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/sci/ - Science & Math

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6571502 No.6571502 [Reply] [Original]

All of math can be reduced to logic.

Prove me wrong, /sci/.
>protip: ya can't

>> No.6571513

>>6571502
Axioms can't
Definitions can't

>> No.6571518

Every time someone orders Principia Mathematica off of amazon, their IP should be flagged so they have to wait at least 2 weeks to post on /sci/ again

>> No.6571523

>>6571513
>Axioms can't
>Definitions can't
sigh...
All mathematical results (i.e., theorems) can be logically deduced from the axioms, definitions, postulates, etc.

I was hoping I wouldn't have to clarify what I meant.

>> No.6571530

>>6571518
Kek'd.

>> No.6571539

>>6571523
>All mathematical results (i.e., theorems) can be logically deduced from the axioms, definitions, postulates, etc.
um no shit?
Does anyone disagree with you?

Are you referring to shit like:
http://en.wikipedia.org/wiki/Mathematical_coincidence
http://en.wikipedia.org/wiki/Freshman%27s_dream

>> No.6571559

>>6571539
I'm talking about

http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Logicism
and maybe also
http://en.wikipedia.org/wiki/Formalism_(mathematics)

>> No.6572122

0.999... = 1

Explain THIS with your logic.

>> No.6572132

>>6572122
You have one cup of water.

You split this cup of water exactly into thirds, each into three different containers.

Each container now has .333... cups of water.

Assuming that no water was lost in the process of moving between vessels, when you pour the water from each container into the original cup, it is full.

You have one cup of water.

3(.333...) = 1

.999... = 1

>> No.6572413

>>6572132
That doesn't work, if you're pouring equally molecule by molecule, you won't be able to have all cups with the exact same number.

One will be 0.333...34

>> No.6572448
File: 142 KB, 1290x1845, ezproof.png [View same] [iqdb] [saucenao] [google]
6572448

>>6572122
k

>> No.6572470

>>6572413
that 0.000...01 can be divided into 3 again to become 0.000...00333...

>> No.6572502

>>6572122
if 0.9999... != 1, what's a number between 0.999... and 1?

>> No.6572854

>>6572413
what if there are three molecules?
checkmate

>> No.6572919

>>6572854
>implying finite number of molecules

>> No.6572940

>>6571518
> Principia mathematica
> 2014
> wut

>> No.6572958

>>6572854

3/3 = 1
1*3 = 3

If there are three molecules, then I'm not seeing an issue.

Zimbabwe

>> No.6573123

>>6572502
>shifting the burden of proof

>> No.6573128

>>6573123
>burden of proof
>math
lel

>> No.6573133

>>6573128
>math
>without proofs
physicist detected

>> No.6573140

>>6573133
>missing the point
i'm a mathematician.

the "burden" is your derp, not the "proof". math isn't debating society. also you missed an obvious intro to reductio ad absurdum in the "what's the number inbetween...", thinking it was some switching of burden.

>> No.6573145

>>6573140
You missed the point and having a B+ in your high school calculus class doesn't qualify you to call yourself a "mathematician". Have you ever seen a rigorous proof? The "what's the number inbetween" question is retarded and doesn't prove anything. If the faggot can prove that there can be no number inbetween, he should do so. Otherwise he contributed no content whatsoever. "Hurr durr the Riemann hypothesis must be true becaus you can't find a counterexample lol." Seriously?

>> No.6573164

>>6571502
>All of <thing 1> can be reduced to <thing 2>
>thing 1 and thing 2 are mutable concepts
>it is possible to argue over the meanings of thing 1 and thing 2
>therefore, as this discussion progresses, the probability of the conversation diverging into a cryptic philosophy argument approaches 0

I call this the law of dumb internet arguments on /sci/ and I'd say it's been observed and tested just as much as any other good scientific law.

>> No.6573165

>>6573164
shit shit shit shit I meant 'approaches 1'.

I'm a fucking retard.

>> No.6573169

>>6573145
>sperging this much
I have a degree in math.

The suppose there exists x such that a < x < b, and then showing this leads to a contradiction, is a fairly standard way of showing a = b.

>> No.6573171

>>6572470
you can't divide a molecule into three you fucking retard

>> No.6573173

>>6573169
What area of math are you specializing in?

>> No.6573180

>>6573173
I'm not. I graduated two years ago.

>> No.6573186

>>6573169
wouldnt showing their averages are equal to themselfs also show this?

for some a and b, and x=(a+b)/2

if x=a or x=b then a=b

>> No.6573187

>>6573169
>I have a degree in math.
Then why do you fail at high school math ITT?

>The suppose there exists x such that a < x < b, and then showing this leads to a contradiction
You haven't yet shown any contradiction.

>is a fairly standard way of showing a = b.
Nope. Show me one textbook using this technique. It's bullshit, impractical and never used.

