MagiOmni wrote: Thu Jun 18, 2026 8:26 pm
nyquistfrequency wrote: Thu Jun 18, 2026 3:50 pm
You have no clue as to the reason for WHY these fundamental properties you listed are valid
Yes I do? All the properties I listed are either basically definitionally true (like substitution) or derivable from their definitions (commutativity, distributivity etc.). I don't view mathematics as simply a set of rules, the point of my comment was that underlying the presumably elementary algebra were those fundamental truths, a clear why to a how. You need to clarify what exactly you mean by why vs how, or else I can't argue or agree with a point I apparently don't understand. What follows is a series of guesses at your true point and refutations of those guesses: If your point is that god is responsible for logic making sense, then sure? But if that's what you meant then your assertion that no true understanding can be reached without acknowledging gods responsibility in creating logic is false. Understanding about god is severely lacking in the modern mathematical community and yet we're continuing to see mathematical breakthroughs; you can view logic as not descending from anything else and gain an understanding of logic, the same way you can view god as not descending from anything else and gain an understanding of god. If your assertions are about why the axioms we assume are true, then again you can have an understanding of the axioms and the things that follow from them without understanding where they originate from, though most axioms are intuitively understandable. You can argue that the understanding we can achieve is limited by our understanding of the origin, sure, but when it comes to the foundations of math we already have, knowledge about them isnt inhibited by a (lack of) knowledge of god, except to the extent by which god grants humans the ability to acquire knowledge.
If our fundamental properties are true purely because we made some definitions and assume those definitions are true, then there is nothing to distinguish them from an arbitrary dogma. To say that an unfounded assumption is "true" simply because it is internally consistent is to say that ultimately nothing is true - because all dogmas would be equally true, even mutually incompatible ones. This is the inevitable result of a secular philosophy that denies God, the Absolute, who is the singular source of all that is True.
This misunderstanding of truth, logic, and mathematics is what allows certain modern academics to rightfully say "math is racist". For if mathematics and logic is nothing more than a localized game played with arbitrary, subjective axioms that human beings invented for utility or persuasion, then it is entirely a cultural artifact. And if it is a cultural artifact, then it is inherently bound to the power dynamics, biases, and historical sins of the culture that codified it. Under this definition and misunderstanding, the academics who claim "math is racist" are not making an error, because logical and mathematical proofs are no longer seen as invariant geometric properties of reality, they are now treated as an arbitrary language framework imposed by a dominant group to maintain institutional power.
Furthermore, if a person argues that truth is just a system built on arbitrary assumptions, that we can simply pick different axioms to have different truths, and that the Münchhausen Trilemma proves no absolute proof exists - they are asserting an absolute proof. Because that proof is itself yet another proposition, it must by its own rule fall into infinite regress, circularity, or arbitrariness. The claim that "all proof is relative" is completely dismantled by the fact that the claim itself would require an absolute proof to be binding. This proves out of sheer logical necessity that there are foundational truths which do indeed prove themselves. For if the Trilemma is absolutely true, then absolute truth exists, and the Trilemma is false. If the Trilemma is only "relatively" true, then it doesn’t actually prove anything - it is just another arbitrary opinion with no binding power over necessary truths.
You claim you don't understand my definition of Why and How, but the reality is that I already defined it explicitly in my original post. I fear that in explaining this again to you, I might be trying to explain color to a person blind from birth, for a simultaneous quality can never be derived from a relational process. You cannot build a timeless essence out of sequential steps, no matter how many steps you take. If you cannot see past the "How" of the mechanical process to the "Why" that guides it, then the distinction will always appear non-existent to you as you conflate the two.
Let me state it again, How is succession whereas Why is simultaneity, I can even explain this in terms of calculus. How is the result of differentiation, it is how the hand must move in succession vector by vector, to draw the curve, whereas why is when one integrates that motion to realize what is being drawn, which was why the hand was moving. In regular life this distinction manifests as the means you take towards some ends. The how is the expression and the why is the meaning it is attempting to express.
Think of written language: a single pen stroke is meaningless. Letters gain sense only when combined into words; words only when arranged in a sentence; a sentence only when it participates in the coherence of a paragraph. Ultimately, the text only means anything to the degree that it approximates the unmanifest meaning it was attempting to express, just like $1.414...$ approximates the incommensurable magnitude of $\sqrt{2}$.
If you need more examples, just read my original post, and there's one I wrote on Cantor's Diagonalization I would advise checking out as well.
When you treat math as an arbitrary rulebook, your "progress" is built on quicksand. If your foundational axioms contain a hidden error, it is only a matter of time before the consequences rear their ugly head and render your entire life's work meaningless - much like when Bertrand Russell dropped his famous paradox on Gottlob Frege, instantly shattering Frege's entire life's work on the foundations of arithmetic.
On the other hand, when an intellect approaches the timeless Why of Simultaneity, it can immediately see the shortest most elegant path to mathematical expression. But the pure formalist, who cannot see the why through the how, simultaneity through succession, is forced to drag themselves through an unnecessary tedious labyrinth of mechanical, sequential steps, completely oblivious to a much simpler proof. When one cannot see beyond the process, one might get good at predicting how the hand moves, but will never know what is being drawn - which is the entire reason why the hand was moving in the first place.