It is always perilous to approach Lacan from a philosophical point of view. For he is an anti-philosopher, and no one is entitled to take this designation lightly.
Considering him in relation to the Pre-Socratics is a still more risky undertaking. References to these thinkers in Lacan's work are rare, scattered, and above all mediated by something other than themselves. There is, moreover, the risk of losing one's thought in a latent confrontation between Lacan and Heidegger, which has all the attractions of a rhetorical impasse.
Having arrived at this perspective on the scope of Lacan's texts, one should not lose sight of the fact that it is a localization, the disinterested examination of a symptom.
The revelatory power of Lacan's references to the Pre-Socratics is secret - I would almost say encoded. Three thinkers are invoked: Empedocles, Heraclitus and Parmenides. The invocation is itself caught up in four principal problems. The first can be formulated as follows: to what originary impulse of thought is psychoanalysis the heir? The question reaches far beyond the point where, with Descartes, we enter the modern epoch of the subject, or what Lacan calls the subject of science. Of course, psychoanalysis could appear only within the element of this modernity. But as a general figure of the will to thought (vouloir-penser), it enigmatically bears a confrontation with what is most originary in our site. Here it is a question of knowing what is at stake when we determine the place of psychoanalysis in the strictly Western history of thought, in which psychoanalysis marks a rupture, and which is not at all constituted by but, rather, punctuated by philosophy.
The second problem concerns the relation - which is decisive for Lacan - between psychoanalysis and Plato. Driven by rivalry and contestation, this relation is unstable. Lacan's references to the Pre-Socratics clarify the principle behind this instability.
The third problem is, of course, that of providing an exact delimitation of Lacan's relation to Heidegger. It is to Heidegger that we owe the reactivation of the Pre-Socratics as the forgotten source from which our destiny took flight. If it is not a matter here of 'comparing' Lacan to Heidegger - which would be meaningless - the theme of origins alone compels us to search for some measure of what led one to cite and translate the other.
Finally, the fourth problem concerns the polemical dimension of psychoanalysis. With respect to what primordial division of thought does psychoanalysis make its stand? Can one inscribe psychoanalysis within an insistent conflict that long preceded it? There is no doubt that Lacan here makes use of the canonical opposition between Parmenides and Heraclitus. Lacan opts, quite explicitly, for the latter.
Freud's work was a new foundation, a rupture. But it was also the product of an orientation within thought that rests on divisions and territories that pre-existed it.
Lacan's references to the Pre-Socratics thus attest - and herein lies their difficulty - not so much to what is truly revolutionary in psychoanalysis as to what inscribes it within dialectical continuities of what we might call continental reach.
Those of Lacan's psychoanalytic discoveries that can be made to enter into resonance with the Pre-Socratics can be grouped around two themes: the primacy of discourse and the function of love in the truth-process.
On several occasions Lacan praises the innocent audacity of the Pre-Socratics, who identified the powers of discourse with the grasping of being [la prise sur l'être]. Thus, in the seminar on transference, he writes: 'Beyond Plato, in the background, we have this attempt, grandiose in its innocence -this hope residing in the first philosophers, called physicists - of finding an ultimate grasp on the real under the guarantee of discourse, which is in the end their instrument for gauging experience." 
How are we to characterize this peculiar balancing of the 'grandiose' and the 'innocent'? The grandiose aspect lies in the conviction that the question of the Real is commensurable with that of language; the innocence is in not having carried this conviction as far as its true principle, which is mathemati-zation. You will recall that Lacan holds mathematization to be the key to any thinkable relation to the Real. He never varied on this point. In the seminar Encore, he says, without the slightest note of caution: 'Mathematization alone reaches a real.'  Without mathematization, without the grasp of the letter (la prise de la lettre), the Real remains captive to a mundane reality driven by a phantasm.
Is this to say that the Pre-Socratic physicists remain within the bounds of the mythic narrative which delivers us the phantasm of the world? No, for they outline a genuine rupture with traditional knowledge, albeit one innocent with regard to the matheme.
The latter point is essential. Lacan does not conceive of the Pre-Socratics as the founders of a tradition, or as a lost tradition in themselves. A tradition is what 'tra-dicts' (fait tra-diction) the reality of the phantasm of the world. In placing their trust in the pure supremacy of discourse, the Pre-Socratics had the grandiose audacity to break with all traditional forms of knowledge.
