Not only it assumes independence, it also assumes that the two competing theories have exactly the same postulates except for a single extra one. That is typically not how things work in real life.
it also assumes that the two competing theories have exactly the same postulates
Er, no it doesn't. Where are you getting this?
Sean Carroll, physicist and proponent of Everettian Quantum Mechanics, has just posted a new article going over some of the common objections to EQM and why they are false. Of particular interest to us as rationalists:
Very reminiscent of the quantum physics sequence here! I find that this distinction between number of entities and number of postulates is something that I need to remind people of all the time.
META: This is my first post; if I have done anything wrong, or could have done something better, please tell me!