The Deconstruction of Identity: Derrida and the First Law of Logic

The Dangerous Maybe
Sep 17 · 21 min read

This post is far from a proof of anything. It is merely a line of thought. An exploration and a consideration. This is merely a sketch of a much bigger project. With that being said, let’s see where it takes us. Jacques Derrida is well-known for deconstructing binary oppositions such as the one between speech and writing. Deconstruction can take on many forms and approaches, but the one I want to use is the style of it we find in works like Of Grammatology and Speech and Phenomena. I’m going to argue that the first principle of logic, the law of identity, can itself be deconstructed. This principle privileges identity over difference insofar as it holds that identities are primary and that differences are always secondary differences between identities. In other words, it holds that difference piggybacks on identity. Logicians often treat this “law” as a pure identity, a full presence, which means that it’s thoroughly rooted in the metaphysics of presence — something Derrida spent a lot of time challenging. Arthur Bradley sums up the metaphysics of presence nicely:

This is another key term (along with logocentrism) that Derrida uses to describe the basic assumptions that underlie western thought. According to Derrida, the western philosophical tradition from Plato to the present day dogmatically posits a pure, full and unmediated presence as the supreme value. To Derrida’s way of thinking, this ‘presence’ can take many forms: the presence of the subject to itself in thought, sight or touch, the presence of something in space and/or time, even a presence which has now been lost or which may be gained in the future. For Derrida, the metaphysics of presence expresses itself through the institution of a series of binary oppositions and hierarchies whereby a superior term will be identified with pure presence and an inferior term with the mediation or loss of that presence: speech versus writing, nature versus culture, the masculine versus the feminine and so on. In the Grammatology, Derrida seeks to deconstruct these binary oppositions by articulating a logic of mediation, difference and deferral that makes them possible in the first place.
(Derrida’s Of Grammatology, pp. 148–9)

Despite how much time and energy Derrida devoted to deconstructing identity, he never, as far as I know, focused his attention directly on the law of identity itself. This is peculiar owing to the fact that all of philosophy’s attempts to establish a primary metaphysical identity (e.g., God, soul, subject, reason, atom, etc.) presuppose the first law of logic. But what if the law of identity fails to be identical to itself, that is, what if “pure” logical identity is thoroughly mediated by a pre-conceptual difference (différance)? It would mean that the category of identity is incapable of living up to its own standards. It means that identity collapses in on itself.

The Law of Identity

What exactly is the law of identity? This law states that each thing is identical with itself. This logical law is formally written as A=A: A is identical with and equal to itself, that is, A is A. For example, in an empirical context, we would assert the identity of a chair by saying the chair is the chair. Philosophers have long taken this logical principle and made it into an ontological one, which is to say that it holds true of actually existing beings, of concrete realities. Now, some logicians might insist on limiting the scope of the law of identity to terms within logical relations, to particular factors in the procedures of logical thought, but I’ll argue that identity is never pure no matter if it’s being conceived of in ontological or logical terms. Both ontological identity and logical identity are non-identical and produced out of a more fundamental play of difference. First, let’s take a quick look at how some of the most famous philosophers have articulated the law of identity.

The first reference to this law in the history of philosophy is often said to be found in one of Plato’s dialogues. This law is implicitly posited in a discussion of sound and color.

Socrates: Now take a sound and a color. First of all, don’t you think this same thing about both of them, namely, that they both are?
Theaetetus: I do.
Socrates: Also that each of them is different from the other and the same as itself?
Theaetetus: Of course.
Socrates: And that both together are two, and each of them is one?
Theaetetus: Yes, I think that too.
(Plato: Complete Works, Theaetetus, 185a)

Aristotle would go on to formally express the law of identity but in a very roundabout way. Nevertheless, he does assert this principle in the following quote:

When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to every C, it is necessary that A and B should be convertible; for since A is said of B and C only, and B is affirmed both of itself and of C, it is clear that B will be said of everything of which A is said, except A itself.
(The Complete Works of Aristotle, Vol. 1, Prior Analytics, Book II, Part 22, 68a)

John Locke would express logic’s first law like this:

