This may be a bit of a hot take, I admit, but there really is nothing more to it than just that...

@yoginho you wouldn't trace the roots of computationalism to logic?

@r3rt0 Nope. The idea that the universe is computable arguably originated with Newton, but computation in the modern sense definitely starts with Church/Turing. Uncountably many logically consistent systems are not Turing-computable.

@yoginho I see. But is Newtonian mechanics an example of computable theory? You can have, for example, a 3 body problem, which is fully Newtonian but not computable.

@r3rt0 Newton and his contemporaries use the verb "to compute" when talking about calculating predictions based on theory. But classical mechanics (in general) is not Turing-computable because of its continuum assumption and the non-computable reals that pop up as parameters in classical models (esp. deterministic chaos, i.e. the three-body problem).

@[email protected] @[email protected] @[email protected] Pardon me for jumping in uninvited, but this is an interesting topic to me and I thought I could offer some food for thought.

I'd recommend checking out this article on computable physics at nLab: https://ncatlab.org/nlab/show/computable+physics especially the discussion and references therein.

A key point is the distinction between type I and type II computability. I don't think anyone could credibly argue that the universe/physics is type I computable; that question was put to rest long ago. However, it seems to me it's still up in the air whether it is or could be type II computable. That nLab post has a reference claiming there are non-computable quantum mechanical phenomena:
Cristian Calude, Michael Dinneen, Monica Dumitrescu, Karl Svozil, Experimental Evidence of Quantum Randomness Incomputability, Phys. Rev. A 82, 022102 (2010) ( https://arxiv.org/abs/1004.1521 )
From the abstract:
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an asymptotic property --- of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
I haven't read this paper or any followups and cannot offer an informed opinion about it. Judging just from the abstract it doesn't sound like a slam dunk proof that there are non-computable phenomena, and there are authors who suggest there aren't, that the universe/physics really is type II computable. Important concepts like the Schroedinger equation have been shown to be type II computable, for instance, which is an intriguing piece of evidence.

By the way, in case you're not familiar, type I computability is what most folks think of when they think of computable: a partial function from natural numbers to natural numbers that can be implemented in a Turing machine or programming language. Type II computability is different: a function from the reals to the reals that can be so implemented. The key difference is that the input to a type II computable function can be any real number, including non-computable ones. Computable analysis concerns type II computable functions as I understand it. None of this lies in my area of expertise, just to be clear.