Tuesday, August 02, 2011
Mathematical Model Theory III
I forgot to explain the significance of the miniature ladder at the tombstone of Wittgenstein. Wittgenstein said (paraphrasing) that "we construct a ladder of ad hoc reasoning to bootstrap ourselves to some higher plane of understanding and once we reach that plateau then we kick away the ladder." This is totally in my own words but it is how I can better understand what he wrote though I may well be mistaken in my understanding. Buddhism teaches that there is an ocean of perplexity which plagues us, the ocean of 100001 things, and we call that ocean Samsara. We must construct a canoe or kayak with whatever is available until we have a VEHICLE to cross the ocean of Samsara and reach the other shore which is called Nirvana (derived from the Pali term which means to "snuff out or extinguish" like a candle.) Buddhism cautions that our little canoe must be discarded once we reach our destination and we should not walk about with our canoe upon our head since the vehicle is only a means to an end and not an end in itself. I am reminded of Odysseus who was ordered to take an oar upon his shoulder until he reaches a land so distant from the sea that everyone he meet asks him what that strange device is that he carries about.Back to Wittgenstein: Bertrand Russell spent much time with young Wittgenstein and admitted once that he felt dwarfed by Wittgenstein's brilliance. Bertrand Russell and Alfred North Whitehead attempted to place all of mathematics on a foundation of logical proof but they failed. Possibly the task is impossible because of things like Godel's Indefiniteness proof and Wittgenstein's Tractatus. Here are two example which I recently encountered.Suppose I ask you "What is THE MOST important question in the world?" You will answer something and I will reply that the very question I asked much be the most important question in the world since IT WILL LEAD you to the most important question. BUT, if my question is the most important then the question it leads you to must be only second most important at best. Different example from one Roman Catholic Jesuit -Consider the statement "There is no absolute objective truth; all truth is relative and subjective!"If that statement is true then it must itself be false because the statement purports to be a statement of absolute truth. BUT if that statement is false THEN there must be an absolute objective truth.