[W]henever the mind with attention considers any proposition, so as to perceive the two ideas signified by the terms, and affirmed or denied one of the other to be the same or different; it is presently and infallibly certain of the truth of such a proposition; and this equally whether these propositions be in terms standing for more general ideas, or such as are less so: e.g., whether the general idea of Being be affirmed of itself, as in this proposition, “whatsoever is, is”; or a more particular idea be affirmed of itself, as “a man is a man”; or, “whatsoever is white is white” [.]
(Essay Concerning Human Understanding, Book IV, Chapter VII, Section IV)

The rationalist Gottfried Wilhelm Leibniz is often credited with most thoroughly establishing the law of identity. He explicitly stated that A is A.

The primary truths which we know by ‘intuition’ are of two sorts, as are the derivative ones. They are either truths of reason or truths of fact. Truths of reason are necessary, and those of fact are contingent. The primary truths of reason are the ones to which I give the general name’ identities’, because they seem to do nothing but repeat the same thing without telling us anything. They are either affirmative or negative. Examples of affirmative ones are: What is, is; Each thing is what it is, and as many others as you want: A is A; B is B; I shall be what I shall be; I have written what I have written.
(New Essays in Human Understanding, Book IV, 2, § i)

This first law of logic would go on to be accepted as the surest of truths by the vast majority of philosophers. One could say that it is the first law of philosophy. Things are identical with themselves. How could this possibly be doubted? How could this immediacy be mediated? How could this turn out to be grounded on a groundless presupposition? How could this actually amount to an article of doxa? Let’s find out. But, first, let’s get a better understanding of what Derrida meant by différance.

Différance

In order to understand différance, we need to know a little something about Ferdinand de Saussure’s differential theory of language. Saussure pointed out that every signifier (word) only signifies its signified (means what it means) by its place in its referential system of differences, i.e., the particular language it belongs to. Now, Saussure makes a distinction between the differences (relations) that form the meaning of a signifier: this is the synchronic-diachronic distinction. The synchronic relations that form part of a signifier’s meaning are the differences (synchronic traces) between the signifier and all of the other signifiers that exist or function in its respective language at the moment. The diachronic relations that help to make up the meaning of a signifier are the relations between its current meaning and all of its past meanings (diachronic traces). Simply put, the synchronicity of a signifier is its relation to all of the other words presently in the language (this is the spatial dimension of the signifier). The diachronicity of the signifier is its history as a signifier (this is the temporal dimension of the signifier).

Now, if one accepts this model of language, like Derrida basically did, then one is committed to the view that language is entirely historical and immanent, i.e., that it’s not grounded in or made possible by anything eternal or transcendent. Saussure didn’t work out any of the metaphysical implications of his differential theory of language — this is what Derrida did. Given the historical/differential nature and origin of language, signifieds (meanings) are not eternal, stable, fixed, transcendent, etc. Signifieds are not pure identities or semantic atoms, that is to say, they’re not universals in the Platonic sense. Perhaps it would be more accurate to say that even if there are universals, language has no relation to them at all. And why is that? One word: différance. The way I see it, this “concept” is basically Derrida’s reformulation of Saussure’s synchronic-diachronic distinction. For Derrida, the meaning of a word is always differentiated and deferred: spatially differentiated by the differences between itself and the rest of the words in the language; temporally deferred by the fact its meaning is not present in the moment it’s spoken, and this is because its signified is nothing but other signifiers that are absent in the moment of speech. Let’s have a look at how Arthur Bradley clarifies différance:

As Derrida makes clearer in other texts, différance brings together two different connotations of the French ‘différer’: differing and deferring. On the one hand, it signifies the way in which the meaning of any sign is spread out across space in the sense that it necessarily refers to other elements that exist alongside it in the system. On the other, it connotes the way in which the meaning of any sign is deferred or postponed in time in the sense that it always refers to elements that exist before or after it in the linguistic system. For Derrida, language works through this process of perpetual differing/deferring where the task of fulfilling meaning is always devolved onto the next sign along in space and time: we never arrive at a fully present meaning or signified which brings the process to an end. In Derrida’s account, différance ultimately becomes a means of exposing the originary state of mediation that underlies logocentrism and the metaphysics of presence more generally: every supposedly ‘present’ element only obtains its identity through differing from, and deferring, other elements that are not simply ‘present’
(Derrida’s Of Grammatology, pp. 147)

