Experience, to my father and my uncle it is experience which matters. All things that one can learn from logic is null and void. They would say, "Yes, I agree with what you say in theory, but in reality the world does not work this way. You need experience."
I will disprove this statement. It is simple as we only need to provide a definition to experience and view if all we know is because of experience.
Experience is a historical account of what has personally happened to oneself. Experience are those times that can be measured through our senses. A thought is not an experience for if a thought were an experience, logic learned through books would be held as true, but accordingly experience must be through our senses; To see, hear, smell, taste, or touch, these are what gives us experience. Do we all agree on this definition?
If so, then now we can disprove experience as a source of ultimate knowledge. The mind can not be sensed in any fashion. You can not see it, hold it, smell it, taste it, or hear it. How then do we know we have a mind? Logic. 1 + 1 = 2; 2 * 1 = 2; These simple mathematical equations are not known through experience. You can not sense 1 + 1 = 2 nor 2 * 1 = 2. They are understood through our logic. Time, space, mind, soul ... these are a few things that can not be proven through our senses and therefore can not be proven through experience by the above definition. Without our mind, time, or space there would be no such thing as the past, no such thing as experience. The mind, time, and space are known a priori, or before hand, so that we can comprehend our experience.
Thus, experience in itself can not teach you anything. Logic teaches that yes, the world does work this way. For experience can never teach mathematics, etc... Experience needs logic.
It is by applying logic that we truly comprehend the world.