Godel's Incompleteness Theorem

[blackzeus]

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.

Godel was able to sh*t on modern math in their own language, that's why it was so profound. Before him it was like "These proletariat gypsy serf shamans dare question our math." When Godel dropped his sh*t there was a whole lot of and goin' on A lot of scientists are the most hypocritical, facetious, sanctimonious people on earth. They will spend their whole lives trying to prove a theory true while sh*tting on people's faiths

 

[blackzeus]

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.

Maaaaaaann, I don't know about you breh. Let's start with the basics, what is deduction (which by the way is not the method used for math proofs)?

http://en.wikipedia.org/wiki/Deduction

Deductive reasoning, also deductive logic or logical deduction or, informally, "top-down" logic,[1] is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.

Logical deduction method:

Birds can fly

I can observe how birds fly, and similar design a vehicle that will allow me to fly like them

I can fly


Weirdo scientist deduction method:

Man must have predecesor

Monkey looks like man

Man must come from monkey

THE FLAW IS IN THE PROCESS OF MAKING A PREMISE.

We can all be logists. Look:

I converse with people through computer

People converse with me through the computer

The computer has the ability to understand conversations

^^^This is the absurdity with using this type of logic in math. Mathematically, it is ABSURD to claim something is true for all N without graphing it first. That's EXACTLY WHY you have divergent series, and why integrals on paper don't add up in real life, etc etc. Only in science/math is it normal to have premises made without a physical basis of some sort. You need to have some sort of standardization for making a premise about something being true for all N. That's why Godel laughed at those guys, because in reality they operated as much on faith as you're ordinary Christian. They BELIEVED their premises was quantifiable to do their proofs. In fact, even in the wiki definition of inductive logic:

Inductive reasoning (as opposed to deductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a deductive argument is supposed to be certain, the truth of the conclusion of an inductive argument is supposed to be probable, based upon the evidence given.[1]

The philosophical definition of inductive reasoning is more nuanced than simple progression from particular/individual instances to broader generalizations. Rather, the premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; that is, they suggest truth but do not ensure it. In this manner, there is the possibility of moving from general statements to individual instances

99% of math is proven via the INDUCTION step breh. Thus the reason why you can't prove sh*t is true for all N, because you're ASSUMING sh*t that's true for a subset is true for all N when there is no physical proof of such thing being true. The flaw is in the very tool you're using to build your argument.

 

[blackzeus]

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?


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.

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.

http://dictionary.reference.com/browse/axiom

1.
a self-evident truth that requires no proof.
2.
a universally accepted principle or rule.
3.
Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.

^^^look at the first two definitions, then look at the mathematical definition. Mike the plumber would never make such a facetious axiom, but Mike the mathematician would Your simple case would never occur because Jones would be like ? But in math it's ok because 99% of the world doesn't understand high level mathspeak. And no, Godel, PROVED that your math is all wrong, that's why it's breaking your heart Pharisee

In the real world you claim pigs fly as a logical premise and people keep it moving, in math you claim it's possible to do an integral of a divergent summation series and people listen and take note, not realizing it's basically the same thing as saying pigs fly


EDIT: By the way TVs and computers came from a common ancestor over the last few millions of years, my Darwinian statement of the day

 

[HideoKojima]

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

I'm black

 

[Blaze500]

I'm confused

what did this Kurt Godel guy do that was so groundbreaking?

 

[blackzeus]

I'm black

Looks at avi, not sure if poster has possible self identity issues

 

[blackzeus]

I'm confused

what did this Kurt Godel guy do that was so groundbreaking?

He basically said math is a faith, which is devastating to any mathematician who claims to be rooted in the scientific principle and proof by logic. That would be like Christians finding out Jesus was never crucified, o Buddhists finding out Buddha was made up, or Americans finding out there was never a Revolutionary War, etc etc.

 

[HideoKojima]

Looks at avi, not sure if poster has possible self identity issues

google my screen name

 

[Blaze500]

Godel was a genius