An example would be helpful here. Take the word “tree”. Suppose that a child asks you what the meaning of the word “tree” is. All you can do is appeal to other signifiers or, as Derrida would put it, “traces”. “Plant”, “roots”, “leaves”, “seeds”, “fruit”, “trunk”, “bark”, “branches”, “sap”, “wood”, etc. But the meaning of the word “tree” is still not fully present because the signifiers that comprise the meaning of all the signifiers just mentioned are spatially and temporally absent (differentiated/deferred) — and this is the play of différance or the trace. Spinoza’s famous maxim helps to articulate all this: “determination is negation” (Complete Works, Letter 50: Spinoza to Jelles, p. 892).

The metaphysics of presence and logocentrism privilege speech and devalue writing, and this is because speech is directly connected to the speaker’s mind, and the speaker’s mind (with all its concepts) is directly connected to the universals, and the universals are anchored in the Logos (the transcendental signified, a pure meaning). And even if meaning isn’t entirely present in speech, it’s still considered to be much more present in it than it is in writing. Writing is removed from the presence of meaning, so it’s devalued based on this absence. But this absential/differential structure of writing is what Derrida establishes as being the very possibility of any semiotic system whatsoever. Derrida also calls this absential structure of language “arche-writing”. With this strategy of generalizing the definition of the devalued term in the binary opposition between speech and writing, Derrida has just deconstructed the binary opposition. Meaning is no more present in speech as it is in writing, and, therefore, deserves no ontological privilege.

The main point is that any identity we posit is ultimately mediated by a system of differential traces. This is not to say that there is no meaning whatsoever, that there is no meaning-effect at all. However, it is to say that there is no pure identity that is what it is in and of itself and that grounds all other identities. There is no full, self-sufficient, stand-alone, pure, fully independent presence. All identities are referentially constituted. Différance itself is not a pure identity, a pure presence or a pure absence. Différance is undecidable: both presence and absence, neither presence nor absence.

Différance is not indeterminacy. It renders determinacy both possible and necessary. Some­one might say: but if it renders determinacy possible, it is because it itself is “indeterminacy.” Precisely not, since first of all it “is” in itself nothing outside of different determinations; second, and consequently, it never comes to a full stop anywhere, absolutely, and is neither negativity nor nothingness (as indeterminacy would be).
(Limited Inc, p. 149)

Extrinsic Critique of the Law of Identity

An extrinsic critique of the law of identity deals with the law’s applicability to actual entities. We must ask when an entity is absolutely identical with itself. Is there ever a moment when an entity is totally equivalent to itself? This problem harkens back to the old Greek debate concerning being (Parmenides) and becoming (Heraclitus). Philosophers have long wrestled with this issue without ever arriving at a final answer to it. For our purposes, let’s look at some of the thoughts of Søren Kierkegaard and a famous thought experiment.

In Concluding Unscientific Postscript, Kierkegaard challenges the concept of the subject we find in German Idealism and especially the concept of it developed by Johann Gottlieb Fichte. According to Fichte, the identity of the subject is the foundation of all knowledge. This self-positing identity can be formulated as I=I (Kierkegaard writes it as A-A). Fichte thought that self-consciousness has a direct intuition of its own self-identity. However, this intuition is not experienced by empirical consciousness. It is a transcendental operation, a structural fact/act, and, therefore, unconscious. Of course, what underlies the I=I is the A=A. The law of identity is presupposed by the idea of the I=I.

