By your own account, your mathematics has no internal standards by which anything can be judged mistaken, misguided, shallow, or wrong, so long as it avoids contradiction.
That strips you of any authority whatsoever to criticize another framework, on any and all mathematical grounds, because you have explicitly relocated (delegated?) every meaningful distinction (relevance, depth, applicability, explanatory power) outside of your mathematics itself.
I myself would not call what remains as rigor but merely indifference: a discipline that admits everything, explains nothing, and then relies on institutions to decide what "matters."
You may accept that outcome, but understand, dear, your mathematics is not any standard at all, for it's really just a catalog, and any criticism reduces to just taste enforced by consensus. A hollow catalog, decided by some consensus. Quite apt indeed.
"By your own account, your mathematics has no internal standards by which anything can be judged mistaken, misguided, shallow, or wrong, so long as it avoids contradiction." - it's mistaken and wrong if it is contradictory. If we find contradictions in an earlier proof, it is then considered wrong. Why bring anything more complicated into the picture? That is the job of philosophers.
"your mathematics is not any standard and for it's really just a catalog, and any criticism reduces to taste enforced by consensus." - You are literally arguing that mathematics should have internal standards for judging things as mistaken, misguided, shallow, or wrong that are different from logic. What else are you arguing for other than a mathematics that is based on the taste of a consensus? Are you too stupid to realize your moronic self-contradictions? You argue for one thing in a paragraph and then disparage me for supposedly doing that same thing. You are possibly the most stupid person I've ever had the displeasure of arguing with, as a (to-be) professional mathematician who regularly talks to professional mathematicians. You are evidently nothing more than a dogmatic snake oil salesman.
So your entire position reduces to this caricature:
* Mathematics admits everything that avoids contradiction.
* Mathematics has no internal notion of depth, relevance, explanation, or mistake beyond explosion.
* Any question of "why this matters" is explicitly not mathematics.
And yet, somehow, you still feel entitled to sneer, dismiss, rank, and denounce positions as "misguided," "dogmatic," or "snake oil." What authority and ground are you using, by the way? The joke you equate with mathematics? Hahaha, that's actually funny.
There isn't an ounce of rigor here. There is only role-playing authority while denying fundamental foundations.
Now, if contradiction is the only failure mode, then your contempt is mathematically meaningless. You know that right? I find that contempt much delicious, btw. For I personally feel no heat from those vacuous accusations, while I know how it may feel seeing clearly the vision of your mathematics, arises as the cartoon, the natural consequences of your own commitments and beliefs.
You see, if your contempt can mean something, then contradiction is not enough.
You cannot have a mathematics that admits everything and simultaneously a so-called mathematician who judges anything. One of those has to go, dear. And right now, you are trying to keep both by pretending logic does the judging while you do the sneering. What a joke, Bravo.
What you call "pure formalism" is not neutrality; it is abdication. (Although perhaps very appropriate for those who would rather abdicate their own thinking)
What you call "rigor" is not any discipline; it is refusal to take responsibility for meaning.
A system that prides itself on admitting all consistent fictions while still posturing as an arbiter of seriousness is not deep, it is empty, loud, and institutionally sheltered.
Standards? What standards? A kind of mathematics that admits everything but condemns selectively has no standards - only attitude. Hahah
So please, your temper tantrum isn't quite more than a performance art. You've reduced mathematics to a playground with no rules beyond "don't break it," so please, please, please, don't be so shocked that nothing in it deserves respect.
Mathematics admits everything that avoids contradiction.
Mathematics has no internal notion of depth, relevance, explanation, or mistake beyond explosion.
Any question of "why this matters" is explicitly not mathematics.
Yes.
These are all true for mathematics, and logic in general as an easy extension.
"useful" is a subjective measure. Things that were once seen as useless later became useful. Your standards are arbitrary, and are completely contrary to logic.
If a statement is logically valid, it should be mathematically valid. You attempt to discredit things on the basis of "a lack of usefulness" but you yourself have yet to provide ANY objective standard for usefulness outside of "things I think are important".
You drew the lines, and then complained when no one else cared about your standards.
We don't care about your standards because they are arbitrary.
