Reflection is also the key to Hegel’s often misunderstood views on identity and difference.
“Reflection is the shining of essence within itself. Essence, as infinite immanent turning back is not immediate simplicity, but negative simplicity; it is a movement across moments that are distinct, is absolute mediation with itself. But in these moments it shines; the moments are, therefore, themselves determinations reflected into themselves” (Hegel, Logic, di Giovanni trans., p. 354, emphasis in original).
He goes on to discuss identity, difference, and the notorious “contradiction” as principal moments or determinations of reflection. Sometimes he uses these terms in the conventional way — of which he is highly critical — and sometimes he gives them his own meaning.
On Aristotelian grounds, I have long had doubts about appeals to an implicitly immediate simplicity or “identity” of substance in traditional metaphysics. I take these to be a form of Platonizing that originated in the neoplatonic commentaries on Aristotle. Hegel’s alternative suggestion of a “negative simplicity” seems much more plausible generally, as well as more consistent with the Aristotelian texts. We just have to get past the difficulty of Hegel’s idiosyncratic metaphorical straining of language about “negation”, and recognize that he is inventing ways to talk about the limits of representation, rather than grossly abusing the “classical” negation of formal logic.
Hegel’s remarks about identity are actually pretty clear, and worth quoting at length. As with negation, in Hegel identity, difference, and “contradiction” only have the meanings that they have in classical logic when he is pointing out their limitations. The alternative meanings that he actually endorses deeply reflect his critique of representationalism.
“In its positive formulation, A = A, [the principle of identity in classical logic] is at first no more than the expression of empty tautology. It is rightly said, therefore, that this law of thought is without content and that it leads nowhere. It is thus to an empty identity that they cling, those who take it to be something true, insisting that identity is not difference but that the two are different. They do not see that in saying, ‘Identity is different from difference’, they have thereby already said that identity is something different. And since this must also be conceded as the nature of identity, the implication is that to be different belongs to identity not externally, but within it, in its nature. — But, further, inasmuch as these same individuals hold firm to their unmoved identity, of which the opposite is difference, they do not see that they have thereby reduced it to a one-sided determinateness which, as such, has no truth. They are conceding that the principle of identity only expresses a one-sided determinateness, that it only contains formal truth, truth abstract and incomplete. — Immediately implied in this correct judgment, however, is that the truth is complete only in the unity of identity and difference, and, consequently, that it only consists in this unity. When asserting that formal identity is incomplete, there is vaguely present to one’s mind the totality, measured against which that identity is incomplete; but the moment one insists that identity is absolutely separate from difference and in this separation takes it to be something essential, valid, true, then what transpires from these two contradictory claims is only the failure to reconcile these two thoughts: that identity as abstract identity is essential, but that, as such, it is equally incomplete. What is lacking is awareness of the negative moment as [that by] which, in these claims, identity itself is displayed. — Or when this is said, that identity is identity essentially as separation from difference or in the separation from difference, then right there we have the expressed truth about it, namely that [formal] identity consists in being separation as such, or in being essentially in the separation, that is, it is nothing for itself but is rather moment of separation.”
“As to the other confirmation of the absolute truth of the principle of identity, this is made to rest on experience in so far as appeal is made to the experience of every consciousness; for anyone presented with this proposition, ‘A is A’, ‘a tree is a tree’, immediately grants it and is satisfied that the proposition is self-evident and in need of no further justification or demonstration.”
“On the one hand, this appeal to experience, that every consciousness acknowledges the principle universally, is a mere manner of speaking. For nobody will want to say that the abstract proposition, ‘A is A’, has actually been tried out in every consciousness. The appeal to actual experience is therefore not in earnest but is rather only an assurance that, if the experiment were made, universal acknowledgement of the proposition would be the result. — And if it is not the abstract proposition as such that is meant, but the proposition in concrete application, from which application the abstract proposition would then have to be developed, then the claim to the universality and immediacy of the latter would consist in the fact that every consciousness assumes it or implies it as a foundation, and indeed does so in every utterance. But the concrete and the application are precisely in the reference that connects simple identity with a manifold which is different from it. Expressed as a proposition, the concrete would be first of all a synthetic proposition. From this concrete itself, or from the synthetic proposition expressing it, abstraction could indeed extract the principle of identity through analysis; but, in actual fact, it would not then leave experience as it is but would have altered it, since in experience the identity was rather in unity with difference. And this is the immediate refutation if the claim that abstract identity is as such something true, for what transpires in experience is the verry opposite, namely identity only united with difference” (pp. 358-359, emphasis in original).
“Identity, instead of being in itself the truth and the absolute truth, is thus rather the opposite; instead of being the unmoved simple, it surpasses itself into the dissolution of itself.”
“More is entailed, therefore, in the form of the proposition expressing identity than simple, abstract identity; entailed by it is this pure movement of reflection in the course of which there emerges the other, but only as reflective shine, as immediately disappearing…. The propositional form can be regarded as the hidden necessity of adding to abstract identity the extra factor of that movement…. Consequently, if appeal is made to what appearance indicates, then the result is this: that in the expression of identity, difference also immediately emerges” (p. 360, emphasis in original).
“From this it is clear that the principle of identity itself, and still more the principle of contradiction, are not of merely analytical but of synthetic nature” (ibid, emphasis in original).
Here he uses Kant’s distinction of analytic from synthetic judgments. Analytic judgments are purely formal and tautological; canonically, the predicate is considered to be literally implied by the subject. Synthetic judgments on the other hand go beyond what is already implied by the subject or premises. This includes most judgments in ordinary experience. Synthetic judgments involve the material inference that Robert Brandom has particularly expounded in recent times.
“Thus the result of this consideration is this: (1) the principle of identity or contradiction, when meant to express merely abstract identity in opposition to difference as a truth, is not a law of thought but expresses rather the opposite of it; (2) these two principles contain more than is meant by them, namely this opposite, absolute difference itself” (p. 361, emphasis in original).
The Postmodern Peripatetic 