Concerning the post about 'two plus two equals four' being a question of belief in a system of instruction, as opposed to a logical and deductible construct ...
I have to say, ridiculous as one might be tempted to make it sound, it does hold water. A religious person might say (or almost should say, or be entitled to say) that belief in God is an equally logical proposition as the simple calculation above. After all, the same mind could behold both notions and ascribe each the same weight. And in either case, although someone with the relevant gifts might deduce the true state of affairs for themselves, in the vast majority of cases, patient and well-versed tutelage is an absolute must, if the individual is to be equipped with a firm understanding of what is meant. Most people will need instruction, if they are to become practicing mathematicians; equally most people will need guidance, if they are to lead morally dignified lives.
OK, so ... the comment above will have people thinking I'm a rabid Christian, with an agenda to push THE TRUTH AS WE WANT IT ... and I am no such man. I simply want to weaken the supposition that, because a cognition concerns ones moral role in the universe, it is in some way different - weaker, unworthy, more base - than another idea concerning practical, physical truths such as addition. To argue, in other words, for the recognition that to some minds, a religious faith will bring the world into the same pleasing order as the enlightenment of science does to others.
This is a difficult thing to suggest, because in either case, the science crowd and the faith crowd see a comparision or equation between the two as being demeaning to their own brand of understanding. Please though, have some patience with what I have to say. Each of these positions has an effectively equivalent value, in that, albeit on completely different wavelengths, they both allow ones position in the flux of existence to be calculated, and therefore both provide the framework for our explorations and adventures within (and without) the world.
All I am really saying is that they both provide the comfort of a worldview, they are both ready-built whether we want them to be or not (and whether we are prepared to challenge them or not), and that despite their both having completely different, if not actually opposing, foundations, they are both identical at least in the function of providing a framework for human existence. To this end, I propose that they are different tips of the same iceberg, and counsel fervently against dismissing the one because it fits ill with the other.
I don't think any idea is actually finished yet, whether mathematical or spiritual, and in fact my own faith is in an existence so vibrant, manifold, and divine as to be founded on whichever cosmic principle manages to expose both views and more in the one breath.
Is this mundane enough for anyone yet? ^_^ As big fat STFUs go, I am far too much the politician ...
