Two kinds of beliefs

Beliefs are the scaffolding of understanding, and they inform, at least in part, almost every decision we make. But they come in two very different kinds, and we do not always appreciate that important distinction

I suspect we have all experienced discussions in which someone appeared incapable of moving on from their initial position, regardless of the argumentation others would adduce, the holes they would point out in their view, or the contradictions they would identify. Perhaps we have, on occasion, found that we were that person. Yet, on other occasions we may have found that we actually changed our mind on something important, or that we persuaded someone to change theirs. It is as if there are two kinds of beliefs.

Axioms and theorems

In my first few weeks of secondary school, Mr Demonie, our maths teacher, introduced us to the mathematical concepts of axioms and theorems. The latter are claims that can be proved — they can be demonstrated to be true, and are therefore not a matter of debate or argument. But the former cannot be proved. An example I remember is Euclid’s parallel postulate — given a line and a point not on the line, exactly one line can be drawn through the point that is parallel…