Sorry that this is late.
Since there is no good place within the flow of the reply for the following I'd like to start by stepping back for a second and briefly outline how human epistemology functions before proceeding. The following is largely the opinion championed and made prevalent in the modern era by Blessed Henry Cardinal Newman, but I do not believe that I lifted it initially from him directly. The human person comes to conclusions by considering probabilities between to logically opposing propositions (X and ~X). These conclusions come in the form of institutions as to the level of probability. Newman calls this the illative sense. Even within the context of formal logic, these intuitions are the source of our basic propositions, our acceptance of the legitimacy of a basing relation, and that a basing relation is functioning. Absolute epistemic certainty accrues only when the epistemic probability of X is actually 100% and ~X 0%. Justification accrues when based upon the circumstances both epistemic and otherwise it is morally legitimate for a subject to ascent to a proposition.
What is faith?
First I want to say that, except insofar as "faith" can some times mean the content of a religion or the religion itself, which is clearly not what we are here discussing, in a religious context "faith" always entails some sort of trust. The definition you give of faith only became prominent in the 17th or 18th centuries and was largely defunct by the end of the 19th century. It was also principally a definition used by opponents of religion. I return to my previous statement that perhaps you are not or have not been sufficiently ensconced in religion to really understand how the term functions. This is largely an assumption I admit. I do not know your history. To prove my point, I simply Googled "what is faith". Here are quotations from every listing on the first page with the exception of Wikipedia, who in my opinion has significant legal failures in its licensing schema:
"It was by faith that Abraham was made able to become a father, because he
trusted God to do what he had promised."
https://www.biblegateway.com/passage/?search=Hebrews+11&version=NCV
"faith in the testimony and authority of others whom we can
trust . . . faith with respect to a thousand things which we take on
trust"
http://biblehub.com/hebrews/11-1.htm
"This definition of faith contains two aspects: intellectual assent and
trust."
http://www.gotquestions.org/definition-of-faith.html
"Perhaps the best word we can use to translate the Greek word “pistis” (usually translated faith) is the word “
trust” or “
trustworthy.” Suppose you tell a friend that you have faith in her. What does that mean? It means two things. First, you are sure the person you are talking to actually exists. And second, you are convinced she is
trustworthy; you can believe what she says and
trust in her character."
http://rzim.org/a-slice-of-infinity/what-is-faith-2
"Faith is belief with strong conviction; firm belief in something for which there may be no tangible proof; complete
trust in or devotion to."
http://christianity.about.com/od/glossary/g/faith.htm
"We began with Hebrews 11:6 stating, “Without faith it is
impossible to please God.” God wants you to learn to
rely on Him—to
trust Him completely in everything! You really do not have a choice if you want to please Him. Like any
human father, God does not want you to fret, worry and agonize over your needs. In numerous places throughout His Word, He promises to provide for you in all circumstances. He will always take care of you. Do not doubt!
Believe God!
Trust Him!
Wait on Him!
Expect Him to keep all of His promises—and He will! Faith is your evidence!"
http://rcg.org/books/wirf.html
"Faith in God is more than a theoretical belief in Him. To have faith in God is to
trust Him, to have confidence in Him, and to be willing to act on your belief in Him."
http://www.mormon.org/faq/what-is-faith
"
The New Strong’s Expanded Dictionary of Bible Word says,
'Pistis is used of belief with the predominate idea of
trust (or confidence) whether in God or in Christ, springing from faith in the same. "Faith" means
trust, confidence, assurance, and belief
'"
http://lifehopeandtruth.com/change/faith/what-is-faith/
"'The main sense of the word 'faith' in the NT is that of
trust or reliance... [
Pistis] bears the sense not of faithfulness alone, but of the reliance and
trust that is the basis of man's faithfulness, i.e., the faithfulness that expresses confidence in the faithfulness of God' (
International Standard Bible Encyclopedia, Vol. 2, 1982, article, 'Faith')."