Kierkegaard had major issues with the I=I. When does I=I? Fichte would insist that this is a purely abstract identity, but Kierkegaard was not at all satisfied with the idea that the subject (the existing individual) is to be primarily identified with this sort of abstraction. For Kierkegaard, to be an I=I is not what it is to be an existing human being. In fact, he would view it as an instance of inauthenticity that leads one to despair (“despair” in his technical sense of the term). Kierkegaard thought that the concept of the I=I is merely a way for human beings to objectify themselves, which allows them to avoid being subjective in the fullest of ways. As is well-known, Kierkegaard held that this tendency towards the objectification of the existential subject is at its strongest in Hegel’s system. As he put it, “Objective thinking is wholly indifferent to subjectivity, and by the same token to inwardness and appropriation” (Concluding Unscientific Postscript, p. 64). Both Fichte and Hegel, according to Kierkegaard, do a sort of violence against human beings by reducing us to abstractions and objectivities. The I=I is deceptive, since it treats the human being as something essentially finished or complete. Kierkegaard disagrees. For him, we are ontologically unfinished so long as we exist, that is, the human being is a work in progress. As long as the indeterminate future is open to us, so long as we have a future to create, we are unfinished and, therefore, cannot be systematically interpreted in an objective manner.

Someone existing is constantly in coming to be; the genuinely existing subjective thinker simulates this existence of his constantly in his thinking and invests all his thinking in becoming. It is the same as with style: the only writer who really has style is the one who never has anything finished, but ‘troubles the waters of language’ every time he begins, so that for him the most everyday expression comes into being with the pristine freshness of a new birth. To be thus constantly coming to be is infinitude’s deceptiveness in existence. It is enough to bring a sensate person to despair, for one feels a constant urge to have something finished, but this urge is of evil and must be renounced. The continual becoming is the uncertainty of earthly life, in which everything is uncertain.
(Concluding Scientific Postscript, p. 73)

Kierkegaard spends many pages opposing his concept of the self, the self as a creative process, to that of the self-identical I=I. When am I identical to myself? What infinitesimal sliver of time must we posit to entertain the self’s absolute identity with itself? Unless one makes appeals to objectifying abstractions, ones that seem to have no real bearing on our lives, on our existential situations, then one cannot apply the law of identity to human beings. We are never fully identical with ourselves.

The I-I is a mathematical point that doesn’t exist at all; so anyone may happily adopt this standpoint and no one will be in their way. It is only for a moment that the particular individual, in existing, can be in a unity of infinite and finite that transcends existing. This moment is the instant of passion. Modern speculation has used every expedient in attempting to get the individual to transcend himself objectively, but it just cannot be done. Existence constrains, and if philosophers nowadays were not pen-pushers in the service of an endless trifling with fantastical thinking, it would have seen long ago that the only, in any way, practical interpretation of its efforts was suicide. But modern pen-pushing speculation looks down on passion; yet, for the one who exists, passion is the very height of existence — and we are after all existing. In passion, the existing subject is infinitized in the eternity of imagination, and yet is also most definitely himself. The fantastic I-I is not infinity and finitude in identity, for neither the one nor the other is actual; it is a fantastic accord in the cloud, an unfruitful embrace, and the relation of the individual I to this mirage is never stated.
(Concluding Scientific Postscript, pp. 165–6)

It’s easy to understand why humans are never identical to themselves, but surely objects are. The law of identity must certainly apply to them, right? Not so fast. Is an object ever truly equivalent to itself? Objects, like humans, are in a constant state of becoming (though not an existential one). Generally speaking, objects obviously remain similar to themselves, certain features of them endure across time (and the same is true of humans), but we are asking about pure identity and not relative identity. We are not primarily concerned with phenomenologico-pragmatic identity, e.g., “My TV is the same as it was yesterday”. Instead, we are asking about metaphysical identity. This brings us to the ship of Theseus. This is one of the most famous thought experiments in the history of philosophy. In his work entitled Theseus, Plutarch explains it like this:

The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their places, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

In short, the question is: does a ship remain the same ship if all of its parts are replaced with new ones? If all of the parts that make up the ship are different, then wherein lies its pure identity? And how could we ever say that the ship is exactly and absolutely the same? Philosophers have been wrestling with this question for thousands of years and I certainly don’t have a definitive answer to it. What I will say is that this thought experiment definitely makes it nearly impossible to imagine that the law of identity fully applies to objects that have had all of their parts swapped out. Perhaps we could argue that what remains the same is the name of the ship, the signifier “Theseus”, but this fails to account for how concrete entities remain the same while having their parts replaced over a given period of time. The name is not the thing itself.

