Indeed, going “beyond” science is exactly what philosophers do—because science itself is basically a “spin-off” of philosophy, a subfield of philosophy known as natural philosophy. Several centuries of Christian philosophers developed the scientific method and a set of rules to distinguish natural philosophy from the rest of philosophy. They realized that setting limitations on the methodologies of natural philosophy restricted it in various ways but in the process such methodologies proved very valuable and effective in answering questions about the natural world.
I’m often amused when philosophy-ignorant “science only” advocates lash out at philosophy as “irrelevant” and “useless” when it was philosophers who developed the rules of logic and the scientific method itself. Many would argue that Science is the #1 most valuable and brilliantly effective product of philosophy, the greatest accomplishment of many generations of philosophers. (Many would also point out that this grand accomplishment was almost entirely dependent on the work of Europe’s Christian philosophers.)
Patrick, I read through the linked material you provided and got the impression that the poster has a poor understanding of philosophy. Of course, I could say the same for many of the mathematicians who get “upset” about William Lane Craig’s logic in his version of the Kalam Cosmological Argument.
I do not claim to be a philosopher but I think I know enough of the basics to see how many mathematicians and WLC critics don’t understand the nature of proofs in philosophy. Formal proofs in mathematics are not the same as the kinds of proofs Bill Craig is talking about when he discusses the Kalam Cosmological Argument. You should not assume that such “proofs of God” are like mathematical proofs which settle some issue once and for all and render all doubt moot. No, in other fields of philosophy a proof [many prefer the term “argument”] tends to be an explanation for why some position is reasonable. That is, it expresses sound reason. I don’t think I can emphasize that enough. [Of course, many would say that some such arguments are more than just reasonable. They consider them overwhelmingly compelling. But philosophical proofs don’t necessarily require such extremes.]
Therefore, the Kalam Cosmological Argument does not mean that all of the world’s mathematicians must now become theists (much less Christian theists) because the logic has eliminated all denials of God’s existence and forced atheists to change their minds. No, the Kalaam is a philosopher’s summary of why the concept of such a deity is reasonable. Accordingly, there are plenty of atheist philosophers who can affirm the Kalam argument as valid and reasonable without feeling compelled to go to church every Sunday.
(By the way, if you want to strain your brain, I dare anyone to engage the current debate among philosophers about the demarcations between the philosophy of logic and philosophic logic! This is yet another of my excuses for not becoming a professional philosopher.)