Four steps:
- Perception - based on the sense organs (subjective) and signs (objective). Pre-Knowledge (semiotic language).
- Knowledge through linguistic skills - based on perception and semiotic language (=> 1) and on linguistic language.
- Knowledge through the pure logic of language - based on perception and semiotic language (=> 1), on linguistic language (=> 2) and on pure logical language.
- Knowledge through mathematical language - based on perception and semiotic language (=> 1), on linguistic language (=> 2), on pure logical language (=> 3) and on mathematical language.
Now, we want to know what a circle philosophically means. Right?
For this we do not need “high” mathematics, because we do not know for sure whether mathematics is more right than philosophy or other disciplines. But we want to talk about it in a philosophical sense. Right?
If we know how and wherefore mathematicians use certain definitions, then this does not necessarily mean that they use it in order to get the truth. They are just searching for consistent statements (in their mathematical language).
The “higher” Occidental mathematics has much more to do with functions than with numbers. Its geometry has mainly become a functional theory too. But what does that tell you about the circle when it comes to the first three steps I mentioned above? No mathematician denies the meaning or/and definition of a circle giving in a currently valid dictionary. We already had a similar discussion in another thread: “Is 1 = 0.999…~?”. 1 and 0.999…~ are never identical, but according to the Occidental mathematics functions have become more important than numbers, because functions do work (just: function) much better than pure numbers.
And what about the physicists? Do they say that sunrise and sunset do not exist according to your perception? Do they deny that the Sun is going up and down according to an observer? Do they insist that you have to always say that sunrise and sunset are caused by the Earth rotation? No.
In other words: Does the answer to the question whether a circle is just circular (without sides) or has sides just in order to calculate in a better, the Occidental way of mathematics not also depend on perspectives?
I mean: Would you say that sunrise and sunset do not exist, namely in the world of your perception? Certainly not.
So do we at last not have the same discussion here as almost always: subjectivity versus objectivity?