Anonymous at Sat, 22 Mar 2025 12:05:34 UTC No. 16625745

>>16625697
Axioms definitionally can't be proven.

Anonymous at Sat, 22 Mar 2025 15:10:37 UTC No. 16625848

>>16625697
>we have already proven that it works well enough for it to be extremely useful
Been just empirically proven isn't good enough for some. Many a mathfag seeks to ascend from /sci/ into /x/ territory. Some seeks absolute certainty without the possibility of been invalidated by possible future experiences.

Anonymous at Sat, 22 Mar 2025 17:18:09 UTC No. 16625926

>>16625697
>there will always be an axiom which cannot be proven simply because trying to do so leads to circular reasoning
Axioms are assumed truths, they can't be proven by definition. Any attempt to prove any axiom in a mathematical system will result in circular reasoning.

Anonymous at Sat, 22 Mar 2025 17:22:37 UTC No. 16625934

>>16625697
Wrong. It's only the artificial axioms (like the ones of modern "set theory") which will forever remain unproven.

Anonymous at Sat, 22 Mar 2025 17:34:29 UTC No. 16625951

>>16625934
Which axiom is provable?

Anonymous at Sat, 22 Mar 2025 17:40:42 UTC No. 16625958

>>16625951
The axioms which underlie the very notion of proof

Anonymous at Sat, 22 Mar 2025 17:51:06 UTC No. 16625973

>>16625958
give an example of 1 (one) [a single instance], and then prove it

Anonymous at Sat, 22 Mar 2025 18:18:35 UTC No. 16626002

>>16625958
"Proof" is the idea of applying logics to a conclusion to see whether or not it can lead back to axioms without any contradictions.
Axioms are unprovable because they themselves are all products of induction and isn't deduced from something more fundamental that can be traced back through logics. And all things induced are assumptions ultimately vulnerable to the Problem of Induction.
The axiom that underlie the very notion of proof is of no exception. There is nothing we know that says the universe won't one day go haywire and things stop acting logically, which if it ever come to pass the axiomatic assumption that the universe always act logically would be empirically invalidated.

Anonymous at Sat, 22 Mar 2025 19:43:55 UTC No. 16626072

philosophy is worthless garbage

Anonymous at Sat, 22 Mar 2025 21:47:47 UTC No. 16626171

>>16626002
Are you saying we can't prove anything unless there's some kind of assumption made?

Anonymous at Sat, 22 Mar 2025 23:17:14 UTC No. 16626218

>>16626171
Yes. There is ultimately always an assumption somewhere. Those are what we call axioms, the foundational assumptions.
"If, Then" is the underlying format of all empirical knowledge, the interplay between induction and deduction. Though for those things that are so empirically consistent in our lifetime, we tend to forget the "If" part.

Anonymous at Sat, 22 Mar 2025 23:30:12 UTC No. 16626227

>>16626218
I thought we were talking about proof from axioms, now you mention empirical knowledge, isn't that derived from experience & experiment not axioms? I guess there would be certain assumptions involved. So I guess all knowledge is sort of provisional.

Anonymous at Sat, 22 Mar 2025 23:51:15 UTC No. 16626236

>>16626227
All axioms are empirical in nature, at least the ones that are useful.
As for empirical knowledge, yes, they are derived from experience & experiment and not just deduced from axioms. Axioms act as the foundational launch pads for deductions, or in another word, predictions. Once predictions are made empirical knowledge through experience & experimentation verifies it empirically to see if either flaw in logics occured or the inital assumptions had been wrong. Hence the scientific method.

Anonymous at Sun, 23 Mar 2025 00:25:08 UTC No. 16626256

>>16626236
math isn't about being useful. that's engineering.

Anonymous at Sun, 23 Mar 2025 00:26:44 UTC No. 16626257

>>16625697
Have you ever talked to a mathematician? They would probably agree with you, but they probably wouldn't give a shit.

Anonymous at Sun, 23 Mar 2025 00:30:13 UTC No. 16626258

>>16625697
>Are mathematicians blind to the fact that math does not actually have to be perfect for it to work?
What you mean by perfect is unclear here.
> To me, it feels only natural to assume that math is not perfect, there will always be an axiom which cannot be proven simply because trying to do so leads to circular reasoning.
No shit, sherlock. Do you think this is a novel idea? That the 180 IQ 20th century geniuses who wrote tome after tome of dense formal logic hadn't thought of this?

Anonymous at Sun, 23 Mar 2025 00:39:13 UTC No. 16626262

>>16626002
The idea that all of our knowledge is derived from experience is false. This is because in order to make conclusions from experience you already need a common sense logic in the first place. This is like an extreme naive empiricism you're portraying here.

