What is axiomology?

Like any other word, it's a made-up thing that represents a concept that I hope to explore in future postings - the more I think about it, the more it seems a useful way to think about a number of scientific, philosophical and personal questions, principals and conundrums.

When you apply axiomological principles to many questions, then the questions and the answers both kind of get both simpler and more complex at the same time - i.e. simpler in that something that seemed to be quite opaque can become clearer through exploration and deconstruction, more complex in that something that seemed simple turns out to be a more involved phenomenon.

So what is it?  At the simplest level, it's breaking things down to their lowest level - their axioms, their atomic foundations. And then, going one step further, and breaking it down again.  By going one step further than we thought we could, we have the opportunity of finding out the components of our dearest principles - and possibly new ways of looking at them - or ways of rearranging our sub-axioms to make new foundations; new beliefs; new science.

This seems both obvious and counter-intuitive at the same time.  We're used to building our science, our beliefs, and our principles on top of firm - i.e. tried and tested - foundations. If we're really smart, we'll look at other people's tried and tested foundations, and borrow ideas from them. In this way, the world looks like a logical and familiar place. It all makes sense.

But what we forget is that all this is built upon axioms - base building blocks - that are so familiar, and so necessary to our proper mental functioning - that we don't question those building blocks, for fear that everything else that we've learned will need to be re-learned, with all the associated effort that entails.

Of course, the reality is far different.  It's still okay for people to believe that atoms are built of great big neutrons and protons, with tiny little electrons orbiting some way away from this nucleus in 'layers'.  It makes sense, and is a model that seems analagous to the planets in the solar system orbiting around the sun - it's useful.  Of course, when we start looking at the quantum model, and subatomic particle physics, the picture looks very different.  Then we're looking more at an electron 'cloud' whose positions are determined by statistical probabilities - a more complex, but ultimately more useful model for the purposes of understanding the wave nature of the subatomic world.  But again, this seems to be an incomplete answer as the macroscopic and microscopic physics of relativity vs quantum effects don't seem to tally - so we're probably dealing again with a model that is a best-fit of our understanding to date.

The best discoveries come from taking an unexplained mystery, and looking at it in a different way by stripping it back to first principles - i.e. the best axioms that we currently have - then trying to strip it back one level further, until we have some new building blocks, out if which we can build a new model, a new way of looking at the problem, and thus, a new way of modelling the solution.

In the 20th century, we became aware of how much our language plays a part in how we think, and the boundaries of what we can think - and hence why we believe, behave, and model reality the way we do.  It's why language changes so rapidly as it tries to find new ways of expressing new concepts, or new ways of looking at old concepts that, at first glance, look like the same thing, but give a whole new way of understanding the meaning behind that 'thing'.

When we look at language, the concepts that they express are the axioms for our thinking - it's why when we are looking to build.

I've said before that my view of axiomology is that it's like upside-down science. You build from the bottom instead of the top. It's just as rich an area of research, and is largely untapped. Just like we're finding that the world beneath us, in the oceans - unexplored territory that we just took for granted and called 'sea with fish in' is in fact a rich tapestry of millions of unknown species - when our view of understanding the universe was largely from looking upwards into the heavens to see how far our consciousness and understanding could reach.

Science has been competitive for some time - trying to beat the next science to the next discovery, using accepted methods that rely on prior assumptions to 'prove' a theory correct.  And often times, they will - because if one model is largely true, and you combine it with another model that is largely true, and has a predictable relationship - there are good odds that the outcome will be fairly predictable - although possibly slightly less predictable if this is indeed a generalisation of another set of generalisations.

From this point of view, Science is effectively a thin veneer on religion. Religion tries to explain the world around us, and or sensory perceptions of these, in fairly broad brush-strokes.  Science looks at the relationships and patterns in these perceptions, and tries to understand the relationships in order to bring some order and predictability into the universe. Yet - it is still based on axioms - somewhat finer brush strokes, agreed - but still basically the same way of approaching our understanding of the world around us.

What axiomology proposes is that we understand that yes, we are limited beings, and that we can only perceive a handful of relationships simultaneously, so we like our grouping to be a coarse-grained as is practically useful, and that once these seem stable, we like to move on and base our thinking and science on these principles, otherwise we get lost in the detail.  That's fine - it's a limitation that we just have to live with.  Axiomology gives a nod to this and says - okay, so let's just take some of these axioms, break them down a bit more, play about with them, and see how we can reconstruct them. Even better if the new construction still seems to give building blocks that give us a rough equivalent to what we had before - but with finer-grained distinctions. It means that chances are - more things will slot into place.

My thought is that this will be useful applied to Science in particular, but also when applied to human endeavour, and to philosophical thinking.

It's hardly revolutionary. But like many things that are obvious, but generally not done, once you give it a name - it's much easier to think about, and do.

I'm going to spend some time finding ways that this can be applied, and explore axiomology in these contexts in future posts.

Welcome to my world.  A bit confusing, more complex than it 'need be'.  But really interesting.