In mathematics there is God

European mathematicians proved after 40 Years the theory of the existence of God's God with the help of computer
There is God; This question has been concerned with philosophers and theologians for tens of centuries. Suddenly a few months ago the news appeared that two European mathematicians, using a computer and the relevant theory……..

of Austrian mathematician Curt Gentel, managed to prove mathematically the existence of God! What exactly they proved and in what way is directly related to the understanding of Mathematical Logic and the rules that govern it.

The God Theorem
Shortly before his death the great Austrian mathematician Kurt Gödel (Kurt Gödel) published a mathematical proof for the existence of God which he had been working on 30 years. This proof is based on modern officer foundation of mathematics, which in turn is a continuation of the ancient Greek mathematical tradition and Euclid's Geometry. In this way of foundation we begin by formulating postulates, that is, assumptions that are not proven but seem obvious.

Subsequently, with the help of axioms and Mathematical Logic, we can prove theorems and build a whole theory. For example, One of the five posts of Euclidean Geometry is that all right angles are equal to each other. Gentel tried to "prove" God's existence as a theorem starting with a set of five axioms that seem "obvious" in the context of mathematical logic.

This "proof" appeared from the beginning to have two weak points. Firstly, are the axioms really obvious and, secondly, are they compatible with each other so that they do not have hidden inconsistencies?; 

We can't do much about the first one, since axioms in Mathematics may seem "logical" but are otherwise arbitrary, so God exists if these posts are true. But the second was the subject of research for over 40 years because it had to be shown that these five postulates do not contain hidden contradictions and are therefore self-consistent.

The feat of two European mathematicians, by the German Christoph Benzmiller (Christoph Benzmüller) and the Austrian Bruno Wolzenlogel Paleo (Bruno Woltzenlogel Paleo), was that they managed to represent Gödel's postulates and his reasoning with mathematical symbols. Subsequently, with the help of specialized software that handles logic concepts on a computer, They were able to find that posts do not contain hidden contradictions on the one hand and to confirm the proof of the theorem.

Idea with ancient bases
It should be noted that, beyond the purely mathematical part, The basis of Gödel's proof of the existence of God was not entirely new since it resembled the argument of the 11th century English theologian and philosopher Anselm of Canterbury, which, in turn, it is based on the method of "abduction out of place" of the ancient Greek philosophers and mathematicians. Anselm's reasoning was as follows:

1. God is the supreme being.

2. The idea of ​​God exists in our thinking.

3. An existence that exists both in thought and in reality is superior to an existence that exists only in thought.

4. If God only existed in our thoughts, then we could conceive the idea of ​​a higher being which exists in reality.

5. But we cannot imagine a being higher than God.

6. Well, God actually exists.

Gödel's main contribution was the mathematical description of the above reasoning and especially the signs 3 and 4. There he used the concept of the possible truth of a sentence, which extends Aristotelian logic which accepts that a proposition is either true or false.

1+1 they do 2;
Gödel became famous at a young age when he formulated the famous "incompleteness theorem". A consequence of this theorem is that, in the context of "Simple Arithmetic" of whole numbers, which is based on axioms such as the well-known "1+1=2", there are propositions that it is not possible to determine whether they are true or not based only on these axioms.

These propositions are characterized by a self-reference and their best-known analogue in the context of simple logic is the paradox of the ancient Greek philosopher Eubulides, according to which “if someone admits to lying, what he says is true or false;».

This proposal leads to a vicious circle, since if the sentence is true we conclude that the interlocutor is lying while if the sentence is false we conclude that the interlocutor is telling the truth. Gödel's incompleteness theorem had very serious consequences in the foundation of Mathematics based on the axiomatic method, which in his decade 1920 it seemed that he would succeed in uniting all the branches of this science into a single edifice.

At the same time, however, there was the reason he was offered the 1940 a position at the Princeton Institute for Advanced Study, where he remained as a professor until his death 1978. Gödel's contribution to the foundation of Mathematical Logic has been recognized repeatedly, most importantly in my opinion the Institute's Einstein Prize awarded to him the 1951 by Einstein himself, who was his colleague in this institution and his close friend.

The circumstances of Gödel's death were very unusual and were the inspiration for the play "Seventeenth Night" by Apostolos Doxiadis. Gödel was suffering from a duodenal ulcer and was following, on his own initiative, a very strict diet. He slowly began to believe that he was being poisoned and ended up refusing to eat his food.

The result of this situation, one would say, constituted the ultimate logical paradox realized – and not formulated – by the founder of Mathematical Logic. If he didn't eat, it was certain that Gödel would starve to death. If he ate he might die of poisoning – but maybe not. Godel, beyond all reason, consciously choose the first option – and died of starvation.

Mr.. Haris Varvoglis is a professor at the Physics Department of the AUTH.
Source : tovima.gr
NewsRoom Mykonos Ticker