Even phenomenologico-pragmatic identity is a very nuanced and unstable phenomenon. It only occurs under very specific situations. The phenomenon’s identity is fundamentally connected to our perception of it, that is, to our experiential position relative to the object. A kind of “altering” is always at play here. Merleau-Ponty explained this wonderfully by describing how the phenomenon of a ship gradually morphs and alters as a person approaches it:

If I walk along a shore towards a ship which has run aground, and the funnel or masts merge into the forest bordering on the sand dune, there will be a moment when these details suddenly become part of the ship, and indissolubly fused with it. As I approached, I did not perceive resemblances or proximities which finally came together to form a continuous picture of the upper part of the ship. I merely felt that the look of the object was on the point of altering, that something was imminent in this tension, as a storm is imminent in storm clouds. Suddenly the sight before me was recast in a manner satisfying to my vague expectation. Only afterwards did I recognize, as justifications for the change, the resemblance and contiguity of what I call ‘stimuli’ — namely the most determinate phenomena, seen at close quarters and with which I compose the ‘true’ world. ‘How could I have failed to see that these pieces of wood were an integral part of the ship? For they were of the same colour as the ship, and fitted well enough into its superstructure.’ But these reasons for correct perception were not given as reasons beforehand. The unity of the object is based on the foreshadowing of an imminent order which is about to spring upon us a reply to questions merely latent in the landscape. It solves a problem set only in the form of a vague feeling of uneasiness, it organizes elements which up to that moment did not belong to the same universe and which, for that reason, as Kant said with profound insight, could not be associated. By placing them on the same footing, that of the unique object, synopsis makes continuity and resemblance between them possible. An impression can never by itself be associated with another impression.
(Phenomenology of Perceptions, pp. 14–5)

The last thing I want to point out is how much more complicated this scenario gets when viewed from the perspective of quantum physics. The various parts of the ship of Theseus problematize the applicability of the law of identity to the ship itself, but quantum physics problematizes this to a degree that we cannot truly begin to fathom. What about the subatomic particles of the ship’s parts? When are they identical to themselves? When can they declare, “I am I”? When does the universe hold still long enough for the law of identity to take its picture?

Whether we’re talking about the application of the law of identity to subjects or to objects, we are faced with enormous obstacles. Particular entities evade formal identification like criminal masterminds evade the cops. A=A? Again, when? When it comes to the A’s relation to an actual being, the A functions as a placeholder, an empty slot wherein an identity can come to be positioned. The abstract A is like a domain name without an actual website. It’s out of a matrix of differential relations that the A takes on a relative identity. However, it is not merely a particular identity designated by the A that is produced by a network of differences — the empty A itself is the product of difference. Now that we understand the extrinsic problem of identity, let’s turn to the intrinsic one, which is the more important of the two. Back to Derrida.

Intrinsic Critique of the Law of Identity

We will now attempt a concise deconstruction of the law of identity itself. In Jean Baudrillard’s terms, we will be trying to “seduce” identity. Is the first law of logic a pure immediacy, a full identity, a non-relational presence? The very formula of identity is comprised of three symbols: A, =, A. We do not assert identity if we simply say or write an “A”. We do not assert identity if we say or write “=” or “A=”. It takes the second A to retroactively determine the meaning of the first A and the =. The meaning of the A and of the = were deferred. Also, the first A and the second A are never exactly the same. For identity to be asserted, there must be a secret difference between A 1 and A 2. Of course we intend for them to be fully identical, but they are not. The thought of A=A occurs in time and, therefore, means that A 1 is only A 1 after A 2 has been asserted of it. A 1 is differentiated and deferred. But this is not only true of thought’s temporal succession, of thought’s linear movement through the A=A, but of the law itself. The A=A is intrinsically and synchronically differentiated, deferred, mediated, relational. Différance is at play in the law of identity.

