Faith is the reality of things hoped for. James Hastings wrote “Faith in God is a moral act; it is not an emotion, an impression, the result of considerations which act upon a man from without; it is an act in which he exercise moral choice. To have faith we must will to have it. This is not to say there can be true faith apart from reasonable grounds of faith. But these grounds may exist, they may be apparent, and yet faith may be absent, because the temper and spirit of the man may make him reluctant to exert his will, or because he misconceives the nature of the act. Men confound faith and opinion; even in opinion a man’s moral habits and tendencies count for a great deal; and what we often predict man’s opinion will be from what we know of his character. But in the formation of opinion he the will has no direct function except to compel the intellect to investigate the facts by which opinion should be determined. In faith the case is wholly different. When the facts which should command faith are present and seen, faith may be withheld. Faith is an act of the will; and if we suppose that we shall come to believe in God in Christ as the result of external forces which compel belief, we shall not believe at all. And when faith, resting on adequate grounds is assaulted by doubt, the doubt must be met by a resolute decision. (“The Great Texts of the Bible; James Hastings; Charles Scribners Sons; 1912).
Faith is not belief without proof but trust without reservations–trust in a God who has shown himself worthy of that trust. To use a trinitarian framework: God the Father makes these promises; God the Son confirms them in his words and deeds; and the Holy Spirit reassures us of their reliability and seals those promises within our heart. What is faith? Now faith is the substance of things hoped for, the evidence of things not seen. (Heb 11:1).
What does it mean to believe by faith or know by faith? The word I have a problem with in that sentence is the word “believe.” I do not necessarily see them as the same thing, so that one could not really “Believe” by “faith.” I can believe, or I can have faith in something I believe is real. I cannot have faith without the “something” in which I believe in. In other words, on issues pertaining to Christianity, if there was no God, then having faith in “God” would be highly illogical to the point, quite possibly, of being psychologically deficient in light of reality. The Hebrews verse goes on to indicate that “we understand that the worlds were framed by the word of God,” which would be an understanding based on the simple fact that no one was around at creation. I do not know that it would be possible to simply believe that “In the beginning God created,” with no real belief that there is a God. As to the second part of the question, the Hebrews chapter goes on to mention people who did various things via faith from great miracles to martyrdom. But the only common base of knowledge in those applications is that the people “knew” God would deliver them, and He did for them all, but some only by death, since death is its own form of deliverance. The true person of faith basically looks beyond this life.
How does one distinguish between someone who says that they know by faith and someone who says that they believe because they believe? The use of the expression “believe because they believe” seems a rather circular reasoning. So, if I was to distinguish between someone who claims to “know by faith” and one who claims to “believe because they believe” I would probably be more receptive to the one who knows by faith as opposed to the other since one I could not even imagine anyone asserting with any stability of reason. However, it would also depend, in a comparison, what the one person is claiming to “know by faith.”
Is belief by faith a valid method to determine what is true? Not sure how to respond again because “belief by faith” sounds rather foreign to me. I suppose it might aid in determining the validity of a future event, like eternity, or a past event like creation, but I dont know how else anyone could weigh it in any objective manner.
How does a believer determine what to have faith in? Again, the mixing of the words, but the faith would come from the belief and not vice versa. How one determines the existence of God varies. It would be hoped that the one applying the faith has already sorted out which “God” he believes in before acting in any capacity of faith.
How should a believer determine what to have faith in? How do you know? Again, the mixing of the word “believe” and “faith” make the question hard to understand. If the believer has not predetermined an object or God to which he is able to use the title of

Faith
How do you know? Through weights, through measures, through investigations, the ways that one chooses a belief are probably endless. My observation has been that most everyone holds some form of world view, even if they could not identify it by asking them, they have some kinds of ways in which they approach the world and determine how they will react in various day to day situations. As long as they remain comfortable and secure in their world view, then they have no reason to weigh any other “reality” outside their own. It is generally during times of trouble, when ones worldview is shaken, that they might make some attempt to climb outside of their world view and decide how to adjust. It is at that time that people will move towards God or against God. However, that time is probably so subjective experientially that to answer “how do you know?” might be different for everyone. The mind is a complicated piece of workmanship.
What is the difference between faith and gullibility? Is faith a virtue? Why or why not? Gullibility would be a person readily believing information sometimes to an absurd extent. It does not necessitate that the information is false or true, as one who is gullible could randomly accept a true objective, however it was probably an accident rather than thoughtful choice. Faith, as I stated previously, is acting on belief and, hopefully, belief of substance. Is faith a virtue? Probably in the eyes of God since, according to the Bible, no one can please Him without it. But no one could act in faith in God without first knowing that God exists. So, in some sense, one might be able to say that faith is an active fruit of belief.
There are two kinds of faith. I shall call one “assenting” and the other “saving.” Assenting faith is an intellectual persuasion of the truth of the thing taught. There are those who have assenting faith, but will not repent, and therefore do not gain a saving faith. Assenting faith often exists without saving faith, for most men have assenting faith. Very few have saving faith; but the latter cannot exist without the former.



