"I am the way, and the truth, and the life." - Jesus '"For this purpose I was born and for this purpose I have come into the world--to bear witness to the truth. Everyone who is of the truth listens to my voice." Pilate said to him, "What is truth?"' (John 18: 37-38)
Thinking about it, there can be just 3 sources of knowledge (and possibly truth) for any human being:
Inherent "knowledge" / common sense / intelligence. This would include things like the laws of logic, which we simply cannot prove, but take for granted since it is somehow hardwired in human beings and forms the basis of intelligence itself. Here we can distinguish between "hardwired" (genetic?) "assumptions" and assumptions which we share because of culture. The last mentioned is commonly included as "common sense", but is not necessarily shared by all people in all cultures and times. Some aspects of mathematics (or at least the assumption that basic mathematics is universal (i.e. 2 + 2 = 4 everywhere and always)) might possibly be included here. Some assumptions are taken for convenience, but again are without proof, although they somehow feel more probable than the alternative (e.g. the principle of Occam's Razor: the simplest solutions are most likely to be true)
Direct Observation / Experience. This is a major part of the empirical sciences where experiments can be designed to see the results of different controlled factors. But everyday observations and experiences is also a major factor in all knowledge.
Faith. We all trust (believe / have faith in) people to some degree to speak the truth (to some degree). Even scientists must believe that the results published in the scientific literature is reliable, because we simply don't have the time to repeat each and every experiment (or research project) ever done in order to do our own observations. If others repeated previous experiments, we still have to trust them to give reliable reports of their results. Of course, in science, because it is likely that somebody may repeat an experiment and scientists' careers are build on being reputable and accurate, the results of scientific research are generally much more reliable than a newspaper report, for example. Part of the scientific method is that results should be testable and repeatable. Faith is therefore not blind. It should be the reasonable result of measuring the reliability of our source of knowledge. In this, direct observation of past events and logic should play a major role. Ultimately, even our trust in our own logic and the reliability of personal observation and experience, is based on faith; a well-placed faith in my opinion, but faith nonetheless.
The issue of faith is important, because many people pit "faith" against "science" or logic. Their understanding of the term is basically a "blind" faith where you believe in spite of the evidence in things that are contradicted by the evidence. This is not at all what is meant by faith as the Bible defines it. Biblical faith has got everything to do with trust. And trust is placed in Somebody who is judged to be trustworthy/faithful/true (depending on the translation). Indeed the very word for believe (l'amin) is from the same root as the word true/truth (emet). The real question is not really if you believe or not, but who you believe or in what you place your trust. And in general, trust is earned. The Bible makes its call to faith based on the repeated faithfulness of God in the past. Cf. my story in Appendix A... if nothing happened the night when I went out in faith after asking for the Holy Spirit, I would have lost all faith in God's faithfulness. That is not what happened. But if I never took the step of faith, I also would never have seen His faithfulness and not have the reason for considering Him (and by extension the Bible as His Word) worthy of my trust. The real philosophical question is then not faith vs. logic/rationality, but how to determine what you consider as trustworthy. Obviously, there will be levels of trust/faith. It would have been nice if the philosophy of science / epistimology (or even philosophy of religion?) could provide us with better tools to determine the level of trustworthiness and also the level of our trust in different sources of knowledge. Unfortunately, we don't seem to be there yet and I have little faith that we will be there any time soon (if ever).
From the above factors, it should be obvious that shared assumptions should form the basis of any discussion about truth or knowledge. Any theory of cognitive dissonance should take into account all 3 possible sources of knowledge.