The classic argument is between reason and divination. The Greek philosophers argued that through reason only can one know the world while the Middle Eastern approach claimed that only through divine insight can one know the world. Augustine and Thomas Aquinas blended these two concepts and made Christianity successful for many years.
Since then, science has come to present itself as superior to both of these methods. I have usually used randomization as my main knowledge method. I only believe it if it has been randomized.
The problem with reason is that it is patently ridiculous. No person has ever been shown to be able to participate in the act of reasoning. Instead, all studies of the matter show that humans decide first and then use "reason" to justify their decisions. Of course, you have the obvious triumphs of reason like Aristotle stating that women aren't as intelligent because they have less teeth.
Science, in theory, can overcome these problems with reason by using data. While our own human minds see patterns where they aren't and fail to perceive them where they are, numbers don't lie. The problem is that people are completely incompetent at knowing how to interpret data. Physics has become an unexperimental metaphysics, with theories rated on how "mathematically beautiful" they are, rather than with how they correspond with reality. Experimental psychology recently had a great shadow overcast when only 30 of 100 experiments were repeatable (is it any wonder?). Nutritional studies are approaching a 50% retraction rate. Most of the biological studies are questionable because they don't start with a firm molecular basis. Until you understand the molecule, you can't understand the cell or the organ or the organism or the ecosystem. Economics is a bit less grounded in reality than metaphysics. The only place where science is superior is in Chemistry, where the Nobel prize went to somebody who used Scotch tape on a pencil tip over and over again.
I only included randomization because it grounded me for many years. I realize that most people don't consider it a legitimate form of knowledge. I am beginning to think that randomness doesn't exist since all proofs of randomness start with the assumption: "Assume an infinite random sequence". I don't think any such sequence exists.
All that's left is Divine Inspiration. Only through Jesus can one know the world. Only with the Holy Spirit can one have wisdom. Only with God is anything possible.
