By LENNOX FARRELL
Is there anything in this life that you can really take for granted that is not also taken on faith? And how many of these things taken for granted are, like faith, substantive without having substance? Are fundamental, yet assumed? Take, for example, Math and its derivative, Science. Is there anything which we value more as absolutes to be fundamental and unshakeable? Yet, are their axioms at best, assumptions?
I wish that articles as this could provide more answers than questions. However, I am persuaded that a more productive life is one challenged by questions we have, and not seduced by answers given by others. In the former, life is lean and muscular; in the latter it is mentally obese. In short, a really good answer should lead to an even better question…emphasis on the letters “q.u.e.s.t.” in “question”.
The musings here, and in a subsequent article, were sparked by Cliff Goldstein, a philosopher and writer I recently saw on the website: http://cliff.hopetv.org/video?id=2045996557001. He raised a series of intriguing questions under the rubric of “Math Problems”. The title contains a pun. As students, we had “to solve math problems” often. A more positive phrase like “Math challenges” might be better than the negative, “Math problems”. But again, this is not the issue in this article, but addressed later.
The issue here is that since no other subject or idea had by society is as solid, unshakeable and constant as “Math”, what happens if as fundamental as Math is for logic and rationality, its major tenets can be questioned? Can the rationality of Math and its axioms be questioned? And with what effects? In fact, even more fundamental is the possibility that our very understanding of axioms is itself also premised on, and accepted in, faith; that faith is itself an axiom. Where will this end? Where does it begin?
Defining an “axiom” is a good place to begin. But even defining such fundamentals as “axioms” becomes even more thorny. For example, according to the Oxford dictionary, an axiom is all of the following: a self-evident truth…that requires no proof; a universally accepted principle or rule; a proposition that is assumed without proof etc.
Wait a Jane-Finch minute! Accepted without proof? In accepting the possibilities of uncertainties in axioms, are we also being encouraged to believe in things for which we have no proof? Didn’t the great Stevie Wonder say, “when you believe in things you don’t understand, then you suffer?” Is this sense of uncertainty, and which is to be avoided, not associated with such things as religious beliefs?
Is it a stretch of credulity to associate some of the uncertainties had with beliefs, with the certainties of knowledge? To revisit the definitions, an axiom is a self-evident truth…so far, so good; but an assumption which does not require proof? A proposition that is assumed without proof?
Can you imagine a lawyer making a case before a judge saying, “Your Honour, my argument is premised on truths which are so universally assumed to be self-evident, they do not require any proof?” You’d be right to exclaim, “Utter madness!” Or is it “utter mathness”?
To add to the quandary, some synonyms associated with the word “axiom” add to the uncertainties; words like maxim, premise, assumption, etc. An axiom is an assumption. Is not the very idea of what “faith” is, also based on assumptions? In fact, one well cited definition of faith assumes that “it is…the evidence of things not seen”. In other words, faith is an assumption, based on some intuitive substance, and deductive evidence?
Between Niagara Falls and St. Catharine’s, there is a bridge built tall enough to allow sea-going ships, or “salties”, to sail to and fro from the Atlantic Ocean, up the St. Lawrence River and into the Great Lakes. This bridge sways in the wind, but families regularly travel over it…in faith that its engineers knew their craft. The bridge is supported on a series of concrete and metal stanchions. What does this bridge and its stanchions have to do with something as non-concrete as faith?
The Greek word for “faith” is “hupostasis”; note the letters, “stasis” or stability. The same Greek word for these stanchions is also “hupostasis”. In fact, whenever you are in a building, the roof overhead, upheld by supporting pillars, are supported by hupostasis, or stanchions. Since the same word in Greek is used for the English word, faith, is “faith” as solid as the stanchions which support bridges over which we pass, or the roofs over our heads in museums, churches, and subway stations?
Or take another example of how substantive is intangible faith. Suppose we stood on the shore of Lake Ontario on different days and times. On one day, the water is calm; the wavelets, placid. On another day, the same water is choppy and the waves boisterous. What is happening on one day, and what on the other to make what we see so different: on one day, water is calm, and on the other, choppy?
Of course, you will conclude that the wind has changed. On one day blowing softly and the water calm; on another day, the same wind, now stronger, causing the water to be choppy. We assume with great faith that it is the wind which is causing these changes. O. K. But who has ever seen the wind? Is not the idea of wind, unseen, to be taken then on the basis of faith? Taken as substantive as hupostasis?
While we do not see “wind”, we see can see the evidence of its presence in the condition of water, and in the swaying of trees. So, here is a reality – wind – that we cannot see, but which we “know” is there because of the evidence seen in the changes in the water; evidence based on something not seen: the wind.
In conclusion, is the practice then of faith, the basis of everything we daily take for granted? Synonymous with ideas like trust and confidence, is faith in ourselves, in each other etc., and in things like love, loyalty, justice, not the only thing we daily take for granted? For while we have never seen love, nor loyalty, nor justice except in their desirable evidences, yet is not our faith in concepts as these, the most substantive, rational, ever-present, cherished, and hupostasis aspect of our lives?
To be continued: Irrational Maths and Rational Faith?