The Trinity Doctrine: Help me out, Christians

[RoadRunner79]

I don't think that the doctrine of the Trinity was deduced logically, but rather it is observed in scripture.

I would say there was some logical derivation (or rather an attempt at it) that happened, using premises in the Scriptures. It's just that the conclusion itself defies logic.

That God is three and God is one.  I don't understand what you are trying to logically make sense of.... I think that you may be trying to use the wrong tool.    However I think you did well in your description.

You don't see how the way I described the Trinity (which you agree is an apt description) defies logic?

If F = G, and S = G, and H = G, is it true that F = S = H?

I suspect, that your mistake, is similar to those who say that there is a contradiction within in the trinity.  This is incorrect;  the law of non-contradiction states that two contradictory statements cannot both be true at the same time, in the same way.  So  I would agree, that in one sense your equation above is correct.  This is similar to the fallacy of equivocation, in that some try to equate this to the other way, and say that they are not equal.  If they are equal and not equal, it is said that this a contradiction.  But this is wrong, because they are not talking about being 3 and being 1 in the same way. 

I hope that perhaps this clears things up.  I realize that I had to make some assumptions, as you didn't really state what you think it is that defies logic.  If you are referring to something else, then please clarify.