Letter to Professor Robert Nozick

Chris Cole

Robert Nozick
Department of Philosophy
Harvard University
October 19, 2001

Dear Professor Nozick,

Here are some comments about your latest book (Invariances). These comments are in the spirit of the book; they are philosophically exploratory and meant to be plausible, illuminating, intellectually interesting and supported by reasons. They also have Popperian content, so they can be wrong.

1. Truth property of facts.  There is a set of Planck units (e.g., 10-43 cm) at which it appears nature is quantized. If any possible universe must be composed of some smallest unit, call these cells, and these cells are connected to one another in such a way that there is some notion of locality, then it may be that there will always emerge from these interactions a set of regularities due to the simple counting of states. States sharing the same symmetry will reinforce one another; states that lack symmetry will not. This is a form of self-organization. Stable structures will emerge and will be the "simplest" mathematically, in the sense that the simpler the symmetry, the more reinforced the structure.

Therefore, the truth property for facts may simply be that the most stable facts are the facts that are the most symmetric. Each kind of mathematical symmetry would correspond to a fact; a "law" would be a fact that is on the higher end of the symmetry spectrum. Thus physics would be the mathematics of symmetry, a conclusion that would not disturb most practicing physicists. The unreasonable effectiveness of mathematics in physics would be explained. Incidentally, it may be possible to carry out this program even for a continuous universe, assuming that the limit can be taken preserving some form of locality.

2. Possible universes.  All of our current laws of physics can be stated in the form of a principle of least action. It is plausible, but to my knowledge not yet shown, that a self-organized cellular universe will always obey some principle of least action. If this were to be shown, it would prove that any universe would have laws isomorphic to our own. Laws might be related to one another in the shape of an hourglass: many laws simplifying down to one, and then expanding out to many possible universes. It might be impossible in principle to see beyond the pinch point to determine what the fundamental interactions are.

3. Unity of nature.  If the universe comprises many identical cells interacting in all possible ways, then no sharp boundaries would exist between one part of nature and another. At a sufficiently fine level of detail, all phenomena would flow into each other. Nature, made of the same stuff throughout, would have no room for paranormal or supernatural laws. On the other hand, laws would have a statistical character, and occasional exceptions (i.e., miracles) might occur. The fully worked out theory should give us a handle on the frequency of these events.

4. Truth property of beliefs.  As you emphasize in your book, it is clearly the case that evolution has selected for beliefs that are effective for carrying out actions. You also emphasize the power a system for registering common knowledge would have, and the difficulty nature would have in finding a material basis for this registering. There has been some recent work suggesting that the brain is using quantum mechanics in an intrinsically non-classical way. Might these two ideas be related? It is known that a quantum computer can search faster than a classical computer, and the material nature has discovered to register common knowledge could be quantum material. If so, then perhaps the truth property of beliefs is that they are the closest approximation to facts that can be compressed and represented in this quantum material.

5. Necessity.  One of the functions of the common registering would be to simultaneously adjust the likelihood of all beliefs based upon incoming evidence. This evidence could include arguments as well as perceived facts. While there is no likely classical mechanism for such a widespread process (there isn’t even a good word to describe it; the best used so far is "holographic"), a quantum material might be able to pull this off. It is likely that evolution has endowed us with a sensation of pleasure associated with finding a way to further compress beliefs. The flip side of this pleasure would be psychic pain associated with a widespread disruption of beliefs. Thus a necessity is a belief the denial of which is too painful to contemplate.

6. Paradoxes.  It is not clear why paradoxes exist at all. However, if beliefs are approximations, then paradoxes may be an inevitable side effect of the compression. Paradoxes represent a tension in the system of beliefs, and their resolution can only occur when a new representation allows the union of the beliefs to be compressed in a new way. If true, then paradoxes should occur more frequently in new areas, e.g., quantum mechanics.

7. Property rights.  It would be nice to show that the Entitlement Theory of Justice is (ethically) true. This would seem to entail some kind of bridge between ethical objectivity and (property) rights. Since rights are very ancient entities, even predating (and some say motivating) writing, it is clear that they were evolutionarily effective. Might this be because they were ethically objective? Rights are peculiar things. They are entirely artificial, in the sense that they cannot be detected by science, and yet they occur ubiquitously across all cultures. We did not inherit them from our primate ancestors. Why were they invented? Perhaps to resolve conflicts of interest in a way that treats all parties symmetrically, in the sense that no factual property of the parties was referred to in the solution.

There probably are many artificial properties that could be invented to solve conflicts, like rolling a die, but when you add in other side constraints that are demanded by ethical objectivity you may be able to argue away the other solutions. Property rights seem to be the most fact-like of the possible solutions, in the sense that they persist over time, belong to a specific person, can be traded, etc. Does this make them more objective than other solutions?

8. Sovereignty. This is pretty topical, but it seems that there is a good deal of mischief going on in the world under the title of sovereignty. It might be a good time for a philosophical criticism of this concept, starting from the desirability of expanding the benefits of mutual cooperation to new groups. Insofar as sovereignty is a vestigial excuse to engage in the "law of the jungle" between nations, it is a concept that deserves to be examined.

Robert Nozick died, after a long battle with stomach cancer, on January 23, 2002.