Simplifying the laws

This morning I realized the following Nomic Simplification thesis is very likely true:

• NS: Any physical theory can be replaced by a practically empirically indistinguishable theory with extremely simple physical laws and very few natural kinds of physically fundamental entities and properties, at the cost of somewhat more complicated psychophysical laws and vastly more complicated and/or fine-tuned initial conditions. For concreteness, the simple physical laws could be the laws of Conway’s Game of Life or of classical mechanics with some simple laws.

What does the “practically” qualifier do here? Well, a theory might have empirical consequences that are not practically available to us, for instance because the mathematics of the theory is too nasty for us to compute the relevant predictions from. So I am restricting the empirical match to those empirical consequences that are practically available given the computational resources we have.

Moreover, NS seems to affect quite a number of issues. But before I get to that, let me give a hand-waving argument for NS that I find quite convicing.

By Church-Turing thesis, any such practically available empirical consequences can be computed by a finite subset of a Turing machine. Thus, we should be able to simulate the physical theory in question by means of a finite subset of a Turing machine, and a Turing machine needs only very simple physical laws. For instance, the laws of Conway’s Game of Life are extremely simple, and yet Turing complete—one can implement a Turing machine in the system. Moreover, we can run the Game of Life with one fundamental natural physical kind, namely cell, and one fundamental property, namely color, in addition to position. If we implement a Turing machine in the Game of Life that simulates the physical theory T in question, we will still need to layer psychophysical laws on top of that to generate empirical predictions. These might be somewhat more complicated than the best psychophysical laws for T, but not by far. For the translation between the Turing machine’s data and T’s physical ontology will not be that complicated (we can design a good GUI, as it were, by sufficiently complicating the code for the Turing machine—i.e., the initial conditions), and we can just add that translation layer to the best psychophysical laws for T. Now, we have good reason to think that any tenable psychophysical laws will be very complicated, and so adding the translation layer is unlikely to increase the complexity by a significant factor. Of course, the code encoding T is apt to be vastly complicated, and will correspond to the initial conditions for the Game of Life.

What goes for the Game of Life goes for classical mechanics with some simple laws—perhaps rigid bodies moving in classical mechanics frictionlessly and powered by flywheels that have been turning for ages.

What are some consequences of NS and of the Church-Turing argument behind it?

1. What got me thinking about NS is that Nancy Cartwright has argued that our messy world cannot be encapsulated by simple laws of physics that cover all eventualities, given the complexities of combination laws for different forces, and has opted for a story involving causal powers. But insofar as that story generates practically available empirical consequences, NS tells us that we can replace the story with an account that has very simple physical laws.

2. It is possible to uphold classical Newtonian physics given all the evidence we have at hand. For we can presumably make an arbitrarily large finite subset of a Turing machine in a world governed by classical physics. Of course, there will likely be horrendous fine-tuning of initial conditions.

3. Sometimes theists argue (or at least I’ve said stuff like this) that laws of nature that would allow a complexly interdependent ecosystem, embodied intelligence, and yet make evil impossible would likely have to be immensely complex. NS shows this is false.

4. We rightly prefer theories with simpler laws and fewer fundamental kinds and properties to theories with more of them other things being equal. NS teaches us, however, that simplicity of laws, fundamental kinds and fundamental properties can be easily ensured in ways that are counterintuitive. We should think it more likely that the fundamental laws, kinds and properties of our world are those of quantum mechanics and the standard model than that they are of Conway’s Game of Life. Thus, we need to make sure that we take “other things being equal” very seriously—in particular, avoidance of fine-tuning of initial conditions and/or seeking elegance in the initial conditions is very important for evaluating theories.

5. If we are willing to accept a very large multiverse, we might be able to simplify the laws, fundamental kinds, and fundamental properties in an aberrant way (say, Game of Life) while yet not having any fine-tuning problem. For in a sufficiently large multiverse, we can explain the existence of fine-tuned initial conditions in some life-supporting universe by means of randomness and the fact that we can only observe a life-supporting universe. How serious a problem this is is depends on whether we can generate a good probability measures in multiverses and argue that given the aberrantly simple laws the right probability measure will generate predictions that do not match our observations. In the Game of Life story, a plausible probability measure is given by making the color of each initial cell be an independent coin-flip random variable. I suspect that this would lead to the prediction that we should expect to see a much messier world than we do, and so we may be able to empirically rule out a multiverse version of the Game of Life hypothesis.

The general lesson is this. We can shift complexity considerations in a theoretical account back and forth betweeninitial conditions and the laws/kinds/properties. We can simplify each at the expense of the other.

Doing, refraining, and double effect

Some people are skeptical of distinctions between doing and refraining. It seems that anybody who accepts classical double effect reasoning must accept such a distinction.

Suppose you’re informed that if you don’t kill Alice, then Bob and Carol will be murdered, with all three innocent. The double effect reasoning says you may not kill Alice, since even if you are aiming to save Bob and Carol, the means to saving Bob and Carol is Alice’s death, and so you would be intending to kill Alice.

But suppose we don’t make a distinction between doing and refraining. Refraining from killing Alice has Bob and Carol’s death as a consequence. But this consequence is disproportionately bad, so by classical double effect reasoning, you are prohibited from refraining to kill Alice. Hence, killing Alice is wrong but so is refraining from killing her. Thus, this is a case of a real moral dilemma. But everyone who accepts classical double effect reasoning denies that this is a moral dilemma: you simply shouldn’t kill Alice, and then you’re doing nothing wrong.

So it seems that double effect cannot apply to both doings and refrainings equally. Thus, it seems that the right solution to the above problem is to say that double effect applies only to doings.

But there are cases where one might think double effect reasoning applies to refrainings as well. To adapt Rachels’ famous case, suppose innocent Tommy is drowning in a bathtub, and you can easily pull him out. But you’ve been informed that unless Tommy is dead by the end of the day, Bob and Carol will be murdered. Because it’s wrong to kill Tommy by double effect for doing, you were steeling yourself to accept Bob and Carol’s death. But now things have changed. Now it seems that double effect forbids you to save Tommy, because a consequence of saving Tommy is the death of Bob and Carol, and that’s disproportionate.

I am very unclear on this case. But maybe the judgment that you are forbidden to save Tommy is correct. Consider this case: you see someone drowning, and you could rescue them, but then someone points a gun at two hostages and informs you that if you save the drowning person, the hostages will be killed. Then you really should refrain from saving the drowning person.

Inseparability and real identity

On a standard (but disputed) interpretation of Scotus, x and y are inseparable (neither can consistently exist without the other) if and only if they really identical.

Let a be God’s asserting to Alice: “I am asserting to Bob the same thing I’m asserting to you but with your name in place of theirs.” Let b be God’s asserting to Bob: “I am asserting to Alice the same thing I’m asserting to you but with your name in place of theirs.” Then a and b are inseparable, since God cannot assert a falsehood. But clearly these two divine assertings are not really identical.