>> No.6573189

>>6573180
Dropping out is not the same as graduating.

>> No.6573193

>>6573186
>if x=a or x=b then a=b

If x=a AND x=b then a=b

>> No.6573198

>>6573187
>>I have a degree in math.
>Then why do you fail at high school math ITT?
I haven't

>>The suppose there exists x such that a < x < b, and then showing this leads to a contradiction
>You haven't yet shown any contradiction.
Nor have I claimed to. I was poinitng out the beginning of this process is not, as anon claimed, a shifting of a burden of proof, but the beginning of a proof by contradiction.

>>is a fairly standard way of showing a = b.
>Nope. Show me one textbook using this technique. It's bullshit, impractical and never used.
How can I show a textbook on the internet? It's used in the one proof of the intermediate value theorem.

>> No.6573199

>>6573189
That's quite correct.

>> No.6573200

>>6573193
no, if either are equal to the answer, they both are

>> No.6573202

>>6573198
>I haven't
You have.

>Nor have I claimed to. I was poinitng out the beginning of this process is not, as anon claimed, a shifting of a burden of proof, but the beginning of a proof by contradiction.
No proof by contradiction has been posted ITT. All I see is a retard trying to shift the burden of proof.

>How can I show a textbook on the internet?
Take a screenshot or a photo or post a link or quote a paragraph or name the title, author and page so we can look it up.

>It's used in the one proof of the intermediate value theorem.
no

>> No.6573206

>>6573202
>No proof by contradiction has been posted ITT.
That's correct, just the hint at the very beginnings of one, the misinterpretation of which I pointed out.

>Take a screenshot or a photo or post a link or quote a paragraph or name the title, author and page so we can look it up.
Why should I bother?

>no
It's a fairly easy exercise to rephrase the proof on the wikipedia page in this manner.

>> No.6573209

>>6573202
>the burden of proof.
There is no burden of proof in mathematics. Things are either proven or unknown.

>> No.6573220

>>6573206
>That's correct, just the hint at the very beginnings of one, the misinterpretation of which I pointed out.
There is no hint. Only a shifted burden of proof.

>Why should I bother?
Because it is your burden of proof.

>It's a fairly easy exercise to rephrase the proof on the wikipedia page in this manner.
It is also a fairly easy exercise to dismiss your garbage. You were talking ignorant bullshit and we proved you wrong. Deal with it.

>>6573209
>There is no burden of proof in mathematics. Things are either proven or unknown.
Exactly. The poster >>6572502 did not prove anything. Therefore his claim is unknown until someone proves it.

>> No.6573231

>>6573220
>>>6573206
>>That's correct, just the hint at the very beginnings of one, the misinterpretation of which I pointed out.
>There is no hint. Only a shifted burden of proof.
So you think math does have a burden of proof?

>>Why should I bother?
>Because it is your burden of proof.
I am not interested in proving it.

>>It's a fairly easy exercise to rephrase the proof on the wikipedia page in this manner.
>It is also a fairly easy exercise to dismiss your garbage. You were talking ignorant bullshit and we proved you wrong. Deal with it.
I missed the post where that happened.

>>>6573209
>>There is no burden of proof in mathematics. Things are either proven or unknown.
>Exactly. The poster >>6572502 did not prove anything. Therefore his claim is unknown until someone proves it.
That's correct, he didn't. But you now seem to be saying there is no burden of proof in math, just proof or no proof.

>> No.6573242

>>6573231
>So you think math does have a burden of proof?
It does. If you make a claim, then you better prove it.

>I am not interested in proving it.
So you admit being wrong?

>I missed the post where that happened.
Learn to read.

>But you now seem to be saying there is no burden of proof in math, just proof or no proof.
Learn to read.

>> No.6573249

>>6573242
>>So you think math does have a burden of proof?
>It does. If you make a claim, then you better prove it.
Only if you claim some truth not already established.

>>I am not interested in proving it.
>So you admit being wrong?
Of course not. Do you believe not proven => false?

>>I missed the post where that happened.
>Learn to read.
Obviously I can read. If you could link the post though, I'd be grateful.

>> No.6573262

>>6573249
>Only if you claim some truth not already established.
You mean like >>6572502 did?

>Of course not. Do you believe not proven => false?
Obviously that's what >>6572502 believes.

>Obviously I can read.
Obviously you can't.

>If you could link the post though,
Read the thread. It's not that long.

>> No.6573274

>>6573262
>>Only if you claim some truth not already established.
>You mean like >>6572502 did?
He asked a question in that post. He didn't make a claim.

>>Of course not. Do you believe not proven => false?
>Obviously that's what >>6572502 believes.
Maybe, but I was asking if you do.

>>Obviously I can read.
>Obviously you can't.
How come we are interacting?

>> No.6573299

>>6573274
>He asked a question in that post. He didn't make a claim.
If you didn't notice his intent, you might be autistic.

