Godel's Incompleteness Theorem

[blackzeus]

I can tell you don't have any understanding of biology or chemistry to any degree.

Its all chemicals so understanding that certain conditisions favor "life" in the manner that we know it may be possible elsewhere.

Thats infinitely more plausible than the deity asserted by theists.

Correct, two wrongs don't make a right. You have to look at each case on its own merit. Faith in math/math being provable logic has nothing to do with the odds of their being another habitable planet or alien life forms. And to state the obvious the odds are highly against there being only 1 in a billion planets that's habitable , but f*ck all that, let's stay on topic

 

[DANKTHRONE]

The "assumptions" in math are just uncontroversial table setting. Like "Assume there is an x such that x is less than three". In modal logic terms you are just marking out the possible world you're talking about. Same as assuming or not assuming the continuum hypothesis.

 

[☑︎#VoteDemocrat]

Really is amazing how much boils down to "trust what you repeatedly observe." even in modern science and mathematics

as opposed to...

Science only asserts what it can confirm, nothing beyond that.

 

[blackzeus]

The "assumptions" in math are just uncontroversial table setting. Like "Assume there is an x such that x is less than three". In modal logic terms you are just marking out the possible world you're talking about. Same as assuming or not assuming the continuum hypothesis.

C'mon breh, you're better than this. Let's assume X is less than three is a definitive statement, you've quantified X as less than 3. There is an infinite set of integers for which that is true, so there is no assumption there.

let's assume P(x) < 3 for all x IS AN ASSUMPTION, not a definitive statement, until you PROVE that your assumption is true for the the set of all integers/real numbers/etc.

That would be like saying let's assume birds can fly and let's assume humans can fly are equal logical premises to use as a base for a statement. One is clearly an empirically quantifiable statement, and the other is obviously something that is empirically unquantifiable, as I have never seen a man fly, I can't accept that as a logical premise for your statement until you prove that part first.

 

[blackzeus]

as opposed to...

Science only asserts what it can confirm, nothing beyond that.

Please confirm the integral of a divergent series for me breh, I see you Pharisees are back to your old tricks

 

[☑︎#VoteDemocrat]

Please confirm the integral of a divergent series for me breh, I see you Pharisees are back to your old tricks

potato

 

[blackzeus]

potato

But woe unto you, @thecoli Pharisees, hypocrites! for ye shut up the kingdom of logic against men: for ye neither go in yourselves, neither suffer ye them that are entering to go in.

 

[Mission249]

first,
Second,
Just read through the thread and damn. I'm just smart enough to understand the concepts (i think), but not smart enough to apply the math to prove them, but as with @rapbeats and @blackzeus the moment I heard "Let's assume..." in calculus i was like .

You're misunderstanding and conflating several ideas. These "assumptions" are either new axioms in the system (in which case, "assume" is somewhat of a misnomer) or part of a technique that scientists, logicians, mathematicians and human beings in general use to prove something. Lets divorce this concept from infinite and give a simple example to understand better.

1) Mike told Jones that all people spontaneously combust when they die
2) Jones tells Mike "No they don't. But lets assume they do. Therefore the next person to die should spontaneously combust?"
3) They then watch someone die and he doesn't explode therefore "All people don't spontaneously combust when they die"

Now, what if a third person walked up and said "You 'assumed' something so your science is all wrong. It's a leap of faith. This is proof of God!". Wouldn't that be a little crazy?

There are many things we don't know to be 100% true, and yet we believe they are true and or we believe they will be proven to be true

I think of it as the "humility" of science that even after we put our hypothesis through the rigor of the scientific method, we still only refer to the result as a "theory". A scientific theory, however, is MUCH more powerful than a colloquial "theory" however. Which seems to confuse people a lot.

for instance the mechanism behind evolution, the theory of man evolving from a monkey (unless i missed something we don't know this 100% to be true)

Nobody says we evolved from monkey. It's a common straw man that anti-evolutionists like to use to confuse people. The idea is that monkeys and humans have a common ancestor.

 

[blackzeus]

The "assumptions" in math are just uncontroversial table setting. Like "Assume there is an x such that x is less than three". In modal logic terms you are just marking out the possible world you're talking about. Same as assuming or not assuming the continuum hypothesis.

You don't see the #inherent fallacy in the word "assume" preceding "proof"?

 

[Mission249]

You don't see the #inherent fallacy in the word "assume" preceding "proof"?