This is why their writings prefigure mathematization, although the latter is not present in its literal form. The premonition appears in its paradoxical inversion, the use of poetic form. Far from opposing, as Heidegger did, the Pre-Socratic poem to Plato's matheme, Lacan has the powerful idea that poetry was the closest thing to mathematization available to the Pre-Socratics. Poetic form is the innocence of the grandiose. For Lacan, it even goes beyond the explicit content of statements, because it anticipates the regularity of the matheme. In Encore, he writes:
Fortunately, Parmenides actually wrote poems. Doesn't he use linguistic devices - the linguist's testimony takes precedence here - that closely resemble mathematical articulation, alternation after succession, framing after alternation? It is precisely because he was a poet that Parmenides says what he has to say to us in the least stupid of manners. Otherwise, the idea that being is and that nonbeing is not, I don't know what that means to you, but personally I find that stupid. 
This text indeed registers an innocence in its trace of stupidity. There is something unreal in Parmenides' proposition on being, in the sense of a still unthought attachment to phantasmatic reality. But the poetic form contains a grandiose anticipation of the matheme. Alternation, succession, framing: the figures of poetic rhetoric are branded, as if by an unconscious lightning flash, with the features of a mathematization to come; through poetry, Parmenides attests to the fact that the grasp of thought upon the Real can be established only by the regulated power of the letter. It is for this reason that the Pre-Socratics should be praised: they wished to free thought from any figure that involves the simple transmission of knowledge. They entrusted thought to the aleatory care of the letter, a letter that remains poetic for temporary lack of mathematics.
The Pre-Socratics' second foundational innovation was to pose the power of love as a relation of being wherein lies the function of truth. The seminar on transference is, of course, our guiding reference here. Take the following passage: "Phaedraos tells us that Love, the first of the gods imagined by the Goddess of Parmenides, and which Jean Beaufret in his book on Parmenides identifies more accurately, I believe, with truth than with any other function, truth in its radical structure..."  In fact, Lacan credits the Pre-Socratics with binding love to the question of the truth in two ways.
First of all, they were able to see that love, as Lacan himself says, is what brings being face to face with itself; this is expressed in Empedocles' description of love as the 'power of cohesion or harmony'. Secondly, and above all, the Pre-Socratics pointed out that it is in love that the Two is unleashed, the enigma of the difference between the sexes. Love is the appearance of a non-relation, the sexual non-relation, taken to the extent that any supreme relation is punctured or undone. This puncturing, this undoing of the One, is what aligns love with the question of the truth. The fact that we are dealing here with what brings into being a non-relation in place of a relation permits us also to say that knowledge is that part of the truth which is experienced in the figure of hate. Hate is, along with love and ignorance, the very passion of the truth, to the extent that it proceeds as non-relation imagined as relation.
Lacan emblematically ascribes to Empedocles this power of truth as the torsion that relates love to hate. Empedocles saw that the question of our being, and of what can be stated of its truth, presupposes the recognition of a non-relation, an original discord. If one ceases to misconstrue it according to some scheme of dialectical antagonisms, the love/hate tension is one of the possible names of this discord.
Freud, as Lacan emphasizes, had recognized in Empedocles something close to the antinomy of drives. In the 'Rome Report', Lacan mentions 'the express reference of (Freud's) new conception to the conflict of the two principles to which the alternation of universal life was subjected by Empedocles of Agrigentum in the fifth century BC'.  If we allow that what is at stake here is access to being in the shape of a truth, we can say that what Empedocles identifies in the pairing of love and hate, philia and neikos, is something akin to the excess of the passion of access.
Lacan, one suspects, recalibrates this reference in such a way as to put increasing emphasis on discord, on non-relation as the key to truth. To this end, he fleetingly pairs Empedocles and Heraclitus. Empedocles isolates the two terms through which the necessity of a non-relation is inscribed; Empedocles names the two passions of access, as deployed by a truth. Heraclitus sustains the primacy of discord; he is the thinker of non-relation's chronological priority over relation. Take, for example, the following lines on the death drive in "Aggressivity in Psychoanalysis": 'a vital dehiscence that is constitutive of man, and which makes unthinkable the idea of an environment that is preformed for him, a "negative" libido that enables the Heraclitean notion of Discord, which the Ephesian believed to be prior to harmony, to shine once more'.  In Lacan's work, the negative libido is constantly connected to Heraclitus. In short, the connections between love, hate, truth and knowledge were established by Empedocles and then radicalized by Heraclitus, the originary thinker of discord, of non-relation.
