By definition: faith is trusting in what we have good reason to believe. We don't have faith in faith but faith in Christ; faith doesn't save, Christ does! It's the object that counts.
"Faith is confidence in what we hope for and assurance about what we do not see," (cf. Heb. 11:1, NIV).
We choose to believe with our volition, it follows from our heart and where that is; if it's in the right place. We don't believe despite the evidence nor demand that all the evidence be presented before drawing our conclusion or taking a stand. Just like in a jury trial we go with the flow, or in the direction of the preponderance of the evidence--which isn't always conclusive or even certain, and there may be unanswered questions or doubts. Belief is not independent of the facts or evidence but concordant with it.
Evidence is not always conclusive, and may be subjective too (it can be circumstantial, indirect, or direct), but is only one argument to consider in making the final decision. There may be evidence pro and con, arguments for and against, we must weigh all the facts pertinent before making the final decision. We don't reach a conclusion irrespective of the evidence; however, some people cannot be convinced no matter the evidence because they don't want to believe.
(Faith is not believing something you know isn't true! Everyone has faith in something, even Secularists have faith that science can answer the questions of man; it's not a matter of faith versus reason, because we all commence with some presupposition we cannot ultimately prove, whether divine revelation or science. Fideism is the belief that we can attain to knowledge (of God) by faith alone, apart from our reason, while rationalism is the opposite, that truth is arrived only by reason--true biblical faith is based on the evidence and respects the mind, it doesn't insult your intelligence.
Fideism is basically the conviction that faith is mutually exclusive of and opposed to reason. Augustine said all knowledge begins in faith, or "I believe in order to understand." You are entitled to your own opinions and faith in them, but not your own fabricated facts. Conclusions must be based on fact, fitting, and following them, the facts aren't made to fit and follow the preconceived conclusions or notions.)
We must not succumb to the notion that believing something makes it true or disbelieving something makes it untrue-- the evidence is either true or false regardless of acceptance or belief. We cannot prove without a doubt that Christianity is true because God requires a step of faith and we can demonstrate that faith is much more reasonable than doubt and even that doubt can be an element of faith itself (cf. Mark 9:24: "I believe, help thou mine unbelief"). We must make our decision in a rational manner and decide which one fits the facts more fully and completely. Christianity is not rationalism, though, and can be defended on the open marketplace of ideas, but is rational--Christians aren't asked to kiss their brains goodbye.
However, we are exhorted to defend our faith and to have a reason or rationale why we believe in 1 Pet. 3:15 (cf. "have a reason for the hope that is within you")--if we don't, we only confirm infidels in their unbelief! If we just go by feelings we may fall by the wayside and not endure testing and challenges to our faith, as people of other faiths may have duplicate feelings about their God or religion. The unique aspect of our experience in Christ is that it's backed up by and the only religion supported by the objective, external, historical evidence of the resurrection of Christ, as well as personal, internal, subjective experience in the life and heart of the believer--Christianity is based on evidence and facts of history, not fable or sayings of wise men such as Confucius or Buddha--which are really philosophies with religiosity. Christianity is a historical faith or it is nothing, and disproving its historical credibility would discredit the faith itself.
Many have tried to disprove historical references or its historicity, but have failed in the process and have even gotten converted to Christianity in the process against their wills. No amount of argument will convince the unwilling, you cannot argue someone into the kingdom of God or persuade him by rationalism; Christianity is rational, but it isn't rationalism. No one will come to faith in Christ apart from the work of the Spirit within his heart, but he must not base his faith on the fact that he feels Christ lives in his heart--going by feelings--a duplicate experience can be had by other faiths, but he must learn to see the power of the Word in changing and sanctifying him.
God asks no one to have blind faith, which is demeaning to believers and outrage to God, but only to take a reasonable step of faith into the light--faith is the antidote to blindness, not its cause! In the end, we all have a rationale for our faith and should be able to defend ourselves with our personal testimony--like the blind man who testified, "I was blind, but now I see." This cannot be refuted and no one can deny the reality of his profession. We are exhorted to testify of what we do know and the reality of our faith, not another person. When we witness we declare the facts as we see them and can verify by experience--it's admissible in a court of law!
The problem with unbelievers who don't believe is that they don't want to believe, not that they cannot. "Even after Jesus had done all these miraculous signs in their presence, they still would not believe in him" (John 12:37, NIV). John Stott adds that "we cannot pander to someone's intellectual pride, but must cater to their intellectual integrity." No one is required to commit intellectual suicide or believe without any answers. However, we all must take that leap of faith in obedience to the faith. The problem most have is moral rebellion, not intellectual problems or hindrances, and their questions or challenges are mere smokescreens to avoid the real issue of surrender to the lordship of Christ.
The heart of the matter is a matter of the heart! Nonbelievers are described in Rom. 2:8 as those who reject the truth, and this truth is true objectively, regardless of whether one believes it or not or who told us. What they do is feign intellectual problems to try to stump the Christian and change the subject from making a decision for Christ in surrender. God is no man's debtor and will authenticate Himself to any seeker who desires to know Him, but Jesus said that also that only those willing will believe: "If any man is willing to do His will, he shall know..." (cf. John 7:17).
In exhorting decisions, one must realize that he doesn't need all the answers to believe, but he can believe anyway if he is willing and wants to believe--no amount of evidence will convince the person whose heart is hardened. Just like a jury making a verdict based on known evidence, not all evidence may be in, so we just go ahead and believe anyway, though we don't know all the answers. The important thing is to know the Answerer!
We must realize that Christianity is a reasonable proposition and we will never be disappointed in our decision. As volumes have been written about the so-called evidence that demands a verdict and God gave us a mind and expects us to use it and inquire of the Lord. The evidence can be presented cogently and there is hardly any question that hasn't been answered--Christianity is not going to come tumbling down by some brand new doubt that hasn't been resolved before!
When the plain facts are presented cogently one will realize that Christianity is based on a rational body of truth, in history, and its veracity was proven in the blood of the martyrs who died for their proclamation about Jesus rising from the dead. Even the historicity of the resurrection is vouched by multiple sources and is probably the most attested fact of antiquity--would any historian doubt the reality of Julius Caesar or Alexander the Great in contrast--Jesus was no myth and his historicity is vouched for by many pagan sources too.
All in all, we cannot deny the facts and one must be confronted with making a decision for or against Him--making no decision, is making a decision against Christ! It is not the believer who has to fear the scrutiny of the facts, but the skeptic who refuses to face the facts and acknowledge the truth! It has been said that Christianity goes beyond reason, but not against it! If the facts of the Bible were presented to any court of law, the jury would have to declare them true based on the evidence which would be admissible.
Most people who don't believe have never examined the evidence or even read the Bible. This is the whole crux of the matter--that we don't have to defend it or prove it, the seeker can do that himself by reading the testimony of the evangelists in Scripture himself. God, indeed, welcomes any honest inquiry and doubt, because He expects no one to believe something he isn't intellectually convinced of, or to commit intellectual suicide. Soli Deo Gloria!