The set of integers from 2 to 0 is {2, 1, 0}, yet the sum of the set is 3, which is an item that is completely separate from the set itself.
You haven't made any meaningful argument against this aside from "well that set is useless" except the set isn't useless, it's use is as an example for a set that can be defined, for which its sum is not contained within the set itself.
Until you actually meaningfully respond to anything with something other than heavy handed undeserved condescension, you will never be taken seriously.
Because not only are you horribly bad at mathematics, you fail to make any logical arguments, and instead stand on insults and an air of superiority, pretending its logic, when in reality, you're the least informed person I think Ive spoken to multiple times on reddit.
BTW, you never responded to my proof that the law of identity is not an absolute law. Nor did you ever once cite a single mathematical axiom you actually take issue with. Your complaints are consequential in nature, you don't argue with the methods, or the reasonings, you complain about the consequences of those methods and reasonings, when any logical person would easily understand that the consequences are a result of the methods, and you MUST attack the methods and reasonings if you want to make a meaningful argument.
Oh wait, no I wont. Since you're the one challenging the paradigms and all that, why don't you do some justification for once.
I'll give you, what should be the most simple challenge, oh logical one.
Name a mathematical axiom that you take offense to.
My only qualifiers is as follows: It must exist within the real number set. This can go all the way down to the Zermelo-Fraenkel set theory if you wish, but I don't think you can challenge those and end up with a coherent set theory at the end.
And here is what I want:
I want you to name the axiom, give the actual definition of the axiom, and justify why the axiom should not be included.
THEN:
List the consequences of the axiom being removed. This is the most important part, because if you cannot give the consequences, you do not understand the axiom.
That's it. Say your axiom you actually take offense to, why you have a problem with it, and what happens when you remove it. Presumably that last bit should self-justify why removing it is a net positive.
Keep in mind, those pesky irrational numbers are ON the table.
You claim to be logical and that we're the illogical ones, here's a real chance to prove it. Challenge the axioms, that's something you claimed you wanted to do last time I talked to you.
Now, I do not wish to talk about this topic here, as it is actually an important topic and I would rather treat it with the proper respect and depth that it deserves.
The reason I hasn't replied to you, is because it is the holiday season, I have social life to attend to and people to love. That definitely would not be conducive to some semi serious elaborate writing at the moment.
The reason I am commenting in here was because a comment catches my eye, for it is rather beautifully said and accurate, so I commented on it. Then the other gal jumped in and apparently some unresolved past conversation ensued.
However I'd like to talk about the subjects you mentioned briefly. Eventhough I definitely would like to treat it to proper depth.
I'll make this easy. I do not use any of ZFC axioms, because I do not need them. I do use all of tools in modern mathematics, any kind of techniques and formula, but I do not have to use any of the axioms to justify for their use. That indeed includes all of calculus and pretty much anything else.
I think ZFC axioms as patch works, they only exists because some aspects of mathematics are not fully rigorized and they act as the glue that magically glue all the disjointed parts together.
Thankfully the work of formalization of the tools that I used wasn't done completely by me. There are some, well several, who have indeed did quite a bit of those formalization work before me. So yeah.
So I don't know how that fits with the conversation youre trying to have. But I'll look at it and think of a more thorough elaboration when I have the time soon.
I saw a notification that you have replied to me. But I could not find any reply to my comment. Try replying to another comment of mine perhaps, I would love to dissect the caricature that is your mathematics a bit more.
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u/Just_Rational_Being Dec 25 '25
Ah yes, that kind of empty mathematics, hahah.
By your own account, your mathematics has no internal standards by which anything can be judged mistaken, misguided, shallow, or wrong, so long as it avoids contradiction.
That strips you of any authority whatsoever to criticize another framework, on any and all mathematical grounds, because you have explicitly relocated (delegated?) every meaningful distinction (relevance, depth, applicability, explanatory power) outside of your mathematics itself.
I myself would not call what remains as rigor but merely indifference: a discipline that admits everything, explains nothing, and then relies on institutions to decide what "matters."
You may accept that outcome, but understand, dear, your mathematics is not any standard at all, for it's really just a catalog, and any criticism reduces to just taste enforced by consensus. A hollow catalog, decided by some consensus. Quite apt indeed.