A further proof of the Pre-Socratics' anticipation of the death drive lies in the consequences that can be drawn from their writings regarding God. Since the God of Empedocles knows nothing of hate, and therefore nothing of the nodal point of excess for the passion of access, one would therefore expect such a God's access to truth to be correspondingly restricted. This is precisely what Lacan, adducing Aristotle's commentary in support, attributes to Empedocles in Encore:
There was someone named Empedocles - as if by chance, Freud uses him from time to time like a corkscrew - of whose work we know but three lines, but Aristotle draws the consequences of them very well when he enunciates that, in the end, God was the most ignorant of all beings according to Empedocles, because he knew nothing of hatred.... If God does not know hatred, according to Empedocles, it is clear that he knows less about it than mortals. 
For the startling consequences that can be drawn from these considerations of God's ignorance, I refer the reader to François Regnault's marvellous book Dieu est inconscient. 
What matters here, however, is that we observe that, after noting the poetic anticipation of the free functioning of the matheme, Lacan credits the Pre-Socratics with an intuition that has far-reaching implications for the resources of truth inherent in sexual discord.
Let us turn to the problem of stabilizing the relationship between psycho-analysis and Platonism.
In Heidegger's strategy, the Pre-Socratics were deployed largely in order to deconstruct Plato and, as a side-effect, to plot the emergence of the system of metaphysics. Does Lacan conduct a similar operation? The answer is complex.
Lacan never pursues purely philosophical objectives. His intention, then, is not to dissect Plato. Rather, Lacan maintains an ambiguous rivalry with Plato. For Plato and psychoanalysis have at least two conceptual undertakings in common: thinking love as transference, and exploring the sinuous trajectory of the One. On these two points, it matters a great deal to Lacan to establish that what he called the 'Freudian way' is different from the Platonic.
In the end, however, it remains the case that Lacan summons the Pre-Socratics to his aid while struggling to mark the boundary between psycho-analysis and Platonism. And it is also clear that the central wager in this attempt at demarcation once more concerns the theme of non-relation, of discord, of alterity without concept; and, consequently, concerns the delinking of knowledge and truth.
Lacan attributes to Plato a desire for being to be completed by knowledge, and therefore an identification (itself entirely a product of mastery) of knowledge with truth. The Idea, in Plato's sense, would be an equivocal point which is simultaneously a norm of knowledge and a reason d'être. For Lacan, such a point can only be imaginary. It is like a cork plugging the hiatus between knowledge and truth. It brings a fallacious peace to the original discord. Lacan holds that Plato's standing declines in the light of Empedocles' and Heraclitus' propositions on the primacy of discord over harmony.
It is therefore certain that, for Lacan as for Heidegger, something has been forgotten or lost between the Pre-Socratics and Plato. It is not, however, the meaning of being. It is, rather, the meaning of non-relation, of the first separation or gap. Indeed, what has been lost is thought's recognition of the difference between the sexes as such.
One could also say that between the Pre-Socratics and Plato, a change takes place in the way difference is thought. This is fundamental for Lacan, since the signifier is constituted by difference. Empedocles and Heraclitus posit that, in the thing itself, identity is saturated by difference. As soon as a thing is exposed to thought, it can be identified only by difference. Plato could be said to have lost sight of this line of argument, since he removed the possibility of identifying difference within the identity of the Idea. We could say that the Pre-Socratics differentiate identity, while Plato identifies difference. This is perhaps the source of Lacan's preference for Heraclitus.
Recalling, in his very first seminar, that the relation between the concept and the thing is founded on the pairing of identity and difference, Lacan adds: "Heraclitus tells us - if we introduce absolute mobility in the existence of things such that the flow of the world never comes to pass twice by the same situation, it is precisely because identity in difference is already saturated in the thing".  Here we see how Lacan contrasts the eternal identification of differences according to the fixed point of the Idea - as in Plato - with the absolute differential process constitutive of the thing itself. The Lacanian conception of the relation between identity and difference - and therefore, in the thing, between the one and the multiple - finds support, contra Plato, in the universal mobilism ofHeraclitus. This is what Lacan observes with regard to the God of President Schreber in the text 'On a Question Preliminary to Any Possible Treatment of Psychosis'. For Schreber, the Creator is "Unique in his Multiplicity, Multiple in his Unity (such are the attributes, reminiscent of Heraclitus, with which Schreber defines him)." 
