Church St Station Is It Closed

Without a certain amount of madness,
firmly believe nobody can be in possession of truth, since
believe the truth is precisely madness
.

Nietzsche

was a logician Kurt Gödel, Austrian mathematician and philosopher-American, recognized as one of the most important of all time. His work has had a huge impact on the scientific and philosophical thought of the twentieth century. Gödel, like other thinkers such as Bertrand Russell, AN Whitehead and David Hilbert tried to use logic and set theory to understand the basics of mathematics. It is best known for his two incompleteness theorems, published in 1931 at 25 years old, a year after finishing his Ph.D. at the University of Vienna.

The most celebrated of his theorem says that for all co axiomáti system self-consistent recursive powerful enough to describe the arithmetic of natural numbers, there are true propositions that can not be proven from axioms. To prove this theorem developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.





In 1931 Gödel published his famous incompleteness theorems in "Über formal unentscheidbare Sätze der Principia Mathematica und Verwandte Systeme" ("On formally undecidable propositions of Principia Mathematica and related systems"). In that article postulated that for any computable axiomatic system that is powerful enough to describe the arithmetic of natural numbers (eg Peano axioms ), it follows that:

1-If the system is consistent can not be complete. (This is generally known as the Incompleteness Theorem.)

2-consistency of the axioms can not be established from within the system.

These theorems ended half a century of scholarly attempts (beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism) to find a set of axioms sufficient for all mathematics.






The basic idea of \u200b\u200bthe incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims to be non-provable for some system formal. If it would demonstrably false, which contradicts the fact that in a system consisting of provable statements are always true. So there will always be at least one true but unprovable proposition. That is, for every set of axioms of arithmetic constructible by man there is a formula which is obtained from the arithmetic but unprovable in that system. However, to clarify that Gödel needed to solve several technical issues, such as proposals for codification and the very concept of provability in the theory of natural numbers. The latter is done through a process called Gödel numbering.

made important contributions to proof theory, to clarify the connections between classical logic, intuitionistic logic and modal logic. It also showed that the continuum hypothesis can not be disproved from the accepted axioms of set theory, if those axioms are consistent.

born April 28, 1906 in Brno, Austria-Hungary (now Czech Republic) and died on January 14, 1978 in Princeton, New Jersey.




truth.

(Del lat. Veritas,-atis).

1. Conformity of things with the concept that they form the mind.

2. Conformity of what is said with what feels or thinks.

3. Property that has always kept one thing from it without any mutation.

4. Trial or sentence that you can not rationally deny.


axiom.

(Del lat. Axiom, and it's gr. Ἀξίωμα).

1. So clear and obvious proposition that is accepted without proof.

2. Mat. Each of the fundamental principles and unprovable on which to build a theory.


theorem.

(Del lat. Theorema, and east of gr. Θεώρημα).

1. Demonstrable proposition logically from axioms or other theorems already demonstrated by accepted rules of inference.

Source: Wikipedia, DRAE
Images: GM