What is ‘evidence’?

As a mathematician, I tend to worry about mathematical theories and how they are applied, particularly how they are misunderstood and misapplied. Hence my blog has mostly about uncertainty and how it can be understood (or misunderstood) by reference to relevant mathematical theories, and in particular why some regard ‘mathematical probability’ as the go-to theory, even when faced with – to take some topical examples – climate change, discrimination (such as ‘institutional racism’) and pandemics, when the theory is clearly not so useful, and has such potential to be misapplied.

But trying to make sense of the UK approach to pandemics, and its claim to be ‘following the science’ I now adjust my question:

What do those with power and influence think ‘evidence’ is?

There is a lot of ‘text’ available, much of it seems to me to assume some sort of implicit underlying theory of uncertainty, such as probability, without addressing the appropriateness of any such theory or even giving much hint of what such a theory might be or how to think about it logically or mathematically. If anyone can suggest something on this topic that I might begin to make sense of (other than as a dogma) and so usefully critique, I’d appreciate it. A related question is:

What kind of logic is appropriate to thinking about ‘evidence’, and how would one judge its appropriateness?

Dave Marsay