This is a horrible question insofar as it demands the respondant to put words to feelings/concepts which exist better aside from the restrictive qualities of language. In any case, I'm going to try to answer this question as best I can!
[H]ow do you come to conclusions, what is the process behind your ability to make these conclusions valid in your mind[?]
The inherent problem posed by this question is explored by Søren Kierkegaard in
Fear & Loathing. His response is that faith is ultimately the concept used as justification for belief (in his work he is talking about religious faith, but I think the broader definition of faither applies to most other subjects).
I think people with a T preference would tend to reject F conclusions because they seem irrational and are based on "hunches". I would say that this is true only inasmuch as this forms the first step in the decision-making process. How I feel about something is a strong indicator to me about how I should think about it, since I "think with my feelings", so to speak. However, it would be wrong to say that (in my case) a hunch was the formation of an entire system of belief. Rather, it would be more accurate to say that a dialectical process is involved, particuarly a sort of
Hegelian Dialectic.
For example, the dialectic may occur like this:
1. I think
Progressive taxation is a good idea because it means the most disadvantaged in society are given a greater chance of experiencing that which is available to the most priviledged.
2. However, some people have worked hard for their money, and feel resentful about giving to those who may just be feckless, lazy, or ungrateful. The pursuit of a good salary would entail a raise in living standards for the person who seeks it.
C. Although there are those who would certainly abuse the system, the tax money received and redistributed would offer opportunities to those who wouldn't have them under another system. Therefore, I feel the premise is justified, but a true synthesis of the problem would entail that the rich not be penalised unfairly simply for having money - it may be the case that they were born rich, and the poor were born poor and there is nothing inherently "wrong" about either circumstance.
This makes things "valid" to me because I feel like I have considered things from all angles and weeded out those arguments which I feel are important/unimportant. Many decisions in life (inc. politics, which I used merely as an exampe) are propounded as being logical but are in fact more "feeling-based" than first imagined.
How do you know your intuition and emotional deductions are matching your systematic conclusions you have about the world around you?
The short answer would be that I feel that they match.
Logic and intuition are not necessarily complete opposites, hence the prevalence of terms such as "emotional intelligence" - there is a grey area which exists between the two notions. However, I am able to perceive when something that I feel to be right might be too hardline, or would not fit in with the "systematic conclusions", as you have termed them, I have drawn about, say, the society in which we live. I mean, ultimately I think humans would prefer in to exist in an anarchist state (do what you want when you feel like it) but that wouldn't work for us now so is not worthwhile pursuing as a line of intellectual consideration or personal belief (well, not in my opinion...). The population is simply too great for that to work and, besides, we have already created so many socio-political structures that it would be counter-productive simply to destroy them all. Therefore, I look to my feelings/beliefs again and analyse how they relate to the situation at this moment. This is what generates many of the hours in which I need to be alone in order to contemplate. It is a massive frustration because, as I see it, the world operates in a self-denigrating manner; I feel as though the beliefs I have regarding many abstract concepts would be of betterment to the world if they were implemented, but I know they won't be. There is, therefore, a constant recalibration between myself and the external world which explains a lot about my character, and probably about the characters of a lot of other INFPs.
I hope I've answered your questions at least somewhat. They were difficult to contemplated because they were so vague, but I get the feeling that you intended them to be that way!