Anonymous at Sun, 23 Mar 2025 00:49:54 UTC No. 16626267

>>16626262
>The idea that all of our knowledge is derived from experience is false.
everything about our experience is driven by qualia

Anonymous at Sun, 23 Mar 2025 01:07:53 UTC No. 16626283

>>16626267
>vague mumbo-jumbo irrelevant to my comment

Anonymous at Sun, 23 Mar 2025 01:17:30 UTC No. 16626286

>>16626283
your comment is drivel and philosophy useless and uninteresting

Anonymous at Sun, 23 Mar 2025 01:56:42 UTC No. 16626301

>>16626286
You were the one yapping about qualia, anon (and where it wasn't even relevant). I see your shadow is rearing it's head...

Anonymous at Sun, 23 Mar 2025 01:59:26 UTC No. 16626302

>>16626262
>you already need a common sense logic in the first place
And where do this "common sense logic come from"?
If it's learned after birth, it's empirical
If it's hardwired prebirth, it's empirical
The only knowledge that is not empirical is unironic /x/ divine revelations where you "just know"
So unless you are refering to this last instance, there is no case for non-empirical knowledge

Anonymous at Sun, 23 Mar 2025 02:05:17 UTC No. 16626305

>>16626302
>If it's hardwired prebirth, it's empirical
What lmao

Anonymous at Sun, 23 Mar 2025 02:11:57 UTC No. 16626307

>>16625697
They're not. In set theory you don't have a canonical universe because you can show in each all others are ill-defined. Nobody is bothered by that except intuitionists.
Mathematicians and physicists have long ago decided to stick to what's useful and works and leave metaphysical sophistry to philosophers.

Anonymous at Sun, 23 Mar 2025 02:12:51 UTC No. 16626309

>>16626305
Empirical knowledge is pattern recognition knowledge through repeated experience. What do you think evolution is.

Anonymous at Sun, 23 Mar 2025 02:13:35 UTC No. 16626310

>>16626302
>If it's hardwired prebirth, it's empirical
No, it isn't. And you yourself are conscious of this, since you originally said "As for empirical knowledge, yes, they are derived from experience & experiment and not just deduced from axioms."

Anonymous at Sun, 23 Mar 2025 02:14:24 UTC No. 16626311

>>16626256
All of mathematics was developed because someone thought a particular concept was useful or interesting.

Anonymous at Sun, 23 Mar 2025 02:18:10 UTC No. 16626314

>>16626309
Well, it certainly isn't pattern recognition knowledge through repeated experience. I suggest you stop using words that have clear meanings in vague and sloppy ways to hedge your bets later. It isn't fooling anyone and you are just making yourself look like an idiot.

Anonymous at Sun, 23 Mar 2025 02:19:23 UTC No. 16626315

>>16626311
Is that meant to be a refutation of what they said? You literally said "or interesting"...

Anonymous at Sun, 23 Mar 2025 02:20:06 UTC No. 16626317

>>16626309
Then clearly divine revelation is empirical as well. Every known premodern society has independently built its own religion and set of superstitions, so it seems that it is likely hardwired into the human psyche

Anonymous at Sun, 23 Mar 2025 02:23:10 UTC No. 16626318

>>16626310
Some things are hardwired. The concept of one vs few vs many is hardwired. Look up Pirahã people.
You can even argue some animals and plants are capable of performing arithmetic. Venus flytrap measures the number of contacts made within a timeframe to determine if it shuts down and measures the number of days before reopening depending on it having caught prey or not. It doesn't seem to be a fixed time period either but actual number of days.

Anonymous at Sun, 23 Mar 2025 02:24:40 UTC No. 16626320

>>16626310
First, what I said there has nothing to do with prebirth hardwares.
Second, deduced predictions from axioms are technically not empirical knowledge in the sense they are not knowledge; they are predictions, hypotheses. Once they are confirmed through repeated experiences to be aligned with current reality, that empirical verification of the pattern is then the knowledge.
I can fantasize a million hypotheticals, but you wouldn't call any of them "knowledge".

Anonymous at Sun, 23 Mar 2025 02:29:35 UTC No. 16626322

>>16626315
Yes it is a refutation because I said that motivation behind maths is part usefulness and part curiosity. So usefulness being irrelevant to maths is false. Obviously it's not ALL that, taking an interest also plays a role but neither is 100%.
I wrote a sentence in English not a logical statement lmao this is not the gotcha you think it is

Anonymous at Sun, 23 Mar 2025 02:35:40 UTC No. 16626323

>>16626317
It's a hypothetical divine revelation. We don't know for sure if any society have truly ever received any divine revelation. But if it's real and it happens, then it would be a direct "download" bypassing experiences, and therefore not empirical.

Anonymous at Sun, 23 Mar 2025 04:25:56 UTC No. 16626369

math doesnt exist its just organized schizopherna of the mind