In fact, what Heraclitus allows us to think - and what Plato, on the contrary, prohibits - is the death drive. The Platonic effort to identify difference through the Idea leaves no room for it; Heraclitean discord, on the other hand, anticipates its every effect. In Seminar VII, when he discusses Antigone's suicide in her tomb, and our ignorance of what is happening inside it, Lacan declares: 'No better reference than the aphorisms of Heraclitus.' Among these aphorisms, the most useful is the one which states the correlation of the Phallus and death, in the following, striking form: "Hades and Dionysus are one and the same". The authority of difference allows Heraclitus to perceive, in the identity of the god of the dead with the god of vital ecstasy, the double investment of the Phallus. Or, as Lacan notes of Bacchic processions: "And (Heraclitus) leads us up to the point where he says that if it weren't a reference to Hades or a ceremony of ecstasy, it would be nothing more than an odious phallic ceremony."  According to Lacan, the Platonic subordination of difference to identity is incapable of arriving at such a point.
The Pre-Socratics, then, provide ample material from which to reconstruct, from its origins, a far-reaching disorientation of Plato. In this sense, they form part of the polemical genealogy ofpsychoanalysis.
Turning to Heidegger, we should of course recall that Lacan translated his Logos, which deals in particular with Heraclitus. I believe that three principal connections can be drawn between Lacan and Heidegger. They involve repression, the One, and being-for-death (l'être-pour-la-mort), All three are mediated by the Pre-Socratics.
First, Lacan believes he can go so far as to say that there is at least a similarity between the Freudian theme of repression and the Heideggerian articulation of truth and forgetting. It is significant for Lacan that, as Heidegger remarks, the name of the river of forgetting, Lethe, can be heard in the word for truth, aletheia. The link is made explicit in the first seminar where, in his analysis of repression in the Freudian sense, we come across the following observation: 'In every entry of being into its habitation in words, there's a margin of forgetting, a lethe complementary to every aletheia."  Such a repression, then, can with good reason be called 'originary'. Its originary character accords with the correlation in origins Heidegger establishes between truth and veiling, a correlation constantly reinforced through etymological exegesis of the Pre-Socratics.
Secondly, Lacan takes from Heidegger's commentary on Heraclitus the notion of an intimate connection between the theme of the One and that of Logos. This, for Lacan, is an essential thesis. It will later be formulated in structural fashion: the aphorism "there is something of (the) One" (il y a de l'Un) is constitutive of the symbolic order. But starting in Seminar III, in a discussion of the Schreber case, Lacan confirms Heidegger's reading of Heraclitus. Commenting on the fact that Schreber only ever has one interlocutor, he adds:
This Einheit (oneness) is very amusing to consider, if we think of this text on 'Logos' by Heidegger I have translated, which is going to be published in the first issue of our new journal, La Psychanalyse, and which identifies the logos with Heraclitus's En (One). And in fact we shall see that Schreber's delusion is in its own way a mode of relationship between the subject and language as a whole. 
It is in the most intimate part of clinical practice - that which deals with psychoses - that the clarificatory power of Heraclitus' aphorisms, supported by Heidegger, now reappears.
Finally, Lacan believes he can also connect the Freudian concept of the death drive to Heidegger's existential analysis, which defines Dasein as being-for-death. The emblematic figure of Empedocles serves, in the "Rome Report", as the vector for this connection: "Empedocles, by throwing himself into Mount Etna, leaves forever present in the memory of men this symbolic act of his being-for-death". 
You will note that in all three occurrences of Heidegger - truth and forgetting, One and Logos, being-for-death - the Pre-Socratics are a required reference. Indeed, they are necessary to the extent that one cannot decide if the Pre-Socratics are a point of suture, or projection, between Lacan and Heidegger; or if, on the contrary, it is Heidegger who allows Lacan access to a more fundamental concern with the Pre-Socratic genealogy of psycho-analysis. I, for one, tend towards the second hypothesis.
For Lacan intends to inscribe psychoanalysis within a destiny of thought that is determined by oppositions and divisions originally informed by the Pre-Socratics. On this view there are two crucial oppositions: one, as we have seen, contrasting the Pre-Socratic sense of discord to the dominance of identity in the Platonic schema. But there is also an opposition, perhaps still more profound, within the ranks of the Pre-Socratics, that sets Heraclitus against Parmenides. The clearest text is in Seminar XX:
The fact that thought moves in the direction of science only by being attributed to thinking - in other words, the fact that being is presumed to think - is what founds the philosophical tradition starting from Parmenides. Parmenides was wrong and Heraclitus was right. That is clinched by the fact that, in fragment 93, Heraclitus enunciates oute legei oute kruptei alia semainei, "he neither avows nor hides, he signifies" - putting back in its place the discourse of the winning side itself - o anax ou to manteion este to en Delphoi, "the prince" - in other words, the winner - "who prophesies in Delphi'." 
