Belief systems versus rationality
Page last updated 28 Oct 2022
Many years ago in my youth I became captivated by born again christianity. I was enticed by the members of a group who struck me as charmingly friendly, charismatic and joyful. They seemed to have something special and I wanted to feel on the inside what they seemed to have as seen from the outside. But as I became more deeply immersed, I began to read the textbook that they said was the rock that their system of beliefs was based on - the bible. It didn’t take long for that reading to start to reveal contradictions within it, contradictions that gnawed at the roots of the beliefs that I had been told were the foundation stones of the house of the one and only existing god - a god whose overriding goal was the happiness of both the human race as a whole, but also of each and every individual human being.
And so, after a time I had to admit to myself that the inherent contradictions showed that the bible could not possibly be an authoritative basis for the beliefs of my group. It became apparent that they simply latched onto the parts of it that they wanted to agree with while at the same time managing to ignore those parts that did not. I came to see that they preferred to live a life based on a lie than a life based on reason. What had been vague shadows became transformed into the realization that they preferred to choose a life that was based on a set of ideas that made them feel comfortable, that made them feel part of a community with the same ideas, with the same beliefs. That they were able to hold beliefs with such conviction that they would refuse to contemplate in any depth any challenge to those beliefs. That they had chosen that over a life based on a continual search after truth. That they preferred the dogma that the truth had been unearthed, eternal, perfect, untarnished, instead of an acknowledgment that one can only ever continue to dig for truth, that one can only ever make a rational evaluation of the evidence that one is able to obtain, and that one must always be prepared to re-evaluate.
I do not deny that the edifice of faith that they inhabited imbued them with what one might call happiness. But such an edifice that imparts such unquestioning happiness on one set of people can, and often does, result in the trampling on the happiness of others. I see the long history of religious conflicts and despair.
Years later I encounter the same problem in a very different guise. I find a community that presents itself to the casual observer as being open to new ideas. However, if you probe a little bit below the surface, you will find that it is only open to new ideas provided that they do not question the underlying ethos. You then see that it operates in exactly the same way as christianity; there are deep-rooted contradictions in their system of beliefs, but they choose to ignore these contradictions, and refuse to even allow discussions about the possibility of such contradictions within their community. In exactly the same way as christians, they hold steadfast to their conviction that they have already found the truth, preferring to uphold a lie than to countenance any deep exploration of the basis of their beliefs.
This community started over a hundred years ago as a small group of mathematicians extolling new foundational ideas, but for some strange reason these foundational ideas have now become almost completely unchallenged as the “correct” foundations for all of mathematics. Now, when a logical flaw in these theories is pointed out, the fundamentalists believe that they can counter it by simply quoting one or more statements from the theories they espouse - in precisely the same way that a bible-thumper will quote a verse from his bible. It does not seem to occur to them that simply relying on authority rather than logic is completely contrary to the basic ethos of mathematics. For more on this see the appendix below.
I would note that it has to be said that many mathematicians continue do their work without any need to reference these foundational ideas, and they seem to prefer to keep their heads below the parapet instead of questioning things. Unfortunately, in so doing, they allow the fundamentalists, as in many religions, to proclaim the substance of the apparent beliefs of the community, and force the direction of that community. The details of these contradictions in these foundational ideas are explored on other pages on this site.
Perhaps I have been over optimistic about the capacity and desire of humans, both collectively and individually, to tread a path towards greater rationality, where both thoughts and actions become ever more based on reason rather than ignorance. Today, looking at the prevalence of absurd beliefs in things such as a 6000 year old earth, a complete worldwide flood, the denial that human activities are irrevocably crushing the possibilities that we leave to our children, and so many other examples, I am forced to the conclusion that I have been naive.
Ultimately, it doesn’t matter; whatever happens, it seems likely that the earth will continue to support life of some sort for many more years, and then, like all things, it must cease to be as it is. The existence of change seems to be the one thing that we can rely on to never cease to exist. It would have been nice to think that one was part of some sort of progression, a progression that humans might almost universally agree to be something desirable, something that one might even say was noble and uplifting. But perhaps all human aspirations are destined to be no more than the dust that time scatters as it marches resolutely onward.
Is there any difference in principle between a bible literalist proclaiming the truth of the bible and a committed set theorist proclaiming that the only “true” foundation for mathematics is Zermelo-Fraenkel set theory (with or without the axiom of choice)? Both are dogmatic and impervious to any logical criticism.
Some people attempt to counter criticism of set theory on the basis that there is currently no alternative mathematical “theory of everything”, but that completely misses the point. Physicists would like to have a theory of everything, but perhaps they are sensible enough that if someone claimed to have devised a theory of everything for physics, they wouldn’t all collectively proclaim, that’s it, done and dusted, that’s our theory of everything which will remain the theory of everything for all time. No, if a physicist suggested a theory of everything for physics, no-one would be surprised that it would be subjected to the most intense scrutiny, and that such scrutiny would continue over time. And even if it was accepted, but was later discovered to have serious flaws, no-one would be surprised if was no longer accepted - even if there was no alternative theory of everything to take its place.
But set theorists have continued over many years to promote set theory as the only possible correct “theory of everything” for mathematics. When the first set theories, such as Cantor’s and Frege’s set theories, were found to be deficient (as shown by Russell’s paradox) set theorists were so convinced that their “theory of everything” contained the essence of the basis of all mathematics that they devised a collection of axioms that had no empirical basis, but where their only purpose was to patch up the holes in their then current “theory of everything”.
It appears that no set theorist ever stops to consider the possibility that there may not be a single simple set of statements that can encompass all of what humans call mathematics - or that, even if some such might be possible, that we humans may not have the ability at this moment in time to invent them.
For more, see the pages that give an overview of set theory, starting at Overview of set theory: Part 1: Different types of set theories.