A friend pointed out to me a 1945 paper (English translation is here) by psychoanalyst and philosopher Jacques Lacan that attempts to reason about knowledge in the sense similar to that used in computer science or economics and game theory much before these two fields started to formally address notions of knowledge. The paper analyzes the following puzzle:
A prison warden has three select prisoners summoned and announces to them the following: ”For reasons I need not make known now, gentlemen, I must set one of you free. In order to decide whom, I will entrust the outcome to a test which you will kindly undergo. “There are three of you present. I have here five discs differing only in color: three white and two black. Without letting you know which I have chosen, I shall fasten one of them to each of you between his shoulders; outside, that is, your direct visual field – any indirect ways of getting alook at the disc being excluded by the absence here of any means of mirroring. ”At that point, you will be left at your leisure to consider your companions and their respective discs, without being allowed, of course, to communicate amongst yourselves the results of your inspection. Your own interest would, in any case, proscribe such communication, for the first to be able to deduce his own color will be the one to benefit from the dispensatory measure at our disposal. ”His conclusion, moreover, must be founded upon logical and not simply probabilistic reasons. Keeping this in mind, it is to be understood that as soon as one of you is ready to formulate such a conclusion, he should pass through this door so that he may be judged individually on the basis ofhis respose.” This having been made clear, each of the three subjects is adorned with a white disc, no use being made of the black ones, of which there were, let us recall, but two. How can the subjects solve the problem?
While the paper (or actually the English translation — which I understand, in the case of Lacan, is usually much clearer than the French original) starts off very clearly, I have to admit that I can’t comprehend much once he starts his analysis, but he seems to consider the asynchrony involved (as we would call it today in distributed computation) . As the paper progresses, the section names become quite delicious: “The Modulation of Time in the Sophism’s Movement: the Instant of the Glance, the Time for Comprehending and the Moment of Concluding”, “Temporal Tension in the Subjective Assertion and its Value Manifested in the Demonstration of the Sophism”, and “The Truth of the Sophism as Temporalized Reference of One self to Another: Anticipating Subjective Assertion as the Fundamental Form of a Collective Logic”.