More and Less Fundamental Beliefs

MORE AND LESS FUNDAMENTAL BELIEFS

One way to axiomatise a system of beliefs is to take every single belief as an axiom. This certainly means all your beliefs can be derived from the axioms using logic, but it has not achieved anything. It would be a bit like a recipe for lasagne where the only ingredient is “lasagne”. Rather, the point of axiomatisation is to understand the roots of a system and what holds it together.

Taking all beliefs as axioms would obliterate the need to follow any sort of logical deduction, and although it’s not exactly illogical (it doesn’t contradict logic) it’s hardly a well-developed point of view. It would be a rather extreme situation, but we do meet people who are unable to justify certain beliefs of theirs very much at all – they take quite complex beliefs as fundamental, without justification. Or in some cases there is some justification but it doesn’t get us very far. For example, a person might say, “I oppose same-sex marriage because I believe marriage should be between a man and a woman”. This might sound like a justification as it does have the word “because” in it, but it’s really just a restatement of the initial belief.

Our fundamental beliefs are rooted in something beyond logic. However, sometimes abstraction can help us find something more fundamental inside what we believe. As I discussed in Chapter 2, I have discovered that my belief in taxation and social services is rooted in a more fundamental belief that false negatives are worse than false positives. We will come back to this in Chapter 13.

As a related issue, I believe that everyone’s situation is a combination of their own input and their circumstances. I believe that humans are not isolated creatures, and that we exist inextricably connected to the communities around us, and thus there is some collective responsibility for both success and misfortune. This in turn comes down to my more fundamental belief that we should understand all things in terms of systems rather than individuals, as in Chapter 5, whether this is people, factors causing a situation, or mathematical objects – the latter being why I do mathematical research in category theory, a discipline that focuses on relationships between things, and the systems those form.

Having said that, I do believe that everyone should take responsibility for themselves, while at the same time believing that we should all look after each other. Where exactly personal responsibility ends and collective responsibility kicks in, I am not quite sure. This does however lead me to another more fundamental belief: that there are many grey areas in life and that it’s important we understand them for what they are rather than ignore them or force them to be black and white. This might mean that we can’t be entirely logical where grey areas are concerned. In the next chapter we’re going to look at the different ways that logic has of dealing with grey areas, and see that some of them are rather undesirable, pushing us to extremes in ways that don’t feel right. We will see that as we move through a grey area things may start out seeming “the same” and then gradually morph into something that seems different, although somehow the framework was the same. In Chapter 13 we will take this further and analyse how analogies work, and how we use them to pivot between things that aren’t the same, by means of some way in which they are the same. A big issue with analogies is deciding when they count as a good analogy or when they have been pushed too far. In Chapter 14 we will talk about when things should count as the same or not. False equivalence is a widespread logical fallacy, but in between true logical equivalence and false equivalence is a grey area of things that are the same in some sense, we just have to find it. In Chapter 15 we’ll look at how we can use all these techniques to engage our and other people’s emotions, to try and better see eye to eye with other humans, and finally in the last chapter we’ll paint a portrait of a good rational human – not a perfect computer – and what good rational arguments should look like.