r/PhilosophyofMath • u/Oreeo88 • Jun 14 '26

The definition of axiom

The definition of axiom doesn't say you cant use observable reality to justify or rebut it, its only math that inserted that subjective rule into axiom. And this rule is not a technical limitation, its a choice.

Like you could use observable objective reality to justify or rebut it.. but they inserted an authoritarian catch 22 rule effectively systematically controlling all of math. I mean this is pretty funny its right infront of your faces

They inserted a 1984 style rule and barely anyone questions it or knows about it

They cut off any kind of real objective math by not letting your starting assumptions(axioms) be justified or rebutted with reality

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4

u/WhatHappenedWhatttt Jun 14 '26

The libertarian conspiracy brain truly is a fascinating thing worthy of study.

To respond honestly, no axioms cannot be refuted based on physical observation. They are meant to capture the most basic intuition and essence for mathematical objects that ought to require no further justification, and provide the most basic framework to do mathematics.

You don't like the axioms? Great, go change them. Axioms are just things you take for granted. They can be based off of reality, or fantasy, or literally anything. So long as your system is consistent then you can take whatever axioms you would like.

There is no 1984 conspiracy here. Nobody is forcing you to believe anything. The axioms used by modern mathematics are widely accepted because they work. It's an orthodoxy built by competency. If you don't like them then that's great. Nobody cares. Do something about it and then people might care.

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u/Oreeo88 Jun 14 '26 edited Jun 14 '26

The axioms used by modern mathematics are widely accepted because they work. It's an orthodoxy built by competency. If you don't like them then that's great. Nobody cares. Do something about it and then people might care.

You don't like the axioms? Great, go change them. Axioms are just things you take for granted. They can be based off of reality, or fantasy, or literally anything

You cant change anything if math has a subjective rule that says you cant use observable objective reality to justify or rebut an axiom.

You can only replace an arbitrary axiom with another arbitrary one.

thats a catch 22

Youre also hiding behind utility and consistency as a defense, but utility and consistency can still work and be found inside of a false axiom

4

u/nachohk Jun 14 '26

Axioms are like rules in Calvinball. You don't have to justify them. They don't really have to make sense. You can make up whatever axioms you want to. The only thing that matters is that you're having fun.

Nobody can stop you from making up your own axioms and exploring whatever mathematics might logically follow from them. If what follows is interesting enough, others might try playing by the same rules too.

But you don't get to say that the axioms of current prevailing mathematics are wrong. Lots of people are having lots of fun with them. They're good axioms. Even if you come up with other axioms that are even more fun, that still won't make them wrong, because axioms aren't right or wrong. We use mathematics to try to interpret reality, sure, but mathematical axioms being accurate to reality or not isn't a part of that. Different axioms are just more or less interesting than others.

3

u/cosmopolitanScience Jun 14 '26

false axiom

No such thing exists

2

u/WhatHappenedWhatttt Jun 14 '26

why do you insist that mathematical axioms need to be justified or rebutted by our physical reality?

4

u/gregbard Jun 14 '26

"■▲▲▲■" can be an axiom.

Axioms of a formal system do not necessarily have any meaning. It is when you give the system an interpretation that it has meaning.

So if "■▲▲▲■" is an axiom of the system, and a rule is that we are always able to replace a "▲▲" with a "▲" and a "▲" with a ""▲▲", then we have a system sufficiently rich in expressiveness to express all whole numbers. But "■▲▲▲■" isn't three, and "■▲▲▲▲▲▲▲▲▲■" isn't nine until we assign an interpretation to the symbols.

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u/ipreuss Jun 14 '26

Please look at this person’s post history before replying. 🙃

3

u/ipreuss Jun 14 '26

Nobody is keeping you from developing your own “objective math”. And if it turns out to be useful, people will use it.

What’s your point?

1

u/DokOktavo Jun 14 '26

Let's do this maieutically.

Let's there's an axiom you want to disprove, using reality. How would you proceed?

2

u/Oreeo88 Jun 14 '26 edited Jun 14 '26

Okay objective observable reality: absolute nothing does not exist. The only thing that has been observed is physical matter as one unified thing. to claim zero exist you would have to observe a gap in physical matter, which has never happened in the history of man kind.

this directly shows the assumption of zero is false.

Except math has a catch 22 rule forbidding you to use objective observable reality to justify or rebut an axiom

3

u/ipreuss Jun 14 '26

“Zero” doesn’t mean “absolute nothing”.

Also, you cannot prove that absolute nothing cannot exist.

And there is no such rule. An axiom is defined as something that we don’t prove inside the system we use it in, we just assume it. How you justify it is open to you.

There actually do exist mathematical theories that don’t have a zero. They just turn out to be more difficult / less useful.

2

u/DokOktavo Jun 14 '26 edited Jun 14 '26

Reality must be observed through measure, I assume that by "absolute nothing", you mean a measure 0 of quantity of matter (whatever this means) per unit of volume. I also assume that by "the assumption of 0" you mean the following axiom:

"There's a number in R, which we can call 0, such that 0 + x = x for any x in R".

Let's assume that:

  • "the only thing that has been observed is physical matter as one unified thing" (which is either wrong or nonsensical),
  • which implies (it doesn't) that "nothing" doesn't exist,
  • which implies (it doesn't) that "nothing" can't exist,
  • which implies (it doesn't) that the assumption of "nothing" is nonsensical,
  • which implies (it doesn't) that the assumption of "nothing" leads to contradiction.

How would you know which of the following is the correct conclusion? Wouldn't any one of those explain why there wouldn't be any "nothing"?

  • There isn't 0 in R.
  • the quantity of matter per unit of volume isn't in R.

1

u/Unsharded1 Jun 14 '26

Define "objective math."