>Maybe, but I was asking if you do.
Why would you ask that? Are you a straw man?

>How come we are interacting?
A deterministic sequence of physical events starting with the big bang.

>> No.6573310

>>6573299
>If you didn't notice his intent, you might be autistic.
If he was claiming 0.999... = 1 then he was claiming something well established. And I am autistic.

>Why would you ask that?
Because you seemed to think that me not being interested in proving something was true, implied I was wrong about that thing. When it simply implies that I might be wrong.

>Are you a straw man
A straw man is something one sets up, not something one is.

I'm going to bed now. You might find your style of posting is more fun with a non autistic person.

>> No.6573687

>>6573171
Theoretically we can.

>> No.6573751
File: 91 KB, 600x974, goedel.jpg [View same] [iqdb] [saucenao] [google]
6573751

Sup man

>> No.6573814

Can imaginary numbers be deduced logically? Nope. Their invention was an act of creativity. Their axioms did not exist before they were invented. Checkmate.

>> No.6573824

>>6571502
All logic can be reduced to axiomatic systems.

Prove me wrong, /sci/.
>protip: ya can't

>> No.6573829

>>6573814
R[X]/(X^2+1)
Checkmate

>> No.6573830

>>6571523
Technically that anon is right. The idea is that you start with a language, then you add rules for evaluating statements as true or false and for producing new true statements from other false statements. This turns your language into a logic. Then you take your logic and couple it together with axioms, undefined terms, defined terms, and theorems, and you've got an axiomatic system. The logic only defines the true/false structure of the system.

On the other hand, logics themselves can be reduced down to axiomatic systems and be studied by mathematics.

It's weird but in a way logic can be founded on mathematics and mathematics can be founded on logic.

>> No.6573859

>>6573164

underrated post

>> No.6573863

>>6571523
What is incompleteness?

>> No.6574114

>>6573169
>I have a degree in math.
Good for you.
1+1=0

>The suppose there exists x such that a < x < b, and then showing this leads to a contradiction, is a fairly standard way of showing a = b.
Show me.

>> No.6574119

>>6573814
>"Can imaginary numbers be deduced logically?"
>I don't know what algebraic completion is

>> No.6574129

dis ain't Python nigger

>> No.6574152

>>6571502
First order predicate logic is complete. Any theory that contains Peano arithmetic is not. The whole of mathematics contains Peano arithmetic. Therefore mathematics does not reduce to first order predicate logic.

>> No.6574160

Can logic explain this?

http://www.youtube.com/watch?v=3_Up_swvN3s

:^)

>> No.6575887
File: 1.93 MB, 320x180, 1398527410458.gif [View same] [iqdb] [saucenao] [google]
6575887

>>6573123
>burden of proof
my zygomatics are aching
you're too /pol/ for me.

>> No.6575896

>>6573140
>>6573133
and the hundred of following posts.

Why on earth God created so autistic persons.
I really hope posting makes you feel good.


Anyway, I'm never tired of reading frustrated people. So be yourself. I'm browsing /sci/ because of you.

>> No.6578365

>>6571502
>Math can be reduced to logic
>reduced to logic
>reduced

Math "IS" logic you dumb nut.
Symbolic logic.

>> No.6578391

>>6574152
>being this retarded in 2014
In "completeness theorem" and "incompleteness theorem", the word "complete" refers to different things. When we say FOL is "complete" we mean that syntactical proof is equivalent to truth-in-every-model. When we say Peano arithmetic is "incomplete", we mean there are truths ___in the standard model___ that are not syntactically provable.

These two concepts are obviously not mutually exclusive. The answer to OP's question is "yes"

>> No.6578597

kek

>> No.6578678

>>6578597

>> No.6578881

>>6574160
what the fuck is this shit

>> No.6578896

>>6578391
>The answer to OP's question is "yes"
>OP's question
Not only did OP not ask a question, but showing a flaw in an argument does not imply the opposite is true.

>> No.6579393

>>6578391
>The answer to OP's question is "yes"

wrong

>> No.6579397

define logic

>> No.6579399
File: 258 KB, 1024x683, 1401658137319.jpg [View same] [iqdb] [saucenao] [google]
6579399

>>6571502
WHAT IS SO CONFUSING ABOUT NUMBERS?
DOES THIS WORD SCARE YOU, NUMBERS?
DO YOU THINK LOGIC IS JUST MORE EDGY THAN NUMBERS?
IS EVERY TODAY A CASE OF EARLY ARITHMETIC DROP OUT?
ARE YOU GIRLS NIGGERS?
NUMBERS MOTHERFUCKER THEY EXISTED BEFORE THE UNIVERSE, IS THIS SO FUCKING HARD TO UNDERSTAND?
THAT NUMBERS ARE FUCKING AWESOME?

>> No.6579404

>>6572919
>what is Avogadro's constant?