absolutized to every impartation of Difference and Sameness in Existence, every thought may be rethought as thinking in Motion.

This re-thinking of thought as thinking in motion also implies that every instance of a contradiction is, from a deeper and higher philosophical perspective, also an instance of difference that may be resolved by setting the contraries into dynamic motion. Plato suggests the Spinozan principle that every determinate differentation also conversely implies a negation of that which is different from the determinate differentiation (determinatio est negatio) when he writes that “in the case of every one of the forms there is much that it is and an indefinite number of things that it is not.” (256e) Hence, whenever thinking determinately affirms the form X, thinking also conversely implies the determinate negation that X is differentiated from not-X, and the determination of X is always implicated in the negatively opposed differentiation of not-X. Since, moreover, the proposition that affirms X and not-X is a contradiction, any formulation of a determinate proposition P may also conversely imply its opposed differentiation not-P.

When every thought is rethought as thinking in Motion, the self-moving thinking may exceed and annul even the formulation of oppositively determined propositions P and not-P: for just as Plato rhetorically demonstrated the antinomy of Materialism and Idealism, and promised to resolve it by dividing reality according to the five-fold Arch-Ideas, in which every ideal opposition is resolved into some third essence (250b), so may every co-impartation of Difference and Sameness in Existence, or identity-in-difference, be resolved in and through the dynamic self-moving of thinking. Plato suggests this rethinking of contradiction when he first denies that “a negative signifies a contrary” and admits only that “the prefix 'not' indicates something different from the words pronounced after the negative” and then affirms that “the nature of the different appears to be parceled out in the same way as knowledge.” (257c) Once the negative is reduced to nothing more than a difference, or an instance of Difference, and every such instance of Difference is imparted in and through the self-differentiating Motion of Existence, which is similar to thinking, then the fixed opposition of determinate propositions P and not-P may also be rethought in and through self-moving thinking.

The re-thinking of contradiction as self-moving thinking promises to re-relate every differential and oppository instance of contradiction in and through the continuously unfolding and enfolding triadic identity-in-difference of Difference and Sameness in Existence. Since, movement operates in the aesthetic realm of space and time, Plato also describes how, although “knowledge is surely one”, difference is parceled out across certain fields that are “marked off and given a special name proper to itself”, including “the parts of the single nature of the different” or of Difference itself. (257d) Difference is parceled out by its impartation into the fields of art, nature, and language: in art, difference is imparted into the distinct spaces that are delimited to include what is the same in relation to one part and exclude what is different in relation to another part; in nature, difference is imparted into the motion of bodies, which are both related to themselves as the object included in motion and also related to others as that which is excluded from the object yet towards which this self-related object is moving; in language, difference is imparted into the oppository determinate differentiations of words, X and not-X, that may be formulated into the contradictory propositions P and not-P.

Plato thus externalizes the logic of Difference into the aesthetic space of the beautiful when he writes that “there exists a part of the different that is set in contrast to the beautiful… whenever we use the expression 'not-beautiful'” for “that which is different from the nature of the beautiful.” (257e) Since this determination of the beautiful is “an instance of something that exists” and the not-beautiful is “set in contrast to something that exists”, and Existence is self-moving thinking, the self-moving differentiation of Existence may unfold into the aesthetic space of the beautiful, even as it reflexively participates to enfold the beautiful back into the triadic architectonic of Existence thinking itself. And since, moreover, this imparticipative unfolding and participative enfolding of Difference through the thinking of Existence is both the Same and Different, and at Rest and in Motion, through its architectronic self-relation of identity-in-difference, this self-moving thinking of Existence also eternally reflects the self-movement of thinking.

Parmenides had prohibited the possibility that non-being could ever be re-thought as a being; for “never shall this be proved, that things that are not, are.” (258c) Yet Plato concludes, to the contrary, that since the co-impartation of Sameness and Difference in language allows us to understand non-being as a being related to others, the 'what-is-not' of the Sophist “unquestionably is a thing, that has a nature of its own... in the sense 'that which is not' also, on the same principle, both was and is 'what is not', a single form to be reckoned with among the many realities.” (258c) Plato congratulates himself on having demonstrated the ontological innovation of the Sophist: “we have not merely shown that things that are not, are, but we have brought to light the real character of 'not-being'... of every part of it that is set in contrast to [or differentiated from] 'that which is' we have dared to say precisely that is really 'that which is not' [i.e. non-being].” (258d-e) The real character of non-being thus cannot be described as absolutely not being, without some degree of participation in Existence, but may rather only be described as that differentiated determination in between the extremes of absolute being, or Existence, and absolute non-being, which participates to some minimal degree in Existence as well as co-instantiates both Sameness and Difference.

For more information on Plato's ontology, see my lecture Plato, Logic, and Ontology

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