A perfect universe must be static.

This is my attempt at a rigorous formulation of a classic Leibnizian cosmological argument. I think that the first premise is quite intuitive when you manage to think about it long enough, and I have an informal proof of it in the last section. I couldn't find this specific formulation of the C.A. anywhere, so that's why this is here!<br><br>***<br><br>**Definitions**<br><br>• *Philosophical materialism* is the position that consciousness, mental states etc. all boil down to purely physical processes in the brain. For the sake of simplicity, let us assume this position to be true.<br><br>• *Computationalism* (given philosophical materialism) is the position that any mental process is purely computational in nature. In effect, it's the position that the brain is a (very complicated) computer, consciousness is an algorithm and thoughts and emotions are the output of running said algorithm.<br><br>• By a perfect being we shall understand a being with *omniscience* (has all the information not ruled out by any a priori principles (e.g. future contingents)), *omnipotence* (is capable of bringing about any possible state of affairs) and *omnibenevolence* (always chooses to do what is best).<br><br>• By a perfect world we shall understand a world that is the best it can possibly be.<br><br>***<br><br>**Formalisation**<br><br>Define an *universe* as a tuple *(space, time, initial conditions, laws)*, where space describes the symmetries possessed by the universe, time is the dimension in which the universe unfolds, initial conditions are the positions, momenta, stresses etc of all the fundamental particles in the universe (at time 0), and laws specifies how said particles interact at each time step.<br><br>• A universe is *static* if and only if there is some *t* such that for all times *t′* the universe is in the same state at times *t* and *t′.*<br><br>• A universe is *perfect* if and only if it is the least imperfect possible universe according to some perfect being.<br><br>• Given a state S a universe is *computationally perfect with respect to S* if and only if the least imperfect possible universe according to a perfect being is *S'*, the computational universe with initial conditions S, laws of motion a universal Turing machine with a random oracle and the constant 0 as its input, and space and time those possessed by *S.*<br><br>***<br><br>**The CA**<br><br>Theorem: Any perfect universe must be static.<br><br>Proof:<br><br>• The state of a perfect universe must be S', the state of a computationally perfect universe U'. (Suppose not, then the least imperfect possible universe must be computationally perfect, so the state must be S')<br><br>• The state of a computationally perfect universe U' must be static. (Immediate since by definition *U'* is static)<br><br>• The state of a perfect universe must be static. (Immediate from above)<br><br>QED.<br><br>***<br><br>**Informal proof that any universe must be computationally perfect**<br><br>• The universe must be perfect by definition<br><br>• A perfect universe must be run on laws that maximise its perfectness. Given a perfect being, these laws most be the simplest possible set of laws that allow for computation since the least imperfect possible solution to any computational problem is the solution to the halting problem.<br><br>• A perfect universe must be run on initial conditions that maximise its perfectness. Given a perfect being, these initial conditions must be as simple as possible, since the least imperfect possible solution to any computational problem is the solution to the halting problem.<br><br>• A computation requires a constant 0, a universal Turing machine with a random oracle and a set of initial conditions, so a perfect universe must be computational with all of the above.<br><br>• Any two states of the universe can be connected by a computation, so any two states of the universe must be equally imperfect.<br><br>• A perfect universe must therefore be static.<br><br>QED.<br><br>***<br><br>**Edit: reformulated the bit about computation very slightly and completely overhauled the proof that any universe must be computationally perfect.