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Reasoning about the reason (Godel) Reasoning about the reason

As I said, when confronted with paradoxes, we seem to encounter the same limits of reason and logic. The Epimenides paradox is a clear demonstration of this, in its simplest form can be expressed as follows, " This sentence is false ." Well
what Godel found is something of that phrase, but in the mathematical aspect. Godel
use mathematical reasoning to explore mathematical reasoning and got inconpletitud theorem.
appeared in an article of his called " About formally unspeakable propositions in Principia Mathematica and similar systems " and goes something like this.

Each class of K w-consistent recursive formulas
correspond recursive class signs so that neither v NIR gene Neg (v Gen r) belong to Flg
(k) (where v is the free variant of r)
If

think they do not understand, I agree with you, it seems Chinese, and as much as I read it, felt neither cold nor hot, I had to ask my brother to me translate it into English.
And I said that saying something more or less;
Any axiomatic theory formulation of proposals includes untold numbers.
And that if a bomb is said to exist in the theory of numbers, you can not know if they are true or false, and we are talking about natural numbers, ie numbers 1.2, 3, 4, ... .. N +1.
It is the simplest of mathematics What can we expect of other mathematical systems? Utilza
language to talk about language is something easy., while not easy to see how a proposition can numbers speak for herself. For this, the self-referential propositions use the theory of numbers.
Now I have to explain this is long, but especially complicated.
Let's see if I can;
A proposition on the properties of natural numbers, refers to whole numbers, integers are not propositions, nor are their properties. A proposition of the theory of numbers is not talking about a proposition of number theory, is only a proposition in theory of numbers. And this is the problem resolved Godel.
He thought that proposition theory of numbers could talk about a proposition of number theory (even about yourself) on condition simply make the numbers fulfilled the function of the propositions. This is to make a code. The Godel code
is commonly called "Gödel numbering " and makes the numbers performing the duties of symbols and sequences of symbols. (The first was not and I do that)
And making a specialized sequence of symbols, each proposition is that the numbers would have acquired a Godel number, something like a phone number, an IP computer through the which one can refer to it. This action allowed the theory of numbers to be understood at two levels, as propositions of the theory of numbers and as propositions about the propositions of the theory of numbers .
With this scheme of encoding and Godel had to elaborate in detail a way to transport the paradox of Epimenides the formalism of the theory of numbers.
transplanted doing so the paradox of Epimenides did not say "This proposition of the numbers theory is false" if not "this proposition theory of numbers has no demonstration."
But here we come to another problem What mean by proof?.
A demonstration is evidence within fixed systems of propositions. In this case the number theoretical reasoning system referred the word demonstration is that of Principia Mathematica , the gigantic work of Russell and Alfred North Whitehead (published between 1910 and 1913)
Therefore another way of saying what I do Godel serious;
"This statement of theory of numbers has no proof in the system of Principia mathematics "
however, this assertion is not Gödel's theorem Godel, the assertion as the Epimenides paradox, is not observed, "The assertion of Epimenides is a paradox."
With that in mind no matter what we did Gödel. While the assertion of Epimenides creates a paradox, since it is not true or false assertion is unprovable Gödel (in the mathematical principles), but true
It was concluded that the Principia Mathematica is incomplete as there are propositions true of the theory of numbers to show is very weak as the method of P. Math.
If it were all, only the method of mathematical principles and perhaps had suffered with some reforms had made another work that would eliminate that flaw. But the phrase the title of the work is very eloquent " and related systems ..." And because the theorem applies to any axiomatic system.
summarize what Godel proved was that provability is a weaker concept than the truth, regardless of the axiomatic system in question.
But that's not a "theory more" is a theorem. And a theorem is always true, and there can be no doubt, by definition.
That means-and here I extrapolate, that never, even in principle we can get to the truth. And the most serious that we can not in principle understand our own mind, using our minds.
Since it looks like a autoreferendario and you know what happens when that happens. And we said that the demonstrations of truth and falsity have a tremendous gap.
That is the limit of our knowledge, If we join Godel's theorem to the Heisenberg uncertainty, there remains almost nothing of what we know. Maybe in future
talk more about this theorem, there is still much to say, most of all its implications. And yet these implications is oco understood by most philosophers, some philosophers of science have done work on this, but it is not widespread, one of the few, but both misunderstood the implications of Godel's theorem as principle Heisenberg was Lacan, and since anyone attempted a serious approach to this revolution of thought .



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