You're equivocating. The definition of "assume" that you're stuck on, the definition we use in normal conversation, is not the same as the mathematical definition of an assumption. A mathematical assumption is an axiom - it's a base definition we use to build our higher level deductions. We're not "assuming" in the colloquial sense, we're defining in the mathematical sense. Software engineers do it everyday when they define a new function in their system. Saying "assume P(x) is true if x is greater than 5 and less than 10" is no different than me writing a line of code as follows:

def P(x):

return x > 5 and x < 10​

Your example, "assume P(x) < 3 for all x" is just as trivial:

def P(x):

return 1​

P(1) < 3
P(121212) < 3

Does it make any sense to say that there's an "inherent fallacy" in a programmer defining some functionality? If that's the case, no piece of software could ever work. Please read some of the wiki page on axioms: http://en.wikipedia.org/wiki/Axiom . Particularly, the line "..nothing can be deduced if nothing is assumed". Once again, a mathematical assumption is a assertion of how things work in the system we've created. When you "enter" that system, you implicitly agree to those assumptions/definitions. Disregarding that, when taken to it's logical conclusion, means we can't even communicate. In a way, just by reading this sentence, you've agreed to numerous "assumptions" in language.

Your original argument, against induction over infinite sets was far more interesting, in a Finitism sense (http://en.wikipedia.org/wiki/Finitism). But this much broader argument you're trying to make doesn't fly. But, don't mind me, please continue disregarding facts in order to rationalize whatever psuedo-religious agenda you need to believe. And, that's not to say I don't believe in religion or spirituality, but those ends don't justify your illogical means.

Unfortunately, "assume" is an overloaded word that means several different distinct things depending on context. You cannot simply disregard context and pick whichever definition helps you win some internet argument.

 

[Blackking]

Y'all need to get to the background of what is going on here, for a deeper understanding, y'all missin' the point like the Miami Heat. Here is a wiki link on Godel:

http://en.wikipedia.org/wiki/Kurt_Gödel#Religious_views



Y'all not realizing that Godel just shat on modern math with his theory. All the major scientists of his era (and let's be real, the 30-50s was the last TRUE era of advancement in scientific theory) were saying evolution this and God doesn't exist that, and faith is b.s. bla bla bla. Godel was like, "O rly? let's have a look see at the basis of your great math, natural numbers. Well I can't believe it, these numbers ain't loyal!

Can I join your religion of math?"

I didn't think anyone would post this..

Then I would, then be called an idiot.

But yes this is what I was taught and what I believe.

 

[Blackking]

It's amazing how much theory and phenomena exists that we can't prove but know to be true Greeks and Egyptians had it right when they called their universities temples of learning. I'll never forget when I was using Fourier diff equations for digital signal processing in my comp-e days, we were learning how to design filters for converting analog signals to digital signals (butterworth, hi pass, lo pass, etc). I'm lookin' at some of the sh*t like , how did y'all prove this, the professor straight up told me "Don't think, just believe". I never forgot because that's the EXACT same thing the pastor at the church I used to go to as a kid used to say.

Amazing...

And rep.

 

[Blackking]

first,
Second,
Just read through the thread and damn. I'm just smart enough to understand the concepts (i think), but not smart enough to apply the math to prove them, but as with @rapbeats and @blackzeus the moment I heard "Let's assume..." in calculus i was like .

Then I started asking questions and as complicated as things get essentially you end up with assumptions and self referencing material...and as blackzeus pointed out there's another group of people who do this...

(granted one does require a more drastic "leap of faith" than the other; the leap of faith is still there.)

The other funny odd thing I've noticed about myself and people who hold fast to things like physics and evolution and such is this...

There are many things we don't know to be 100% true, and yet we believe they are true and or we believe they will be proven to be true, for instance the mechanism behind evolution, the theory of man evolving from a monkey (unless i missed something we don't know this 100% to be true), the myriad of things we will most likely never know but can sorta explain via math (e.g. the inside of a blackhole), things that occur on the very macro and very micro level, the list goes on and on. The optimal word in the last run on sentence is BELIEVE. Regardless of whether the idea is proven to be correct or not RIGHT NOW we believe based on faith and a limited understanding that what we believe is the truth. The part I find funny is that science has a built in "i don't know" clause whereby someone can go, "whoops I had it wrong, turns out black holes don't exist after all...another win for science" which conveniently discounts the years people BELIEVED with all their hearts and minds that black holes were the truth. (not that black holes don't exist it's more an example)

Ape... evolved supposedly from apes.

 

[HideoKojima]

damn, you nikkas really do have certs and probably pawgs too. Cats really breaking down mathematics

 

[blackzeus]

damn, you nikkas really do have certs and probably pawgs too. Cats really breaking down mathematics

Whatever, y'all Japanese nikkaz got that electrical engineering game on lock though