What proves the most basic math axioms? I'm talking about simple things like 1 = 1, 1 + 2 = 3, 0 is a number, etc.
Axioms are like bricks that we can use to build walls, which are mathematical proofs. But what can prove the axioms themselves?
Is this the point of Godel's theorems?
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great, I'll read more about that, thanks user
ZFC obviously
>starts counting with 0 instead of 1
Into the trash it goes.
>Is this the point of Godel's theorems?
Yes. You can only decompose really basic logic so much.
...
Axioms arent proven, thats why they are axioms
that seems a bit fucked up for me
>I'm going to prove this Y hypothesis while assuming X is true
>I have to prove Y
>I want to prove Y
>It's important to prove Y
>I'm not going to prove X though, fuck that, it's not important, even though everything is based on the X
it seems a bit weird to me, it makes me thing of mathematics as child's play, kind of like doing shit just for the sake of doing it, for no real reason, just fucking around
So you believe that having an infinite regression of theorems makes more sense?
Literally every chain of reasoning is based on unprovable axioms, except maybe cogito ergo sum
Just a fact of life
Math generally works something like this
>defines axiom x
>defines axiom y
>looks for logical conclusions and stuff that (directly) follows from those axioms.
>Z can logically be derived from y and x
If you define different axioms, we can also derive different stuff.
It's just that stuff like the peano axioms are so nice
yes, in the sense that it would feel less arbitrary to me, but I understand that some things are impossible to prove, it just seems weird to me that mathematics would be so arbitrary, i mean, if the starting point of mathematics if the most basic axioms are arbitrary then the whole thing is poisoned / corrupted and feels arbitrary and not really absolute, pure and objective
It IS fundamentally arbitrary, just like all logic
>What proves the most basic math axioms?
Nothing, that's what makes the axioms.
>But what can prove the axioms themselves?
You can't and don't need to prove axioms, math is a game of symbol manipulation and your axioms are simply the set of rules you are "playing" with. It's like asking for the justification behind the rules of Blackjack, there are none, those are simply the rules you follow when "playing blackjack".
>So you believe that having an infinite regression of theorems makes more sense?
>yes
Well you're in luck because any axiom can be interpreted as a theorem that proves itself.
The real reason we prove stuff is to make sure it's consistent with the picture we've already developed, which is itself based on some situation or class of situations we want to model.
If you don't have a model in mind then it really is just a game.
Discrete math is essentially what youre asking. Look at that somewhere.
you just don't "understand how math works" and trust me I don't mean this as an insult. read some book on mathematical logic and your present questions will be answered.
How do you prove that we use 1=1 as a consistent idea and that our mind is not fooling us?
Axioms are things agreed upon to be true. This is necessary because without making some assumptions to start with, you can't know nothin
and the notion of equality requires a very narrow view of anything which exists in the real world
two hydrogen atoms in the same state are not the same hydrogen atom
their energy state may be equal, but the state itself is a manthink creation to model some behavior (for simple situations) of the hydrogen atom
>prove
>axioms
Here's your (you).
>prove
>axioms
In general, axioms are taken to be non-controversial, and are adopted with no real attachment (exception axiom of choice).
For the most part, you can go up to any math department and tell them you don't believe anything they say because you're rejecting their axioms. They'll nod and say okay.
Nobody gets fired up or argumentative over axioms, they're basically religious beliefs for sciency people.
For a look at what "reasoning" without axioms looks like, see Nietzsche's anything, or anything continental philosophy. Then >>\lit\.
Ta ta, and farewell.
certainty in logic is probably impossible
i mean, the only reliable thing we have to evaluate the validity of logic is...logic. and if human logic is wrong then...oh wait, I just used logic to reach this conclusion.
fuggg...D:
Mathematics does not concern itself with what type of thing we're modeling. It only tells us what the rules are and what can be inferred from them. It is the job of the physicist to choose how to mathematically model the thing in question.
If you're interested in the state of two hydrogen atoms it's up to you to find the equations that model the state.
>hey every time you step on the first square of monopoly you receive 20k monies
>PROVE THAT IF YOU STEP ON THE FIRST SQUARE YOU INDEED RECEIVE DATS
Protip: you don't. It's a rule.
>it seems a bit weird to me, it makes me thing of mathematics as child's play, kind of like doing shit just for the sake of doing it, for no real reason, just fucking around
You're basically right t b h.
I do want to point out that theres nothing special about axioms. You can interchange most theorems with axioms and vice versa
Please don't troll. I know it's april fools and all, but trolling really degrades the quality of this board.