I should have clarified that one such idea is that of intellectual intuition, which is in that translation simply called "intuition". This intuiotion is conscious, supra-rational, supra-human and has nothing to do with the kind of "intuition" you seem to have in mind, by which is meant, it seems, nothing more than superficial assumptions.
Fair enough. Could you explain exactly how this form of intuition works and why it is always true? I think I may already understand, but I don't want to jump to any conclusions.
edit: Never mind, I understand your position now. Instead I'd like to ask how do you define god and how you do know god exists?
I am interested to know how radical your empiricism is. What do you make of mathematical and logical truth? Presumably there is an important sense in which mathematical and logical truths are not grasped empirically. Then again, you keep talking about the existence of things which would suggest that your position is that you cannot justifiably believe in the existence of any entity except through empirical means. That is something I would agree with.
My empiricism is radical TO THE MAX!
Mathematics deals primarily with abstract concepts. In proving mathematical truths, a set of axioms is established, then through the use of defined concepts, postulates, and deductive reasoning necessary conclusions and new concepts are reached. These abstract concepts are just tools we use. They only really mean things to us when we apply them to reality. At that point, they can be judged empirically. It just so happens that there has never been a mathematical concept which can't be applied to a real world concept. In other words, math has an excellent (perhaps unsurpassed) track record. Therefore, it is a highly reliable tool.
Logic is a form of reasoning. In theory, it typically deals with abstract notions (much like math). It is also merely a tool. Again, however, it only really means things to us when we apply it to reality. Logic can be a tricky subject, however, because different people accept/reject it to various degrees.
To summarize, math and logic are conceptual tools. Only when they are applied to reality do they yield actual truths. 1 + 1 = 2 is mathematical true, but what does it mean. 1 is not a thing; it doesn't exist. 1 Apple + 1 Apple = 2 Apples is something that is true within reality and verifiable. I hope this clears things up.