Occam's razor, or the law of parsimony, states that the simplest explanation for any given data is most likely the correct one.
Some have attempted to use Occam's razor in a metaphysical sense, to say that, for example, God is unlikely because to assume that God exists introduces additional, and unlikely, complexity. However, I'm wondering how this can be applied. The Wikipedia article for Occam's razor gives a few justifications, but the only justifications that seem to work for metaphysics are the mathematical ones (correct me if I'm wrong), for all the others are either empirical, which is not related to metaphysics, or "aesthetic," which does not seem to be very rigorous.
The mathematical justification seems to state that because the probability of the assumptions needed, for example, to say God exists is less than 100%, each additional assumption decreases the probability of God. However, I have a few questions about this.
Why assume that the probability of any two given metaphysical ideas are the same? For example, how can you assign any probability to whether or not God exists? Why assume a uniform distribution any more than any other distribution?
Why assume that the assumptions to be made have a non-100% probability? Of course, you could then say that they are not really assumptions, but how could you justify that they really are assumptions at all?
Why is there a distinction between "positively defined" and "negatively defined" assumptions? For example, to say that God does not exist, you would have to assume that there is no being that exists that is all-powerful, no being that exists that is all-knowing, etc. It seems fairly easy to come up with additional assumptions that have to be made even in a "negatively defined" case, and how can you meaningfully assign probabilities to these assumptions?
I've also seen justifications based on minimum description length and Kolmogorov complexity, but I don't see how these computationally-based ideas have anything to do with metaphysics. How can one say that a metaphysical reality is in any way defined in a computational sense? Do simple statements that can be said to define metaphysical realities, such as x is true, y exists, etc., somehow link to computation?
While I don't really see any problems to these objections, I assume that there is at least some validity in using Occam's razor in a metaphysical way, given that so many well-known (and lesser-well known) atheists, such as Richard Dawkins, base their beliefs off of it. So what, if anything, is wrong with my objections?