Monday, December 22, 2008

Close Reading: Logical Time and the Assertion of Anticipated Certainty

On the advice of David Wittenberg, I read this essay, subtitled "A New Sophism".....

Lacan begins his story with a logical puzzle of sorts: three prisoners have had colored dots fastened to themselves, out of their direct line of sight, so they they may only infer what color their dot is from the dots of the other prisoners. In the example, the prison warden only uses white dots, not making any use of the black ones.

The perfect solution, Lacan outlines is one in which all three of the prisoners walk through the door at the same time:

"I am a white, and here is how I know it. Since my companions were whites, I thought that, had I been a black, each of them would have been able to infer the following: "If I too were a black, the other would have necessarily realized stragiht away that he was a white and he would have left immediately; therefore I am not a black. And both would have left together, convinced they were whites. As they did nothing of the kind, I must be a white like them."

Lacan offers this solution as a sort of sophistic provocation He defines sophism as "a significant example for the resolution of the forms of a logical function at the historical moment at which the problems these forms raise presents itself to philosophical examnation". I will attempt to break this down.

"For the resolution of the forms of a logical function". So the problem itself is viewed as a sort of object on which perform logical operations? It is a palette on which we can paint with dialectic. That doesn't really sound like exactly what I mean, because he seems to intimate that applying logic has a certain sort of constraining effect (his consistent swipes at Sartre standing), and painting seems less limited (but it also is, by the size of the palette, the available colors, the sorts of paints and brushes one has). Upshot: the problem is an object to perform a proof upon.

"at the historical moment at the problems these forms raise presents itself to philosophical examination". Well, thats a mouthful. Sophistry of course carries all sorts of negative connotations, recent attempts to save them (ie Poulakos) nonwithstanding. I feel most comfortable forwarding the following generic notion of what "sophistry" tends to be thought of- distracting from the proper with reference to verbal/rhetorical guile and cunning. This at least seems to be the most common pejorative lobbed at the sophists.

So the problem itself is a space for problems embedded within logic itself to come out, to demand their own interrogation. A sort of new form of Zeno's Paradox, perhaps. Zeno's trickery about space served to make the point that one could not actually get anywhere else if they moved in halves. Of course folks could still make it from point x to point y, but the upshot seems to be that sophistry deceives or alters reality, or at least its perception.

The sophism, we should remember, is the solution itself. We should question its "neat cuteness", as a sort of rom com of logic. We will determine its sophistry if its presents itself "as a logical error" (163).

Lacan wants to unseat the clever solution to the problem by acting as "the good logician, odious to the world". He wants to nuke and fracture this particular "meet cute" of problem and solution. His "discussion of the Sophism". He draws out a "hestitation problem", one that the sophistic solution finds difficult. The immediate movement of all three figures towards the door would probably cause them to hesitate, and second guess the motivations of their fellow prisoners.

Essentially the problem is as follows: how does a subject conclude anything when everything is learned/apprehended at the same moment? The answer seems to be something along the lines of: the moment of judging and the moment of acting are inseparable. I will try and clarify this insight.

If the subject may only take into account real behavior, and the subjects all act according to what they observe, then all subjects move at precisely the same moment, eliding the possible moment in time in which one subject could obtain from the actions of others information about their own status as white beaded or black beaded. (Again, Lacan's reference to Sophism is really interesting here- it made me think again of Xeno's paradox, and how the use of rhetorical trickeration in that case made it seem possible that a subject might never be able to reach a destination. Similarly, here we find that a number of destinations are foreclosed a priori by the spatialization of time).

So actions only occur concurrently, owing to the fact that the anticipation of a future anterior blackness/whiteness has encouraged the subjects to act/judge in a particular way in a moment. The moment of contemplation about all of this is present in the logical discussion but seems somewhat fictive- what is important is that in acting in the moment, each subject has made it so they believe themselves to be white beaded. The suspended motions necessary to make the logical outcome of whiteness so never actually occur. But it is the figuration of their possibility that makes the subjects behave in ways so that they believe themselves to be a particular color.

The moment of contemplation of actions and of observing the actions of the other prisoners does not exist temporally, only spatially. Logic, Lacan encourages us, is not to be thought spatially. Logic is capable of finding things within its own terms, quite capably (this is analagous to the first position found in Lacan's Seminar on Poe's Purloined Letter). Logic is able to find its answers, however, by neturalizing and denying its own status as another position in a realm of coordinates. The logical viewpoint is the one from which other subjects and actions and thoughts may be viewed. Thus a spatialized logic is no logic at all, in a sense.

Thinking spatially CANNOT explain why the suspended motions do not occur. It provides only a rather uninteresting answer to the asked question- are the prisoners white, or black? The intial objection (that the subjects will doubt owing to the behavior of others), only makes sense if we conceive of this problem in the essay spatially. The suspended motion would be thought to be information disclosing, that is, revealing something about a world of subjects out there and their views about the world.

It is, however, in this essay that Lacan does some work to point the way for the theory of the "as if" that has become increasingly important, discussing "times of possibility". As a rhetorician, I was immediately drawn to the kairotic possibilities here. The subjects, in behaving "as if" the logic outlined by Lacan was operative, have essentially made themselves into the color predestined by the future anterior which excludes "so there will not be" a subject left behind, without proper knowledge of their color. As Lacan draws explicit parallells in this essay to his essay on the Mirror Stage, I do not feel too far gone in noting that a subject who "does not know his color" so to speak, yet is situated collectively by a drive to "outdo" the other is the paradigmatic case of subjectivity (and Lacan says as much here).

