Notes from the underground
barang dot sg
Updated 2 December 2023
Newcomb’s problem

1. The problem
2. Why you should take just box B
3. Why you should take both boxes
4. A paradox?
5. An old principle
6. A simpler version
7. The birthday gifts
8. Compatibilism
9. The modified predictor
10. References

Other Sites

Thinking inside the boxes: Newcomb’s problem still flummoxes the great philosophers (2002), by Jim Holt.

Newcomb’s paradox: an argument for irrationality (2010), by Julia Galef.

Theology throwdown: Newcomb’s paradox (2010), by Jethro Flench.

Newcomb’s problem divides philosophers. Which side are you on? (2016), by Alex Bellos.
10. References

The solution described is easily adapted to the original version of the problem, in which, needless to say, the recommendation is to take just box B.

Newcomb’s problem is really very beautiful and the solution (as I see it) just as sublime. The orthodox entreaty to take both boxes does not do the problem justice at all.

William Newcomb apparently wrote nothing on the problem but we know he was a one-boxer from Robert Nozick who was in contrast a two-boxer. Newcomb passed away in 1999.

Robert Nozick’s seminal paper, ‘Newcomb’s Problem and Two Principles of Choice,’ was first published in Essays in Honor of Carl G. Hempel (Reidel 1969), edited by Nicholas Rescher. It was the first thing written on the problem and possibly the best. It’s a must-read. It introduces every element of the problem in loving detail. Nozick also tries to disarm the case for one-boxing.

Here’s a copy if you need one →

This paper is also reprinted in Nozick’s collection, Socratic Puzzles (Harvard 1999). Nozick passed away in 2002.

Martin Gardner’s entertaining piece, ‘Free Will Revisited, With a Mind-Bending Prediction Paradox by William Newcomb,’ appeared in his Mathematical Games column for Scientific American in July 1973.

Here’s an old scanned copy →

He subsequently invited Robert Nozick to write a guest column analyzing reader responses. This appeared as ‘Reflections on Newcomb’s Problem: a Prediction and Free-Will Dilemma’ in March 1974. You can also find this in Nozick’s Socratic Puzzles.

Or have this copy →

Gardner and Nozick combined provide one of the best possible introductions to Newcomb’s problem.

Terence Horgan is a well-known one-boxer. His 1981 paper, ‘Counterfactuals and Newcomb’s Problem,’ Journal of Philosophy, vol. 78, is a fascinating attempt to get to the bottom of the problem.

It isn’t widely known that Michael Dummett is a one-boxer in Newcomb’s problem but see the appendix to his paper ‘Causal Loops,’ in The Nature of Time (Oxford 1986), edited by Raymond Flood and Michael Lockwood. The paper is also found in Dummett’s collection, The Seas of Language (Oxford 1993).

John Martin Fischer is a well-known two-boxer. His take on Newcomb’s problem, not to mention numerous other things, may be found in his book, The Metaphysics of Free Will (Blackwell 1994).

David Lewis was probably the most distinguished two-boxer around. One of his best-known papers was ‘Why Ainch’a Rich?,’ found in the philosophy journal Noûs, vol. 15, 1981. There, Lewis introduces the notorious defence that one-boxers end up richer than two-boxers because the predictor is for some reason rewarding irrational people! Under his influence, a whole generation of students have come to accept that two-boxing is correct in Newcomb’s problem. Lewis passed away in 2001.

The Port Royal Logic (also called Logic or the Art of Thinking) was published in French in 1662 by Antoine Arnauld and Pierre Nicole. It was the most famous logic manual of its time. This was also the time of Blaise Pascal and Pierre de Fermat, two probability pioneers. The St. Petersburg paradox also dates to this time and was dreamt up by Nicolas Bernoulli, another famous guy. See also Maurice Kraitchik’s two-wallets problem which leads directly to the two-envelope paradox, a relatively recent invention in contrast.

The picture shows a standard work of causal decision theory of the sort produced in the last two decades in response to Newcomb-type problems. Such problems, and there is a small family of them, have actually produced a huge surge of interest in decision theory.

This one is The Foundations of Causal Decision Theory by James Joyce (Cambridge 1999). I don’t know enough about the technicalities of such causal decision theories to know if they would still have a point if taking both boxes in Newcomb’s problem is wrong but I’m prepared to offer anyone a ten to one wager that taking both boxes is wrong.

Joyce says in the book (pp. 150-1):
Proponents of causal decision theory, like me, regard [one-boxing in Newcomb’s problem] as entirely wrongheaded ... I am convinced that causal decision theory has it right here.
A confident remark like this is not uncommon among two-boxers.

A distinguished decision theorist torn both ways by Newcomb’s problem was Richard Jeffrey. At various points in his life, Jeffrey was either a one-boxer, a two-boxer, or believed that Newcomb’s problem was somehow an “illegitimate” decision problem – in that order I believe. Jeffrey passed away in 2002.