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/sci/ - Science & Math

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7677059 No.7677059 [Reply] [Original]

Can all of math be reduced to logic? Can all of logic be reduced to math?

>> No.7677069

Logic is just one part of math.

>> No.7677070

>>7677059
no
See: Godel's Incompleteness Theorem

>> No.7677076

>>7677070
That doesn't mean what you think it means.

>> No.7677131

>>7677076
What do you think it means? I think people just like to dismiss it.

>> No.7677153

>>7677131
I think what you meant to say is that people like to dismiss crazy philosophical interpretations of it that deal with words like 'logic' and 'math'

>> No.7677160
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7677160

Yes. No.

>>7677070
Fucking idiot, Incompleteness doesn't have anything to do with this.

>> No.7677168

>>7677153
It has to mean something. Most people seem to just dismiss it as a trivial fact like "oh we can't prove shit, ha how about that?"

I don't see how that isn't a big deal. I understand it doesn't have much impact on day to day life or even ordinary uses of math but its still pretty damn weird.

>> No.7677174

>>7677160
Yes it does. If op is talking about completely describing math through formal systems of logic then yes it is related.

>> No.7677176

>>7677174
And that is not what he is talking about.

>> No.7677212
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7677212

>>7677174
>implying math is more than strict finitism

/x/ please go and stay go

>> No.7677216

>>7677212
Godel's shit does sound a little /x/tier sometimes. Doesn't necessarily make him wrong.

>> No.7677221

>>7677216
>sounds
>"necessarily"

refrain from making opinions on things you haven't studied

>> No.7677223
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7677223

>> No.7677224

>>7677160
literally
can you describe math with a set of axioms and have the description be complete and logically consistent
the answer is no by the incompleteness theorem
therefore
fuck you retard

>> No.7677226

>>7677223
>physics
>study of real world
>completely inside axiomatic systems

fuck off with your dumbass chart

>> No.7677231

>>7677226
These are infinite sets

>> No.7677233

>>7677224
to be fair OP never specified the logic had to be consistent or complete.
I guess im the retarded one sorry lad

>> No.7677239

>>7677224
Any axiom that you use will be inside logic, I am not implying you can describe math with a finite set of axioms, I am saying all axioms are inside Logic, and Logic is infinite.

>> No.7677241

>>7677239
You can't even do it with an infinite set of axioms.

>> No.7677244

>>7677241
What? You can. That is literally the Gödelian statement.

>> No.7677247

>>7677239
Can you prove that there are an infinite amount of unique axioms?

>> No.7677249

>>7677244
No it's not.

>> No.7677254

>>7677247
Are asking if I can make you sane?
>>7677249
Well, then you don't understand it.

>> No.7677257

>>7677254
Or you don't

>> No.7677260

>>7677070
Goëdel's incompleteness theorem says axioms can't prove themselves to be consistent, a stronger theorem may be able to prove it though.

The answer is maybe.

>> No.7677266

>>7677260
see:
>>7677233
made an assumption about OP's question
my bad

>> No.7677278

>>7677266
At least you admitted it and didn't shitpost to get your way

>> No.7677281

>>7677260
Then the consistency of that theorem would fall under question.

Any axiomatic system of sufficient complexity (complex enough to contain the principals of math) either falls to incompleteness or inconsistency.

It's strange and kinda shocking but apparently that's the way things are. Doesn't change the things we "know" to be true, but our ability to formally prove things is fundamentally limited.

>> No.7677287

ITT: People misunderstanding Gödel

>> No.7677321

>>7677287
Explain it then.

Threads that touch on Godel are worse than threads about QM, just a bunch of people claiming to know shit and other people being dismissive while adding nothing to the conversation.

>> No.7677348

>>7677069
this, I think OP thinks that real analysis == math

>> No.7677355

>>7677287
Elaborate please.

>> No.7677362

So, Gödel's incompleteness theorem (and other similar results) rely on a diagonal lemma which, if I remember correctly, works only if the theory is recursively enumerable. So... to succeed we simply have to construct a sufficiently strong non-recursively enumerable theory?

>> No.7677596
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7677596

>>7677321
>>7677355
As far as I saw, people think mathematics is outside of logic, because they got confused with Gödelian statements. Gödel just said any finite set of axioms cannot be complete, jesus christ. I take it for granted that it must be consistent, so I don't even mention it.