Personal Axioms

WHERE DO OUR PERSONAL AXIOMS COME FROM?

Axiomatising our belief system in our own lives is somewhat like axiomatising a mathematical system from an external point of view. We can start by thinking about all the things we believe to be true, and then we can try to boil them down to some basic beliefs from which everything else follows. Anything is valid really, as long as it doesn't cause a logical contradiction, in which case your system of beliefs will collapse. Of course, this is only the case if you are trying to be a logical person. If you are not trying to be a logical person you might be perfectly happy believing a contradiction. But even two people who are logical might disagree about things just because they have different core beliefs – they are using different axioms. It doesn't necessarily mean that one of them is being illogical.

There are then two slightly separate questions: how can we work out what our personal axioms are, and where did we get those axioms from?

We can work out what our fundamental beliefs are by starting with anything we believe and asking why we believe it. The process of repeatedly asking "Why?" is a way of uncovering the deep logic behind something. It is one way of understanding what mathematics is: if we ask why aspects of the physical world work the way they do, the questions may be answered by science. If we ask why science works the way it does, the questions are answered by mathematics. If on the other hand we ask why aspects of the human world work the way they do, we are likely to end up in psychology and ultimately philosophy.

Being able to answer our own "Why?" questions about beliefs requires us to have a certain amount of logical proficiency, so that we can uncover long chains of logical implications, as well as self-awareness. On the other hand, finding out what someone else's axioms are requires us to have logical proficiency coupled with empathy. So we see that an interplay between logic and something more emotional comes in.

My personal axioms fall into three main groups:

1. Kindness: I believe in being kind to people. From this I deduce other beliefs about helping others, contributing to society, education, equality and fairness.

2. Knowledge: I believe in the frameworks that we have set up to access knowledge in various different disciplines. So I believe in scientific research and historical research, for example, within the confidence levels that those disciplines have established.

3. Existence: I believe we exist, mainly as a pragmatic approach to getting on with life. I'm not so sure about this one and I suspect that if I believed the opposite it wouldn't make much difference, so I've chosen to include it as it seems more helpful than the opposite.

The second point is important to me because it means that I will take some things on trust if I judge that the evidence makes that reasonable. This is not exactly logical overall, because I have not traced all of those conclusions back to their fully logical beginnings. But adding this second axiom means that I have traced those conclusions back to their fully logical beginnings inside my axiom system. For example, I believe in gravity although I don't understand it logically. So I don't know how to trace it back to first principles in mathematics, but I do know how to trace it back to the axioms of my personal belief system as it comes from my belief that scientists are probably right about it.

I think we have to accept some starting points in our logical system in order to get anywhere. This is true in mathematics and life. The important thing is to be clear what they are. This can help us trace more complicated beliefs and identify where someone else’s reasoning starts from different assumptions.