After all, to have an "if...then" statement, the if must proceed the then. But if the if proceeds the then, there must be a moment of time in between the if and then. However Lacan seems to be raising a major problem with this mode of thinking: What if the "if...then" proposition makes itself operative by appearing to be confirmed by behaviors that fall in line within the proposition yet not interrogating the conditions for the possibility of "if...then" to be operative. More concretely, it is misleading to explain the way the prisoners come to their conclusions in the way when it seems to be the case that the prisoners came to this conclusion not through a process of logical testing, but rather making the situation through their judgment of their own status via the act of advancing toward the door. Right or wrong about their own status, they proceed, with the future anterior here posited as that of the situation of not properly knowing ones status- the idea being that gathering information is a sort of zero-sum game, and one is better off making a certainty than being subjected to anothers certainty. This possibility is allowed by lacan, when he argues that a subject who paused after the other two moved would have simply subjected themselves to the world made by the other two subjects.

Embedded within the decision to move towards the door is a conclusion and thus an act of judgment about ones status, much as the act of becoming a subject is itself a decision which guarantees the reaffirmation of the simultaneous fiction and possibility of being a whole subject measured against the Other. The possibility for truth lies in the existence of others, who may confirm or deny, giving rise to rightness and error, each of which is already predestined. Entering into the symbolic is an already chosen departure towards a door with a conclusion in hand about one's "color", and it occurs regardless of what one's "actual color" is.

I might write more on this essay but man, its rugged. Anyone with an angle on spatialization vs. temporalization in this thing, I am all ears.


  1. You don't set up the warden's problem here, which will help this make sense for others: Three prisoners are told that whoever can ascertain what color dot he has on his back he will be set free. Each prisoner may only observe the dots on the backs of the other two prisoners. There are three white dots, but only two black ones available (so, if one prisoner sees that both others have black dots, he can say "I have white!" and run out the door). If the prisoner sees one white and one black, he can assume that he is white, because if he was black, someone else would be walking out the door (here temporality is introduced: there is a second moment when the prisoner must take stock of how others are reacting). But what happens when the prisoner sees two white dots? Here a third moment is introduced: the prisoner realizes that since no one is moving toward the door, then everyone must be seeing two white dots. At this third moment, the prisoners simultaneously reach the conclusion that all three must have white dots, and they walk out the door together (a conclusion which takes a considerable amount of faith in the intelligence of your fellow prisoners...and how smart can they be?--they're in prison!)

    If we imagine that this was an operation carried out by avatars in a computer simulation, then the outcome would be much more certain. Here's a simple program:
    Dear Computer,
    If you see:
    2 black dots, go to door
    1 black dot and other avatars are stationary, go to door
    2 white dots, go to door

    A computer would never fail to reach the door for several reasons: the computer does not doubt the logical capabilities of its fellow avatars; the time of calculation is reduced to near-zero, since the commands for each possible scenario are planned in advance; all possible scenarios are win scenarios; computer avatars cannot die.

    The game is developed on a binary schema: yes/no, black/white, if/then, move/stay. The ego may be perfectly happy with this schema, structured as it is according to the rules by which the ego's world is structured and sustained. But there is this other time which intercedes, or something intercedes to interrupt time. It is the unconscious that interrupts: the psychic agency which does not say "no," and thus cannot respect the binary structure of the logic problem. "Doubt" is anathema to logic, yet here we are faced with a logical problem that must in some way account for doubt if its resolution is to be recognized as valid. It is as if this logical problem wants to make room for the unconscious, for the parapractic interruption of the signification that would carry the operation to its simple success (at least if computers were in charge).

    In short: there is no temporal dimension to the prisoner problem as such (the computer example proves this). The temporal dimension only arises when humans try to solve it, and this temporality must be understood to extend from the existence of competing psychic agencies.

    What I'm saying here is pretty obvious I guess. I need to revisit this is difficult.

  2. Lacan seems to be saying the prisoners are "programmed" to move towards the door no matter what, owing to the fact that the movements toward the door have the effect of making the assumption of whiteness a sort of fair accompli. That your computerized example only includes "win" scenarios is interesting, because we can imagine that it is the computer subject which possesses a non-investment in the situation to the extent that we can program it to account for "losses", but the human subjects make everything into a win through judgment-in-action.

    I think a really crucial part of this essay is that because each prisoner is assigned a white dot, its possible that all the prisoners could be stuck there forever, without knowing which color they are. Subjects being driven and such, this is rather unacceptable, and so understanding is made with reference to others, by acting as though the prisoners know their colors. This is why Lacan closes the essay with his formulation of human subjectivity- humans claim to be humans because they are afraid of finding out that they are not humans. There is no external referent to guarantee what humanness is, except "doing" human. What curious about that example is that its not exactly parallel to this one, because in the game one is assigned a colored dot, making it so that there is a right and wrong answer, at least in the eyes of the warden, who will hear each prisoner tell what color they are.

    The only explanation that makes any sense as regards this problem is that symbolically the warden plays the role of the Ideal-Ego, striking down attempts to assert identity as always-already inferior to the imagined ideal. The problem is that some prisoners may guess right......

  3. "humans claim to be humans because they are afraid of finding out that they are not humans."
    I like that.
    I'll try to read the essay over break and anticipate that we can talk about it with certainty later, at some time that is logical for both of us.

  4. In the computer example, shouldn't "hesitation" also be included with the 2 white dots command. the prisoner's being freed hangs on their ability to correctly guess their dot color. 2 white dots on the other(s) alone is not enough information. 2 white dots plus 2 hesitations is.