http://www.freebiblestudyguides.org/bible-map/what-is-faith.htm
Enough with the shock and awe lets get to the numbers (and I know this is an insufficient data set but it's the amount of effort I'm willing to put into it). Having given these a cursory reading, 9/9 say that faith involves trust of some kind. 8/9 say/imply that it is principally trust and the ninth may imply that it can be simply trust. 6/9 say/imply that the primary object of this trust is not a proposition but a person, namely God. 5 of those 6 say/imply that propositional faith functions as a result of this personal faith, and the sixth says that at least in relation to the proposition "God is" its functions in principally important for the purpose of personal faith. only 4/9 couch it in terms of epistemic weakness and only 1/9 possibly implies that it lacks warrant. In short religious faith, as I have been saying, is not principally belief in a proposition and most importantly is not principally a belief in an unwarranted proposition.
Faith is principally trust. As such it is chiefly not an intellectual act though it will involve the intellect, but chiefly an act of the will. Trust can be put in persons, objects, or the truth of propositions. Christian faith at least is principally a trust in God as a person. The belief in any given proposition is largely a result of and/or in the service of this faith in the person. Insofar as it does pertain to the truth of a proposition faith is identical to belief. In this regard it is necessary for the holding of propositions. As you pointed out, yes we all have faith (at least though of us who haven't completely spiraled into a pit of sceptical despair). Insofar as assent is an act of the will faith is often reserved for that assent which are less certain as they require a greater act of the will and thus "more" faith. However not being certain and not being warranted are not the same thing. Still absolute certainty require faith just by a lesser act of the will. Still even if that were not the case, excluding a supernatural infallible faculty, which we will get to later, humans lack the capacity to know anything with absolute certainty, at least in this life, and thus must always act on faith. Your faith is not religious faith because it does not pertain to religious objects. The fact that Western Christians often imply that a supernatural aid is necessary to gain Christian faith is accidental to the faith itself. It is as though I were not capable of climbing stair and need to be carried by someone to get to the second floor. Being on the second floor is in no way defined by my needing to carried up the stairs. Still some times the word "faith" is used secondarily to refer to the means or aid by which we attain faith proper.
It is the use of faith in this manner which I was alluding to in number 4. Personally I'm opposed to using the word faith in manner (especially of the first kind), but I acknowledge it is often done and if The Cadet is to understand what these people are saying then he would need to understand it in this manner. Part of my initial response was to suggest that The Cadet may not be understanding those who suggest faith leads to knowledge because he does not understand what they mean by "faith" and how they understand it to lead to knowledge.
As I alluded to there are two basic ways that faith in this poor sense can be seen to function. The first is by a strengthening and guiding our our own natural capacities. This is typically seen with regard to strengthening at least as ultimately correcting the ills caused to our natural epistemic faculties caused by the Fall. Imagine two people are on some sort of survivalist television show and are expected to race through the wilderness from point A to point B, but one has been taking performance enhancing drugs and has the filmcrew constantly manipulating the situation in his favor. What the two will be doing is essentially the same, and the manner of judging between them will be essentially the same, but one will be at a distinct advantage. Likewise one person (A) whose faculties have been helped can argue with one (B) whose have not, because A is just doing normal reasoning, but unless B is capable of keeping up A will not be convincing to B. If their intuitive faculties are functioning differently then there remains no middle ground. B intuits one set of probabilities from the situation and A another. This is why your proposed conflict resolutions methods fall short. They will only resolve an issue insofar as the incorrect person is capable of and epistemically inclined towards making the same epistemic movements that the correct person has, if they lack the same capacity either qualitatively or quantitatively then they will not resolve the issue. This is true for all epistemic faculties.
When the aiding faith is understood as this strengthening and/or guiding type, faith proper is also often associated with authority as I hinted at before, where the trust is put in propositions based on ones trust the person telling you something. This is largely the meaning within the context of Hebrews 11:1. One's trust in God functions as evidence for one's belief that He will fulfill a promise. Again Hebrews 11:1 is not a definition but a relation of accidental qualities of in faith in God. And insofar as the trust in God is warranted the conclusions which follow from it are warranted.
