I: Christianity and Contradiction

More than any other, Christianity is the religion of difference.  For, Christianity uniquely acknowledges the God of difference (heteros theos), in whom the Son is different from the Father, and the Spirit is different from this ‘divine difference’, in a triadic circuit, that is the gift of love. (1 Jn. 4:8)

A contradiction is the singular concentration of difference.  For, it states the singular opposition of positive and negative judgments.  The Law of Non-Contradiction (LNC), that a statement cannot be affirmed and denied of the same thing in the same way, regiments speech in singularly determinative or apophantic statements that must be assumed as the premises of arguments in any possible scientific demonstration.

The LNC has since been consistently upheld as the most incontestable principle of logic.  Yet it has also come to be radically doubted.  For, as a principle of logic, it cannot be directly demonstrated by the arguments of logic.  All of the arguments for the LNC are, on the contrary, indirect or apagogic arguments, which, in negatively annulling the contrary denial, ultimately fail to positively demonstrate the LNC as a principle of logic. (Aristotle, Metaphysics, 4.3-4., 1005a20-1007b30)

However, recent developments in philosophy of logic have authorized creative alternatives to the LNC. In ‘paraconsistent logic’, a contradiction does not result in triviality, but rather and only restricts the universal jurisdiction of the LNC. (Priest, Routley, & Norman, 1989) And in ‘dialetheism’, such a restricted contradiction can be evaluated as both true and false. (Priest, 2006)

These alternatives have suggested a suspension of LNC, in which, as in Kierkegaard’s ‘real paradox’, a ‘paradox’ in logic appears as a cipher for ‘participation’ in theology. (De Lubac, 1987) For it seems that if the LNC holds in some cases but not in others, then its ultimacy and universality can be suspended as a contingent hypothesis of reason before the higher calling of faith in a paradoxical God.

The Sophist is, among Plato’s later dialogues, an exploration of the figure of the ‘sophist’, the pretenders to wisdom who make falsehoods appear true, by an investigation into the possibility of speaking of nothing, as the negative is related in and from the division of the forms.  It has often been read to demonstrate an excess of difference beyond the LNC.  Yet it can, as this study will suggest, also be read to show how the LNC can be legislated from the higher ground of the Logos in Christian theology. The tragic aporiae of Plato’s dialogues call for a creative reinterpretation, not only of Plato, but of the entire Platonic tradition, in a recapitulation of the transformation of Platonic into Christian and Trinitarian Ontology. 

II: From Sophistry to the Simulacrum

In The Sophist, Plato addresses the question of the ‘sophist’ by analyzing falsity as a statement of non-being corresponding to semblances of being as true, in a virtual realm of representations, or a simulacrum.  The climax of the dialogue (258b) occurs when he defines non-being, not as that which is absolutely opposed to being, but rather and only as that which is different from being, as the originary genera of Being itself is divided across the intrinsically related difference of the paradigmatic forms.

Dialectics, Plato says, is the art of “dividing according to kinds.” (253b-e).  His method of ‘division’ (diaeresis) divides one into many, and collects many into one, such that the specific distinction of each particular form can be subsumed under and spoken of from a higher generic idea. (253e) He initially restricts his analysis to the ‘first’ and ‘greatest kinds’ (megista gene) that are “capable of combination”, so that, with this analysis, we may “assert that what is not, really is what is not.” (254b-d)

Plato then analyzes the five ‘greatest kinds’ of (i) Being, (ii) Rest, (iii) Motion, (iv) Sameness, and (v) Difference.  He argues that since (ii) Rest and (iii) Motion can be analyzed to partake of (i) Being, but neither (ii) Rest nor (iii) Motion may be combined with one another, (ii) Rest and (iii) Motion are the same for themselves, but different for each other, as the megista gene of (iv) Sameness and (v) Difference. (254d-255e) 

Difference itself is, at this point, defined as that which is “relative to (pros) other (heteron).” (πρὸς ἕτερον) (255d) As the fifth of the megista gene, it ostensibly appears sui generis.  Since, however, it is also defined as a relation to an other, difference is not the same as itself, but rather “pervades all of the forms”, as “each one is different from the rest”, and as the ‘different’ of each “partakes of the character of difference” itself. (255e)

However, in dividing Being into difference, Plato also produces a series of dialectical paradoxes.  Being itself is pure, abstract, and indistinct.  Yet once divided, Being is determined in and beyond the forms themselves.  And since, as the foregoing has shown, motion is differentiated, and all of the forms partake of Motion itself, it must ultimately be possible for ‘that which is not’ to be “the same and not the same” (256a), not only in the case of motion, but of all the other kinds” of forms. (256d) 

Once set in motion, this movement of dividing the forms threatens to produce endless dialectical paradoxes. Nevertheless, we must, Plato insists, not simply discard such paradoxes.  We must, to the contrary, hold on to this contradiction “without boggling at it.” (256a) For the ‘same’ and ‘not the same’ are not said in the same sense.  Rather, every form is said to be ‘the same’ by participating in Motion itself, yet ‘not the same’, as it “separates it off from the same, and makes it not the same but different”, in every movement from one point to the next. (256b)

III: The Paradox of Participation

Plato suggests an answer to the ‘paradox of participation’. This paradox holds that any particular instance shares in a proportionate similitude that is both like and unlike the universal idea in which it participates.  In the Parmenides, he had previously attacked his own theory of the ideas with six devastating criticisms. (Parmenides, 130a-134e) Essential to these criticisms is the paradoxical coincidence of opposites, of identity and difference, and of an explosive difference that exceeds the singular ground of the ideas themselves.

