Comment by bubblyworld

Yeah, not suggesting philosophers are the only people using logics, but they've certainly been using them the longest!

Indeed, I've seen various attempts to tackle the problem including what you are suggesting - expressing the semantics of different logics in some base formalism like FOL in such a way that they can interplay with each other. In my experience the issue is that it's not always clear how two "sublogics" should interact, and in most cases people just pick some reasonable choice of semantics depending on the situation you are trying to model. So you end up with the same issue of having to construct a new logic for every novel situation you encounter, if that makes sense?

Logics for computing are a good example - generally you use them to formalise and prove properties of a program or spec, so they are heavily geared towards expressing stuff like liveness, consistency invariants and termination properties.

I haven't read about CTL though, thanks! I'll check it out. Hopefully I didn't write too much nonsense here =)

> Just like mathematicians don't worry much about switching back and forth from geometry/algebra [...]

As an ex-mathematician I think we worry a lot about transitioning between viewpoints like that. Some of the most interesting modern work on foundations is about finding the right language for unifying them - have a look at Schulze's work on condensed mathematics, for example, or basically all of Grothendieck's algebraic geometry work. It's super deep stuff.

> then you may be stuck with some irreconcilable continuous-vs-discrete or deterministic-vs-probabilistic disconnect

Agreed, I think this is one of the cruxes, and lately I'm starting to feel that maybe strict formal systems aren't the way to go for general-purpose modelling. Perhaps we need to take some inspiration from nature - completely non-deterministic, very messy, and nevertheless capable of reasoning about the universe around it!