Mathematics is essentially logical reasoning about abstract objects. It has nothing to do with reality other than that we humans sometimes can abstract away from reality and create abstract objects to approximately model reality and thereby reason about reality in a systematic fashion.

I have to disagree with the phrasing: "Mathematics is not proof". Mathematics is nothing but proof. The old joke on campus was that we mathematicians were contraptions for transforming cups of coffee into theorems. Indeed, mathematics and its fundamental sub-domain of logic are the only realms of thought where anything can be truly proven. Of course, that's because at the end of the day mathematical proofs are tautological in nature as they express nothing more than logical transformations on an axiomatic basis.

However, in the real world, we have to rely upon empirical observation to supply us with our axioms, and thus we leave the realm of pure thought and can no longer truly prove much of anything as our axioms are merely abstractions and the truth of our understanding of them is always subject to the next empirical observation.

The physics equation is not an axiom, but it is not an empirically proven theory either – it is an empirically derived theory with a certain level of confidence attached to it. Gravity is not proven to exist. The next time I drop a book, it might simply float around for all we know and thereby invalidate our notion of gravity.

All of that to say that in essence I agree with this post. It is very important to distinguish between empirical evidence and pure logic. Logic and axiomatic thinking are certainly useful as is empirical observation, but a blurring of the two and failure to scrutinize one's axioms leads to nonsense like Ayn Rand's Objectivism or the absolute faith some have in Neo-Liberal Economic Theories.

But back to the point, it is ONE concept of many. Not the ONLY concept. Have you ever tried to describe a feeling, a taste or a melody with that? The most important things are not mathematicalizable, I think. That is why I am not impressed.

I am absolutely in agreement. My first point was that mathematics are not descriptive, they are explanatory. And even more specifically, they are explanatory only in a limited area. So they can transfer information about amounts but not about feelings. This is why we also utilize logic and language. And like you cannot describe a feeling with mathematics, you also cannot describe amounts with (non-mathematical) language

I think we make too much a system out of what surrounds us and it kind of bores me to death.

But this is not about being precice, it's about the fact that mathematical concepts are useful to transfer information you want about particular issues: numerical ones. That they can be used for precision is a feature, not a necessity.

Well, I still use the terms "some" and "many" and "enough". That is where I do neither need nor want precision.

You've still not avoided mathematic concepts though. You're simply betting that the other person has roughly the same number in mind about "some", "many" and "enough". You'd certainly be annoyed if you asked for "many" beers and the other guy brought you 3.

But back to the point, it is ONE concept of many. Not the ONLY concept. Have you ever tried to describe a feeling, a taste or a melody with that? The most important things are not mathematicalizable, I think. That is why I am not impressed. <span class="idc-smiley"><span style="background-position: -12px 0pt;"><span>:D</span></span></span>