There’s a big difference between saying, “This is true because I feel it is so,” and “I can prove this is true, and here are a few reliable sites.” Logic must be based on the examination of facts, not on antecdotes, or feelings.
If a person is able to defend their position by information which is supported by the scientific community, I will give more weight to it than “evidence” from a religious source, or a theory which has no peer credibility. Evidence to prove or disprove a theory must come from a reliable source, stand up to reasonable scrutiny, and make logical sense.
By logic, I mean taking what I know from the fields of sociology, history, science, archaeology and biology, and comparing the proposed theory to the facts I have gleaned from these sources. If something is seriously awry, then I will not accept it without deeply convincing evidence.
Just as an example: to me, the existance of black holes seem “far fetched,” simply because I am not sufficiently educated in astronomy. However, someone could lead me to information from respected astronomers and scientists which would explain them to me in excrutiating detail. They could show me examples of the effects of gravitational pull on surrounding astral bodies. Thus, I could weigh the evidence presented and come to accept their existance.
As a comparison, someone could claim that angels definately exist, and post links to Christian websites which list encounters with angels. Considering that the site most likely has an agenda (conversion, or selling their book on angels) I would not give the evidence the same weight as I would the scientists in the above example. Also, the only evidence would be antecdotal stories from people whom I do not know, and thus cannot accurately judge their credibility.
You must also consider the bias of the source. For example, I would put more trust in the CDC statistics on abortion than I would from a Right To Life site. Nor would I accept information on the Holocaust from a Neo-Nazi source, or evolutionary theory from a Creationist.
So, when I see a theory presented and defended, I ask myself if it stands up to scrutiny from a scientific/sociological/historical standpoint? Is the logic used circular in nature? Is the evidence reliable, from a respected, non-biased source? Are both the evidence for and against the theory examined evenly? Would it stand up in a court of law, or would it be rejected as hearsay, or speculation without basis?
But that’s just me. Others may have more stict or lax standards of what constitutes evidence. Some may accept evidence which only supports what they believe. But personally, I have always operated on the basis of “Know thine enemy.” I want to know what supports “the other side’s” convictions before I dismiss them out of hand. Only by studying an issue with an open mind can you see both sides, and then come to a reasoned, informed decision. In this way, I am prepared to defend my beliefs, because I already know what flaws the other side sees in them and have resolved them in my mind. But again, no belief I have is so deeply rooted that I could not be dissuaded by reliable evidence.