Parmenides had formerly prohibited the possibility of speaking of nothing as something.  “Never”, he held, “shall this be proved, that things that are not, are.” (258c) Yet once Difference itself can be analyzed into the “single form” of ‘what-is-not’, and Motion can be analyzed to differentiate while partaking of itself, all of the ideas can be analyzed into concentrically related forms, where each is differentiated from another and yet equally related from an other in and for itself.

Non-being can, at the interstitial gaps of this movement of division, not be described as absolutely not being, or nothing, without some degree of participation in Being, but can, on the contrary, only be described as an interstitial determination situated between the extremes of absolute being, and absolute non-being, which participates to some relative degree in Being.

Once, therefore, all of the paradigmatic forms have been analyzed from their source, and held apart in a standing potency of dynamic relations, Plato’s division of the forms in The Sophist can be read to announce the birth of the virtual, a virtual realm of representations, or a simulacrum, in which all of the forms of grammar and logic can be freely constructed, and analytically calculated for the productive demonstration of scientific knowledge.

IV: From Difference to Determinacy

With this analysis, Plato has radically transformed the grammar of negation.  Rather than signifying an opposition, negation now signifies a difference.  And rather than simply negating a subject, the negation of a predicate instead signifies the difference of the predicate, that is, a ‘determination’.

Before Aristotle, a determination is here indicated by this reciprocal folding of difference into negation, and the negation of a predicate as a determination of the subject. (256e) This division of the forms is a determination of one as not an other, a negation of the other, and a relation as not the other. (257a)

Negation is thus crucially redefined, not as the absolute opposition of non-being to being, but rather and only as the relative difference that can be spoken of from an other in and for a further determination.  Plato explains that “that which is not” does not mean “something contrary to what exists but only something that is different.” (257b) Hence, “the prefix ‘not’” does not signify its absolute contrary but rather “indicates something different from the words that follow.” (258c)

Plato thus recommends a new grammar of negation. Where, for Parmenides, the negative ‘not’ had designated the originary opposition of nonbeing to being, for Plato, the negative ‘not’ indicates a lateral difference from one form to an other.  Before Aristotle, Plato can begin to analyze every statement of a contradiction into its constituent terms, differences, and relations, such that contraries share in the relation of participation.

Plato’s dialectic thus authorizes a post-Aristotelian logic of contradiction.  In contrast to formal logic, a contradiction is, for Plato, not simply a statement of a singular opposition that annuls one or both of the contraries, but rather a statement that invites a further analysis of any singular opposition into relative difference, of difference into relations, and, ultimately, of all such dynamic relations that can be sublated in and from the first principles of theology.

V: A Theology of Contradiction

The concluding aporia of Plato’s Sophist concerns how it is possible to speak of non-being.  Since, as the foregoing has suggested, the ideas can be analyzed from the source of being, and yet this source can only be spoken from within the simulacrum of the forms of language, as of logic, the originary genera of being appears paradoxically to be spoken of from the production of something from nothing.

At the conclusion of this dialogue, Plato schematizes the production of discourse (logos) of something from nothing across the Divided Line (Republic, 509d–511e), such that the ‘horizontal’ productive mixture exceeds the ‘vertical’ ambit of participation (methexis) in and for the divine Intellect (Nous). (266a) Since, moreover, this horizontal difference of the production of mixtures must itself be subsumed to participate from the vertical difference of the division of the forms, this fourfold schema can be read to constitute a noetic triad, consisting of the source, the simulacrum, and the production of a surplus of signs. 

From the caesura of this aporia, the Logos of divine and human discourse appears to be spoken of in the production of noetic triads in excess of its source.  Since, furthermore, every difference is determinative, and every such determination is productive, even this virtual difference of the simulacrum from its source must be productive of a surplus of intelligible signs in and beyond the inferentially opaque genera of Being itself. 

Since, therefore, difference is productive, and this difference of the simulacrum exceeds its source, the noetic triads of Plato’s Sophist can be creatively read for theology as a protoevangelion that anticipates the Johannine annunciation of the ‘divine difference’ of the Logos that is with God and in God. (Jn. 1:1)  This dialectical sublation of opposition into difference is absolutely the sublation of every opposition in and from the difference of God from God, in which the Trinity is the principle of difference itself, as its difference is inscribed across the difference of every form, and every instance of thinking.

The Christian Trinity may initially appear to suggest an ontology of paradox, in which paradox is a cipher for participation.  Since, however, already in Plato’s Sophist, difference is determinative in the production of all noetic triads, and the singular opposition of any contradiction can be analyzed into relatively different predicates, the contradiction of any such paradox can ever again be freely analyzed in and through the dialectical circuits of the Logos, and communicated by Christ, in and from the center of God as Trinity.

Rather than the apotheosis of unreason, the Trinity should be celebrated as the essential principle of reason itself.  For, as this study suggests, the Law of Non-Contradiction can be simulated from the higher ground of the Logos.  Although admitting occasions of paradoxical judgments at the margins of reason, the Logos eternally secures the higher ground for the resolution of all such paradoxes.  And, we may conclude,  it is only from this absolute difference of God from God that anything can be related from another and for itself, as every opposition can be analyzed, reflected, and determined, such that, for the religion of difference, it is once and forever possible to know in loving the highest ideas.

Ryan Haecker is a PhD candidate at Peterhouse in the Faculty of Divinity of the University of Cambridge.  He has previously studied history, philosophy, and theology at the University of Texas, the University Würzburg, and the University of Nottingham. His research investigates theological interpretations of logic.