Pruss versus Deleuze on whether there are sufficient reasons for an approximate universe

Further down, Delueze has a better explanation than Pruss for the times the universe seems arbitrary (why is pi irrational?).   Just below, Pruss wins out on making sense of why the world contains order and not just disorder. Are either correct?

"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.

-- Alexander Pruss' blog, July 2013



"Difference is not diversity. Diversity is given, but difference is that by which the given is given, that by which the given is given as diverse. Difference is not phenomenon but the noumenon closest to the phenomenon. It is therefore true that God makes the world by calculating, but his calculations never work out exactly, and this inexactitute or injustice in the result, this irreducible inequality, forms the condition of the world. The world ‘happens’ while God calculates; if the calculations were exact, there would be no world. The world can be regarded as a ‘remainder’, and the real in the world understood in terms of fractional or even incommensurable numbers. Every phenomenon refers to an inequality by which it is conditioned. Every diversity and every change refers to a difference which is its sufficient condition."

-- Giles Deleuze, Difference and Repetition, 1995 (English translation,Paul Patton)