No, abstraction is the point and formal reasoning is a tool. And yes, what Euclid did is obviously abstraction, I don’t know why so you consider this stance nonsense.
Can you say how mathematics is inherently abstract in a way consistent with your day-to-day life as a concrete person? Or is your personhood also an abstraction?
I could construct a formal reasoning scheme involving rules and jugs on my table, where we can pour liquids from one to another. It would be in no way symbolic, since it could use the liquids directly to simply be what they are. Is constructing and studing such a mechanism not mathematics? Similarly with something like musical intervals.
Of course I can. I frequently use numbers which are great abstraction. I can use same number five to describe apples, bananas and everything countable.
> to describe apples, bananas and everything countable
An apple is an abstraction over the particles/waves that comprise it, as is a banana.
Euclid is no more abstract than the day to day existence of a normal person, hence to claim that it is unusually abstract is to ignore, as you did, the abstraction inherent in day to day life.
As I pointed out it's very possible to create formal reasoning systems which are not symbolic or abstract, but due to that are we to assume constructing or studying them would not be a mathematical exercise? In fact the Pythagoreans did all sorts of stuff like that.
> An apple is an abstraction over the particles/waves that comprise it, as is a banana.
No, you don’t understand what abstraction is. Apple is exactly arrangement of particles, it’s not abstraction over them.
> hence to claim that it is unusually abstract
Who talks about him being unusually abstract (and not just abstract)?
> is to ignore, as you did, the abstraction inherent in day to day life.
How am I ignoring this abstraction when I’ve provided you exactly that (numbers are abstraction inherent in day to day life).
I’m sorry but you seem to be discussing in bad faith.
> Apple is exactly arrangement of particles, it’s not abstraction over them.
No. You can do things to that apple, such as bite it, and it is still an apple, despite it now having a different set of particles. It is the abstract concept of appleness (which we define . . . somehow) applied to that arrangement of particles.
> I’m sorry but you seem to be discussing in bad faith.
