In this context, most of computer science is more a form of applied mathematics.
Of course there are different ways to look at science, like making a distinction between analytical (or empirical) science, and synthetic science; the science that makes stuff, rather than analysing it. Not sure if that's really a good distinction; the latter is really technology, isn't it?
There is such a thing as computer science, but the majority of what gets called that is really engineering, not science. People often get those two things confused because they have a fair bit of overlap in the Venn diagram, but they are two different things.
Math is itself indeed not science. It is the language of science. It follows different rules than empirical sciences. But note that word "empirical" there; Popper was really only talking about empirical science, and according to him, that was the only real science. You could argue that there are non-empirical sciences.
Another problem with Popper is probably that outside of physics and chemistry, there are a lot of less exact sciences where predictions and refutations of a theory are never that clear cut. Like his issues with the theory of evolution.
Ultimately, I guess science is also simply "getting to stuff that works by trial and error".
How much engineering could we do without Mathematics? How much commerce?
I don't see it as exclusionary. You won't find many scientists in doubt about the fact that everything they do is built upon Logic and Mathematics, in addition to observation.
But don't we need a word to group fields that try to systematically describe, understand, and make predictions about the physical world? (Rather than seeking to explore and characterise idealised logical constructs?). What would you suggest?
You may not see it as exclusionary but many people do. Just look at the comments!
It's precisely the grouping I am talking about.
If you group science in such a way so that logic/mathematics/computer science falls outside the group then isn't that an erroneous grouping?
Isn't that a silly definition?
True and False are idealized logical constructs. It's the idea; and the idealization of the notion that there is a difference between Truth and Falsehood. Or if you want to get biblical - there is a difference between Right and Wrong.
Of course there are different ways to look at science, like making a distinction between analytical (or empirical) science, and synthetic science; the science that makes stuff, rather than analysing it. Not sure if that's really a good distinction; the latter is really technology, isn't it?