[merijnv]

> Also, "Sound philosophy demanded that these mathematical concepts be tested by evidence, logic and rigor from some very basic premises that were built up to more complex and powerful structures of thought which were proved to be true. " So how did one prove these structures of thought to be true?

There is some excellent essays answering the points you raise here in some of the Less Wrong sequences. Rather then butcher them here I will just point you to the "Map and Territory" sequence going into the subject "What is truth?", "Can we determine truth?", etc. the essays are here: http://wiki.lesswrong.com/wiki/Map_and_Territory_(sequence)