Introduction to The Resolution of Newcomb's Paradox

Introduction to The Resolution of Newcomb's Paradox

by Chris Langan

This is the first of several issues of Noesis for which I have agreed to be responsible. Past issues have contained reference to matters which, while seemingly unrelated, involve concepts similar to those which figure in the resolution of Newcomb's paradox. They will be dealt with in subsequent issues; this one is dedicated to the paradox itself.

Also in this issue is a letter which I wrote long ago, but did not submit. It addresses what I perceived at the time as a kind of identity crisis in the Society, and helps explain my hesitation to submit my work on Newcomb's paradox and other topics. There is also a request for personal information, apparently from a student doing a science project. Her letter is reprinted verbatim; members may cooperate as they see fit.

I apologize for the delay in contacting those members originally scheduled to edit the next several issues. Should any of these members be particularly anxious to put their thoughts into circulation, they need merely notify me- I'll make space between a couple of the issues I'm editing, or within one if possible.

The reason I agreed to this arrangement has to do with my use of the journal in an explicitly formal capacity. Ever since I mailed in my thoughts concerning Newcomb's paradox, there has been an expectation that I would back up my general comments with the detailed explanation to which they alluded, I am now prepared to deliver, but only with the expectation of some reasonable considerations from you in return.

Newcomb's paradox is as famous as an enigma can get. Had anyone but me developed as complete a resolution as the one I offer, he would have been extremely likely to seek initial publication in an accredited scientific or philosophical journal. Then again, he would probably also be an academician of some kind, and would thus believe in his prospects for the fair editorial consideration of his work. I, on theother hand, am not in a position to rely on the established system of sponsorship and review; I am unknown among those who assume that solutions to problems like this will natrually be discovered within their own ranks, and who act in blind accordance with their assumption. I therefore propose to spare myself the futility of pounding on doors to which only they have keys, by using instead a door which is open to me.

This doorway, Noesis, passes into a rather small room. It is therefore important that those within it bear witness to the origin of the material to follow. That is, against the potential for plagiarism or spurious "independent discovery" of my results by professionals who see my position as invitingly vulnerable. I must rely only on your honesty and fairness. I am sure that some among you have hoped that Noesis would one day become a vehicle for significant original research. I am no less certain that you understand that this kind of glamour is generally accompanied by responsibility.

The paradox has a history both within and without this group. It was invented by William Newcomb, a physicist, and adopted by Kobert Mozick, whose exposition of it has long been regarded as definitive. Nozick introduced it to Martin Gardner; Gardner has probably done more than anyone to popularize it. Notable among its attempted resolutions was that of Bar-Hillel and Margalit of the Hebrew University of Jerusalem; this attempted to reconcile the concept of rationality with the distinction between logical and probabilistic independence. But as it failed to give a mechanism spanning the distinction, it was not acknowleged as final.

The problem was apparently introduced to this group by C. Cole, who agreed with a solution affirming the mental and behavioral independence implied by the standard localistic versions of physical reality embraced by most modern scientists. I took written exception to this view, on the basis of the resolution to follow. Subsequently, two contributions by D. Inada appeared in Noesis, both affirming the one-box solution of the problem. Along with the second of these appeared pieces by Cole and K. Raniere. The latter of these was the more detailed, and was notable in that it adumbrated several aspects of the actual resolution. However, it too skirted the issue of mechanism.

This is the first publication of the resolution. Neither Nozick nor Gardner has seen it; I lack current information on the former, and I am told that the latter refuses unsolicited correspondence on the grounds that most of it turns out to be "crank call" ( if I have it correctly, some of this mail has contained death threats from would-be geniuses frustrated to the point of murder; if this is fact, one can't begrudge him his precautions). I therefore do not claim backing by any expert consensus. On the other hand, truth is not determined democratically, but logically relative to syntax, and this development is clear enough in point of logic. It therefore does not require a quorum of outside agreement to be pronounced correct.

I have lately received correspondence from another member which convinces me that confusion exists concerning both the structure and meaning of Newcomb's problem, AKA Newcomb's paradox. Newcomb's problem calls for one to infer, from given a set of well-defined conditions, which of two alternatives should be selected in order to maximize a certain monetary expectation. It is apparently the impression of some members that the correct solution is "obvious" unless a certain condition ("omniscience") is suspended, at which point all possible solutions are trivial conversions of unknowns into other unknowns. This, however, is where Newcomb's paradox enters the picture. The paradox evolves from higher level (meta-linguistic) consideration of mechanisms implied by the "obvious" solution, whatever that may be to a given solver; it is the upper floor of a split-level maze. The controversy exists solely among those who wander its lower corridors without being able to reach the ledges above, More's the pity, for there resides all meaning.

My belated best wishes to all the members. I hope you find the contents of this issue worth the wait, and that it finds you well on your way into a full and satisfying new year.

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