However, my primary focus is on the objects themselves, such as the Cartesian coordinate system. I believe this system needs a parts-from-whole, continuum-based reinterpretation, as the current understanding relies heavily on the notion of actual infinity. — keystone
Sounds interesting. Life in the complex plane. By the way have you seen much of the modern graphing software that's so good at representing complex functions and Riemann surfaces and the like? Don't you wish you'd had that back in the day? I wish they'd had LaTeX, I always had bad writing. — fishfry
Reminds me of Tim Gowers's distinction between problem solvers and theory builders. — fishfry
Thus the make up isn't at all close to the natural 50/50 divide, hence mathematics is male dominated. — ssu
wouldn't this mean then that mathematics is different from being just a social construct of our time? — ssu
Yet today, set theory is a basic part of the undergraduate math major curriculum — fishfry
Math is very much a social process. — fishfry
Isomorphisms have everything to do with structuralism. An isomorphism says that two things are the same that are manifestly not the same. That's structuralism — fishfry
So, I am really really interested in whether or not mathematical objects exist in a mind-independent way. Would there be numbers even if we weren't here? I want to say yes. I think that numbers would be here — Pneumenon
a societal phenomenon and a power play that a group of people (read men) do — ssu
More like that the truths in mathematics are tautologies: a statement that is true by necessity or by virtue of its logical form. Wouldn't that description fit to mathematics? — ssu
when it's just what mathematicians declare doing. — ssu
perhaps the old idea of math being a tautology comes to mind — ssu
The only reason you don't want math to fully apply to reality is because you suspect a problem with infinite divisibility, right? — Gregory
Perhaps a very stupid question: why isn't Math referred simply to being a system? — ssu
Why is it that the intro to calculus/analysis textbooks I’ve read never mention topology? — keystone
How is that any less of a leap than starting with curves, which are inherently continuous? — keystone
It works fine for me — Art48
My emotional involvement is because the Bible tells enormous lies about God — Art48
The validity of Christianity was once a philosophical topic. Are you saying it's been excluded from modern philosophy? — Art48
Continuous object: In 1D, the proposed fundamental objects are of two types: (1) open-ended curves, which are inherently continuous — keystone
And it is these ignorant people, the most uneducated, the most unimaginative, the most unthinking among us, who would make themselves the guides and leaders of us all; who would force their feeble and childish beliefs on us; who would invade our schools and libraries and homes. I personally resent it bitterly. — Art48
A continuum is a decomposition of a hyperspace module with sidewise-partitionable step-wise radii — TonesInDeepFreeze
"The standards society adopted" are largely unexamined. It is a card house of assumptions and I'm challenging a specific one — Benkei
Therefore, affirmative action or equal opportunity initiatives would be justified to help these individuals reach their potential — Benkei
This could mean adopting hiring practices that prioritize diversity, ensuring that supply chains are free from discrimination, and promoting workplace cultures that are inclusive and supportive of all employees. — Benkei
The entire point of q2<2 is to define that set without reference to irrationals. — fishfry
I did convince myself that if you take the rationals by themselves, you can define a topology by all the "open" intervals (p,q) with p and q rationa — fishfry
What is your point? What do you think? — I like sushi
Different issue I think — Benkei
I find the issue becomes more or less about what an individual can do and what others believe they should do — I like sushi
Assuming this statement is true, what do you think is its philosophical significance? — 180 Proof
Isn't the subconscious process deterministic? Doubts are not allowed in a deterministic system. — MoK
The subconscious process cannot resolve the conflict when we have doubt in a situation. That is true since the options are real when we have doubts and we don't have any reason to choose one option over another option — MoK
If I recall correctly, another poster mentioned point-free geometry. — keystone
Only a special infinity can subsume the whole of math — Gregory
As a complex analysis guy you use the hypothetical point at infinity of the Riemann sphere all the time, don't you? — fishfry
Well, the Zeno paradox certainly threatens mathematics, especially the continuum concept. — MoK
Anyway, the idea of someone, who doesn't understand that the set of natural numbers is not a member of itself, trying to grapple with how ultrafilters play into proving the existence of hyperreals is ridiculous — TonesInDeepFreeze