A real question:
What are Fi values? Can you list some concrete examples of Fi values?
Now, you can't just choose your Fi-axioms willy-nilly. If they're inconsistent, you'll make yourself completely miserable. E.g., "Axiom 1: I should be able to eat anything I want whenever I want. Axiom 2: I want to be healthy and slim and sexy." I wouldn't recommend adopting either axiom, of course, I'm just demonstrating in a very obvious way how Fi-choices can be very bad without even being particularly evil.
Te has a very important role, here. Te is able to objectively determine that your axioms suck. It's no good at figuring out what they "should be," but it's great for telling Fi to go back to the drawing board and try again. It can help you see the implications of a set of values before deciding to adopt them. Ne, for xNFPs, can serve a similar role, if well-trained, for more quickly identifying potential downfalls than the slightly-too-objective Te.
Now for an example of a real Fi value of mine. There's a gazillion ways to phrase it. (Wow, "gazillion" doesn't make my spell checker barf!) One way to phrase this particular value, which I've referenced before, is that "love is more than a feeling."
[YOUTUBE="http://www.youtube.com/watch?v=Fm_-sW4Vktw"]Ne moment ... [/YOUTUBE]
More precisely, love is an ability, a choice, an act of will. It's bigger than that, though. Every feeling is as much a choice or an act of will as love: it's just easiest to see with love.
So, whenever I see a love story where two people just "fall in love" and enter into all sorts of tragedy because they let that love dictate asinine choices, it makes me cringe. It violates this core Fi value of mine. That is not to say I do not understand how they feel, or how it all happens. It is that it makes me upset to see such poor choices being made, that they could be so much happier by making ever so slightly different choices (which is where the Fi "nuances" to which Satine was referring come in). They could still completely acknowledge and fulfill their love, and well ... not fuck it up.
I should note that this is a particularly INTJ Fi value, in that it values the Te analytical side to make sure that you don't let your feelings make you do something stupid. INTJs tend to take it too far, and just not listen to feelings very much. My personal axiom, restated again, is more akin to "listen to your feelings, then come up with a plan to make your dreams come true." (It's all the same axiom, stated in lots of not-quite-complete ways.)
A somewhat contrary, but equally valid Fi-value would be "I will follow love wherever it takes me." In this case, one is not as worried about messing up, and more worried about missing opportunities. One with such a value, and holding other consistent values, would still feel bad about messing up, but always retain the hope that the next time will be better. It's a good value for gaining experience, while the "don't mess up" INTJ version is more risk-averse.
Then things can be adjusted and nuanced even more, taking a bit of both: e.g., "don't take steps that unnecessarily eliminate opportunities for love" combined with "don't take steps that will obviously result in catastrophic failure with respect to love." As things become more nuanced and precise and personalized, it becomes much more difficult to describe.
As a final example, one of my other Fi rules is, "always express warmth and kindness when it is genuinely felt, don't hide it." After having seen how other INTJs interact with me, I've felt their tentativeness as rather icily cold: I hadn't realized that's how it came across. It was like seeing myself from the outside, and I didn't like what I saw. I resolved that I wouldn't do that anymore. The only thing holding me back was my natural shyness: I didn't want to offend by being "too affectionate" or "too forward." I realized that, as an INTJ, I really needed to err in the other direction: I'm in absolutely no danger of being perceived as too affectionate or too forward.
All of these Fi-rules are very fundamental. They don't get very specific, e.g., "always take out the trash without being asked to do it." That might be a "rule" that is implied by one of the core axioms, but it would never be a core axiom/value itself. The Fi rules address fundamental attitudes toward life. It's all about who you are, what kind of person you are, what kind of choices do you make. What is it that makes you you? The rules get changed when you realize that you don't like something about yourself, and you want to change yourself. I decided to be more warm. It was an act of will. A choice. I saw that it would make me become more like I want to be.
Upon adopting the axiom and living with it and believing it, you learn whether it is right for you. it's possible to make a wrong choice. It is possible that there are implications that you did not foresee. It is possible that you cause yourself a great deal of pain. The pain, in particular, is why processing Fi requires a degree of resiliency (if not stubbornness, PB ): you need to face the pain to figure out what the heck is going wrong, because it's not obvious. You've chosen a bad axiom, but you don't know which one is wrong! They all work together, and it's slow work figuring out where the wrong choice lies.
And one last reminder: I'm using MBTI terms to express things that I've learned the hard way. I did not use MBTI to derive these conclusions, I'm just using MBTI as a common language to show others "where to look." I wouldn't use MBTI as a starting point for deriving the conclusions I make, but it's rather useful as a shorthand for conveying some very abstract ideas.