The second way in which faith in this poor sense can function is by means of something like inspiration. It seems to me that this would have to function as a deep seated intuition that something is the case even though one could be aware that on the basis of natural epistemic activity it would not be justified. Think of it like asking someone how they know they should do x or y and they reply "I just know." When there is some sort of natural epistemic activity associated with this it typically revolves around the interpretation of signs. The a good analogy for our purposes is the faculty of sight. The purpose of the faculty of sight is to give epistemic content to the person seeing not to share it with someone else. If a seeing man and a blind man stand before a smooth two dimensional picture the seeing man can tell the blind man what it is a picture of. The blind man can choose to believe him or not. The seeing man can attempt to convince the blind man by a faculty other than sight that the blind man should believe him, but he can never transfer that sight to him. Nor does the the blind man's incapacity to see in any way diminish the seeing man's capacity. The blind man may even deny the capacity of of sight exists and may find the claim by the seeing man that the blind man is unaware of something because he cannot see unconvincing, but this doesn't change the legitimacy of the seeing man's claim nor make the seeing man unable to see. Likewise if two people capable of sight stand in the same place and one (A) sees something and another (B) does not, A might conclude from this alone that B has gone mad, that B's sight is not very good (he is mistaken about what is there), B is lying to him, or B is self-delusional. However, many people who claim this capacity also claim that it is of it's very nature an infallible faculty and one which is capable of self reference. Within the context of natural reason they claim this because it is the direct activity of God and God cannot lie to them (You may see here Chris B that I was not suggesting that God gets us out of the traps but that He makes them harder to get out of). Ignatius of Loyola seems to be of this opinion. If this is the case it is not a cop-out for A to assume the first two of the four options are no longer options. The only rational choice becomes that the person is lying to others or two himself. Your objections to the claims of person A are essentially the same. You claim that he is deluding himself essentialyl because he wants to have the faculty or because he wants the things he learns by it to be true. But person A's conclusions are not about convincing you they are about maintaining consistency within himself. Your primary objections seem to focus around the fact that the person is not giving what he sees as a lesser epistemic faculty pride of place within his epistemic framework, but why should he. Moreover because the truth of his own claims are so clear to him how could he concluded subjectively anything else other than by acknowledging the weakness of his own epistemic faculties and going to someone else with better faculties to be trained by him, in short by another form of faith. I should add self delusion and lying are regular activities within the human sphere. It may not be convincing to the person being accused to claim this about him but it is entirely legitimate internal conclusion. Especially within the context of self delusion, people do regularly engage in this (often without recognizing or at least acknowledging that it is happening), and the Christian message of sin influencing us makes this conclusion entirely consistent with the system as a whole.
This will have to be part I. I hope to answer more directly the questions of How does one know one has it, especially in the case of myself. I suppose how one resolves conflict has been largely answered but I may want to add somewhat to that. At the moment I need to get to work.
For the purposes of complying with forum rules regarding quotation:
http://www.thomasnelson.com/the-new-strong-s-expanded-dictionary-of-bible-words
http://solo.bodleian.ox.ac.uk/primo_library/libweb/action/display.do?tabs=detailsTab&ct=display&fn=search&doc=oxfaleph013721374&indx=1&recIds=oxfaleph013721374&recIdxs=0&elementId=0&renderMode=poppedOut&displayMode=full&frbrVersion=&dscnt=0&scp.scps=scope
OX)&frbg=&tab=local&dstmp=1434028329682&srt=rank&mode=Basic&&dum=true&vl(304942529UI1)=all_items&tb=t&vl(1UIStartWith0)=contains&vl(353692469UI0)=any&vl(freeText0)=International Standard Bible Encyclopedia&vid=OXVU1
