Context
One can hardly overestimate the importance of Logical Time for Lacan’s thought. Although this short text was originally published quite early in his career as an author (Lacan, 1945) and nearly a decade before the public Seminar started (1953), Lacan returned or alluded to it in almost every text in his Écrits and in each year of his teaching. Even the mere place of Logical Time within the corpus of the Écrits can be considered as an additional argument for paying special attention to it: the text is not included at the ‘right,’ that is chronological, place where one would expect it. Following the chronology of Lacan’s writings, it should have been a part of Section II of the Écrits, and included amongst texts such as Presentation on Psychical Causality and The Mirror Stage. In the actual edition of the Écrits, however, it forms, together with Presentation on Transference, a separate Section III, where it takes on the function of mediating between earlier texts and later ones. Or, as Lacan put it in Seminar II (1954–1955), the sophism discussed in Logical Time is ‘designed to draw out the distinction between language applied to the imaginary…and the symbolic moment of language, that is to say, the moment of the affirmation’ (Lacan, 1991: 290–291; my italics).
The odd place of the text illustrates one of the text’s major arguments: if we try to understand human subjectivity in its relation to time, relying on a plain, and simple chronological conception of time does not suffice. This questioning of chronology and the struggle to theorize another conception of time is already present in Freud’s work. As has been well documented before (Forrester, 1990: 192–206), Freud frequently used the common German substantive and adjective, Nachträglichkeit and nachträglich, but in doing so, gave them a specific meaning. Freud used Nachträglichkeit to refer to the phenomenon that an event at a moment in time, t2, connects to a memory at t1 and turns it into a traumatic one as if it had always been traumatic. Yet, the connection between the event (at t2) and the memory (at t1) is not established randomly, but through an association of representations (Vorstellungen), which allows one to consider the memory as anticipating the event that will turn it into a traumatic signifier. This active awaiting of a future event that will give a specific meaning to a (past) memory and, vice versa, the determination of the past through an event yet-to-come allows for a speculation on subjective time which is different than the usual conception of time as a unidirectional line, an arrow, onto which events can be precisely and unambiguously located. In this respect, Logical Time consists of an argument against chronology and in favor of a conception of time that can do justice to the strange idea that something may be chronologically posterior, yet logically anterior (and vice versa). More generally put, in Logical Time one finds the elements of a psychoanalytic theory of causal determination, far removed from the psychoanalytic cliché according to which infantile experiences determine adult psychic life.
The question of time never left Lacan, and tellingly the titles of his two last seminars – The moment of concluding (1977–1978) and Topology and Time (1978–1979), both unpublished – take up questions stemming from Logical Time. In between Logical Time and the very last phase of his teaching, Lacan had singled out Nachträglichkeit – often obfuscated by loose and differing English translations of Freud’s works – as an important notion, which eventually leads to its inclusion as après-coup in Jean Laplanche and Jean-Bertrand Pontalis’ classic vocabulary of psychoanalytic notions (Laplanche and Pontalis, 1968/1988: 111). While the authors do credit Lacan explicitly for drawing attention to Freud’s thoughts on Nachträglichkeit, at one occasion he objected to not being credited (Lacan, 2006: 394).
This highlighting of an, at the time, obscure Freudian notion leads Lacan to consider the time of the subject as the future anterior, as that which ‘will have been.’ This implies that the subject is not to be considered as a substance unaffected by change, but as determined by time on a fundamental level. When Lacan famously stated that the subject is a lack-of-being (manque-à-être), this needs to be related to its temporal nature: the subject is not, for it has to realize itself through a dynamic of an anticipated future and a retroactive determination of its past.
Yet, in Logical Time one finds neither a reflection on trauma and its double inscription on a timeline nor much discussion of linguistic tenses. The article mainly consists of the analysis of a riddle that Lacan was told at a party in February 1935 (Roudinesco, 1999: 176). A prison warden summons three prisoners, shows them three white and two black disks and puts a white one on the back of each prisoner. The first one able to tell the color of the disk on his back, solely relying on logical reasoning, will be released. After some time looking at each other, the three prisoners all walk up to the warden and use an identical argument to explain why the color of the disk on their back is white. The question is: what is the argument made by the prisoners? The interest of Logical Time does not reside in Lacan’s solution to this problem. Moreover, the ‘(new) sophism’ as Lacan names it, can hardly be considered to be an original logical puzzle, since it is known in many variants – ‘the muddy children,’ ‘three wise men,’ etc. – which have been discussed in various sources and contexts, including mathematics (Bollobás, 1986: 25), epistemology (Fagin et al., 2003: 4–7), philosophy of mind (Floridi, 2005), and literature (Tahan, 1999: 220–226). The novelty of Lacan’s discussion resides in his discrimination of three different times. Here, the word ‘time’ refers first and foremost to the three different ways the prisoners can possibly relate to the given situation. What at the end of the game is presented as a logical argument with a certain conclusion can, according to Lacan, only be reached if the prisoners go through three different, yet tightly interconnected ‘moments of evidence,’ three steps implying three different subjective positions and three different ways in which time is experienced. Lacan emphasizes that time, as something one can lose – as it is for human beings by definition finite – emerges from within the logical process and propels the latter to a conclusion.
This insight had consequences for the Lacanian view on psychoanalytic practice, in the sense that the psychoanalyst uses the time to make the analysand experience his existence as temporal. This eventually led Lacan to argue for the variable length of the psychoanalytic session. Deviating from the standard 40 or 50 minutes session allows, on one hand, the analyst to end the session at a moment that makes the last word(s) said to resonate with something that was said earlier and, on the other hand, it prevents certain analysands from dutifully sitting through the standard duration and makes them experience time as inherently limited by an end they cannot foresee.