It is interesting to note that Lacan attributes the foundation of the philosophical tradition not to Plato, but to Parmenides.
I said at the outset that the grandiose innocence of the Pre-Socratics was to have broken with the traditional forms of knowledge. But Parmenides himself is also the founder of a tradition. We need, then, to locate two ruptures. On the one hand, the Pre-Socratics break with the mythic enunciation, with the tradition of myth that 'tra-dicts' the imaginary reality of the world. But on the other, at least one of the Pre-Socratics founds a tradition with which Lacan in turn breaks: the philosophical tradition. For Lacan is an anti-philosopher. This anti-philosophy, however, is already manifested, in a certain sense, by Heraclitus. The philosophical idea is that being thinks, for want of a Real (l'être pense, an manque le réel). Against this idea, Heraclitus immediately puts forward the diagonal dimension of signification, which is neither revelation nor dissimulation, but an act. In the same way, the heart of the psychoanalytic procedure lies in the act itself. Heraclitus thus puts in its place the pretension of the master, of the oracle at Delphi, but also the pretension of the philosopher to be the one who listens to the voice of the being who is supposed to think.
Finally, Lacan has a dual, even duplicitous relation to the Pre-Socratics, as he does to the entire history of philosophy. It is embodied by the relationship between two proper names: Heraclitus and Parmenides. Parmenides covers the traditional institution of philosophy, while Heraclitus refers to components of the genealogy of psychoanalysis. Lacan will adopt the same procedure to stabilize his relationship to Plato, distributing it between two proper names: Socrates, the discourse of the analyst, and Plato, the discourse of the master.
But this duplicitous split is an operation carried out within the signifier. "Parmenides is wrong, Heraclitus is right," says Lacan. Should we not take this to mean that, as thought from the point of view of psychoanalysis, philosophy appears as a form of reason that stagnates within the element of this wrong? Or as a wrong which, within the maze of its illusion, none the less makes sufficient contact with the Real to then fail to recognize the reason behind it?
The Pre-Socratics, then, who remain for us little more than an assortment of proper names to whom scattered phrases are ascribed, serve for Lacan as a formal reservoir. These names - Empedocles, Heraclitus, Parmenides - have just enough literal weight, just enough aura of significance, to allow him to separate out, to draw together and, finally, to formalize the internal dialectics of anti-philosophy.
 Jacques Lacan, Le Séminaire de Jacques Lacan, Livre VIII Le transfert, 1960-1961, ed. Jacques-Alain Miller, (Paris: Seuil, 2001), pp. 98-9.
 Jacques Lacan, The Seminar of Jacques Lacan Book XX: On Feminine Sexuality, the Limits of Love and Knowledge, 1972-1973, trans. Bruce Fink (New York, 1999), p. 131.
 Jacques Lacan, The Seminar of Jacques Lacan Book XX, p. 22.
 Jacques Lacan, Le Séminaire, Livre VIII, pp. 66-7.
 Jacques Lacan, "The Function and Field of Speech and Language in Psychoanalysis", in Écrits: A Selection (London, 2001), p. 112
 Jacques Lacan, "Aggressivity in Psychoanalysis", in Écrits, p. 24.
 Jacques Lacan, Seminar XX, p. 89.
 François Regnault, Dieu est inconscient (Paris: Navarin, 1986).
 Jacques Lacan, The Seminar of Jacques Lacan, Book I: Freud's Papers on Technique 1953-1954, ed. Jacques-Alain Miller, (Cambridge, 1988), p. 243.
 Jacques Lacan, "On a Question Preliminary to Any Possible Treatment of Psychosis", in Écrits, p. 225.
 Jacques Lacan, The Seminar of Jacques Lacan Book VII: The Ethics of Psychoanalysis, 1959-1960, (New York, 1992), p. 299.
 Jacques Lacan, Seminar I, p. 192.
 Jacques Lacan, The Seminar of Jacques Lacan Book III: The Psychoses, 1955-1956, (New York, 1993), p. 124; translation modified.
 Jacques Lacan,"Function and Field", p. 114.
 Jacques Lacan, Seminar XX, p. 114.
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