Monday, July 22, 2013

Fine-tuning and best-systems accounts of laws

According to best-systems accounts of laws, the laws are the theorems of the best system correctly describing our world. The best system, roughly, is one that optimizes for informativeness (telling us as much as possible about our world) and brevity of expression.

Now, suppose that there is some dimensionless constant α, say the fine-structure constant, which needs to be in some narrowish range to have a universe looking like ours in terms of whether stars form, etc. Simplify to suppose that there is only one such constant (in our world, there are probably more). Suppose also, as might well be the case, that this constant is a typical real number in that it is not capable of a finite description (in the way that e, π, 1, −8489/919074/7 are)—to express it needs something an infinite decimal expansion. The best system will then not contain a statement of the exact value for α. An exact value would require an infinitely long statement, and that would destroy the brevity of the best system. But specifying no value at all would militate against informativeness. By specifying a value to sufficient precision to ensure fine-tuning, the best system thereby also specifies that there are stars, etc.

Suppose the correct value of α is 0.0029735.... That's too much precision to include in the best system—it goes against brevity. But including in the best system that 0.0029<α<0.0030 might be very informative—suppose, for instance, that it implies fine-tuning for stars, for instance.

But then on the best-systems account of laws, it would be a required by law that the first four digits of α after the decimal point be 0029, but there would be no law for the further digits. But surely that is wrong. Surely either all the digits of α are law-required or none of them are.


William said...

I take it that a best system could not contain vagueness? Any good reasons why not?

Alexander R Pruss said...

Let's think about how that might work. Maybe the best system contains the claim "alpha is approximately 0.0030". Well, then, we still have the awkward condition that it's required by law that the first two digits after the decimal place be 0 (0.0130 is definitely not approximately 0.0030), and we have no requirements of law about the 100th digit after the decimal place. So we still violate the intuition that either all or none of the digits are a matter of law.

Richard Davis said...

It seems there could be some laws which can be simply stated and which, in effect, render it highly objectively probable that something like a multiverse or pluriverse will exist. That should get us to the existence of a universe like ours, without requiring any really long decimals to appear in the basic laws.

Alexander R Pruss said...

Maybe. But the best-systems account should still work in possible worlds where there is no such multiverse.

Richard Davis said...

Mm. Supposing, though, that these laws were necessarily true?