Commentary on the text
161, 1
The introduction sketches the context within which Logical Time was published. The article was originally published in the first post-war issue of Cahiers d’Art, of which only a thousand copies were published. It contained contributions by, amongst others, Fernand Alquié, Gaston Bachelard, and Georges Bataille, lavishly illuminated with reproductions of works by, mainly, Pablo Picasso, Georges Braque, and Henri Matisse. Lacan highlights the significant dates on the cover of the issue, 1940–1944, one of the references to the Second World War in this article. As mentioned already above, the article’s particular inclusion in the Écrits illustrates its main argument: the past anticipates a future within which it can retroactively find a place.
A logical problem
161, 2
A prison warden states he has to release one of three prisoners. In order to determine who will be set free, they are invited to participate in a test. The warden takes five disks, three white ones, and two black ones. Each prisoner gets a disk on his back, which means he cannot see this disk, yet the other prisoners can. The first to deduce the color of the disk on his back will be released. There are two important rules to the game the prisoners need to observe: they cannot communicate with each other, and the solution should be based on exclusively logical grounds, merely calculating the most probable case is not acceptable.
162, 1–2
Having agreed to participate, each of the prisoners has a white disk attached to his back, which means that no use is made of the black disks. How can the prisoners solve the problem?
The perfect solution
162, 3
After spending some time looking at each other, the three prisoners walk together to the door and give a similar explanation. Let us take the perspective of one prisoner, A. He makes the following hypothesis: ‘I am black.’ If this were the case, a second prisoner, B, could make the same hypothesis, ‘I am black,’ which would imply that the third prisoner, C, is facing two blacks and should leave at once. For, if C sees two black disks, he knows immediately that the disk he is wearing is white, as there are only two black disks in the game. As C does not leave immediately, B could conclude he is not wearing a black disk and walk to the door. Yet, as B is also not leaving, A can conclude that his initial hypothesis – ‘I am black’ – has been proven wrong. Hence he knows he is wearing a white disk and has a logical argument underpinning this knowledge.
Sophistic value of this solution
162, 4–5
Lacan relates the situation of the prison to the general political context within which the article was written. During the Second World War, a large part of France was occupied by the German national-socialists, a situation which made daily life prison like, with its specific rules and regulations, and its division between the imprisoned and the imprisoners. As the translator, Bruce Fink, notes in an editorial comment (2006, p. 782), this situation made Jean-Paul Sartre conclude that the French never were freer than under the German occupation. This paradoxical statement can be explained if one relates it to Sartre’s conception of freedom. Freedom is not about the absence of external limitations to one’s inclination to do this or that – it is obvious that under the occupation, as in a prison, a lot of things cannot be done or are difficult to do – freedom is a matter of choosing where and how one positions oneself with regards to a given situation and acting accordingly. A prison, therefore, does not limit one’s freedom, but rather highlights it, forcing each prisoner individually to consider his position within it. This leads to dilemmas such as ‘Will I completely identify with the role I am given as a prisoner or rather oppose it?’ and ‘Will I collaborate with those in power, or rather become a member of the resistance, or remain passive?' On an existential level, this means that one is always free in the sense that existence lacks any positive content except the one that is chosen.
Here, Lacan takes distance from Sartre, who wrote Huis Clos (No Exit, a play written in 1943 and first staged and published in 1944) which describes a situation similar to the one analyzed by Lacan: three people locked up and dependent on the others for determining their identity. Despite this similarity, Lacan does not think that being imprisoned actually helps one to discover freedom as the fundament of one’s existence.
163, 1
Lacan states he tried out the game with various groups of people, ‘appropriately chosen, qualified intellectuals,’ which may have been the people he met at the meetings of the Collège de Sociologie, founded in 1937 by Georges Bataille, Roger Caillois, and Michel Leiris (Roudinesco, 1999: 136).
163, 2–3
Whatever the results obtained by an experimental testing and however the sinister situation of a prison may reflect (post-)war France, Lacan’s sole interest resides in the logical value of the sophism. What was first presented to Lacan as a riddle – what argument do the prisoners use to conclude that the color of the disk on their back is white? – is now qualified as ‘a sophism’ for it includes the solution, which sounds acceptable, yet also raises questions regarding its soundness. Like any sophism, it contains a seemingly correct reasoning, whose conclusion is nonetheless not convincing. The problem with a sophism is thus that one is at the same time seduced by the argument and not able to accept the conclusion. It challenges our trust in reason and forces us to both look for the hidden mistake and to question the rules of sound logical reasoning. Lacan will take on the role of the logician – not unlike Edgar Allan Poe’s detective Dupin in The Purloined Letter (see pp. 6–48) – and deal with both aspects, i.e. the possible objections and the logics used to reach the conclusion.
Discussion of the sophism
163, 4–5
The first objection to the sophism can be formulated as follows: if A is black (that is his hypothesis), then B and C have to remain undecided. For as soon as C (or B) would move (thinking the other sees one black and one white disk), B (or C) would have to doubt his conclusion based on C’s (or B’s) standing still. Hence A cannot conclude that his initial hypothesis is wrong and therefore he cannot determine the color of the disk on his back. Lacan replies to this objection that this is a logical supposition on behalf of A. The conclusion A derives from this supposition does not refer to B or C’s actual departure (as the first prisoner who found out the color of his disk), but, indeed, on their mutual hesitation. Everyone has to hesitate, for only the situation of wearing a white disk and seeing two black disks on the other prisoners’ backs allows one to know immediately one’s own color and to leave prison at once. Therefore, B and C’s indecision is not a counter-argument to A’s reasoning, for the latter is precisely based on their standing still.
164, 1
Yet, the objection returns at the second stage of A’s reasoning: the moment A has reached a conclusion, the other two prisoners, B and C, move as well, which should make A doubt whether his conclusion is valid.
164...