One might desire for A=A to be a pure immediacy, but as Derrida said, “Immediacy is derived” (Of Grammatology, p. 157). Someone might want to argue that we have to think the law of identity in a differential/deferred way, but that it is possible to have a direct intellectual intuition of it after the fact. As if différance were like Wittgenstein’s ladder. We cannot kick différance away once and for all! But, again, the problem is that the relative coherence of the law of identity depends on its three separate symbols, all of which take on a relative meaning within the structure of language. What is true of particular identities is true of the law of identity — différance makes the difference and the difference makes the identity. The A is a mark, which means that it is iterable. Derrida’s concept of iterability involves the idea that every repetition is an alteration, every recurrence is a difference (this is true of identity’s A 1 and A 2).

Iterability supposes a minimal remainder (as well as a minimum of idealization) in order that the identity of the selfsame be repeatable and identifiable in, through, and even in view of its alteration. For the structure of iteration — and this is another of its decisive traits — implies both identity and difference. Iteration in its “purest” form — and it is always impure — contains in itself the discrepancy of a difference that constitutes it as iteration. The iterability of an element divides its own identity a priori, even without taking into account the fact that this identity can only determine or delimit itself through differential relations to other ele­ments and that it hence bears the mark of this difference. It is because this iter­ability is differential, within each individual “element” as well as between the “elements,” because it splits each element while constituting it, because it marks it with an articulatory break, that the remainder, although indispensable, is never that of a full or fulfilling presence: it is a differential structure escaping the logic of presence or the (simple or dialectical) opposition of presence and absence, upon which opposition the idea of permanence depends. This is why the mark qua “non-present remainder” is not the contrary of the mark as effacement. Like the trace it is, the mark is neither present nor absent. This is what is remarkable about it, even if it is not remarked.
(Limited Inc, p. 53)

None of this is to say that there is no such thing as presence. The point is that every presence is never fully and absolutely present. Every presence, be it a word, an object or an event, only is what it is in relation to a network of absences, differences, traces, supplements, etc. This is what Derrida had in mind when he famously said “There is nothing outside of the text [there is no outside-text; il n’y a pas de hors-texte]” (Of Grammatology, p. 158). He’s not asserting that all of reality is reducible to language or that language is all there is. This is not the declaration of a linguistic idealism. Derrida explained it like this:

We can call “context” the entire “real-history-of-the-world,” if you like, in which this value of objectivity and, even more broadly, that of truth (etc.) have taken on meaning and imposed themselves. That does not in the slightest dis­credit them. In the name of what, of which other “truth,” moreover, would it? One of the definitions of what is called deconstruction would be the effort to take this limitless context into account, to pay the sharpest and broadest attention possible to context, and thus to an incessant movement of recontextualization. The phrase which for some has become a sort of slogan, in general so badly understood, of deconstruction (“there is nothing outside the text” [il n’y a pas de hors-texte]), means nothing else: there is nothing outside context. In this form, which says exactly the same thing, the formula would doubtless have been less shocking. I am not certain that it would have provided more to think about.
(Limited Inc, p. 136)

The A=A is always thought, said and written in a context. The three symbols only signify within a context and a context is always differential, absent-present, relational, mediated, etc. I am not arguing that identity is always an illusion, but I am arguing that identity is never as pure and simple as logic and metaphysics would like for it to be. Identity is never singularly identical with itself — the law of identity cannot even pull this off. The category of identity isn’t going anywhere, but we need to be aware that a certain concept of it has long marginalized difference.

In Difference and Repetition, Gilles Deleuze argued that the standard concept of identity is an essential aspect of the “dogmatic image of thought”, which is the way we typically conceptualize thought itself. Deleuze claims that the primacy of identity reduces difference to differences between independent and substantial identities. Philosophy has long viewed difference as a secondary category. However, according to Deleuze, there is a difference that is not the difference between identities. This “pure difference” is a virtual-intensive matrix out of which actual entities emerge. For example, if you want to turn popcorn kernels into actual popcorn, then you have to heat them up. The microwave generates a field of “differences” (intensities) that actualize certain virtual potentials within the kernels. All beings are ultimately produced from within a field of intensities (temperature, pressure, rates of flow, etc.). Though Derrida’s différance and Deleuze’s pure difference are different from one another, they both serve to show how identities are the products of differential relations. Identity is differential. A=A depends on difference.

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