Three hairs in Loki`s soup (questions about logic)

[Trestone]

Three hairs in Loki`s soup

In former times humans were on more familiar terms with gods and they could even bound Loki
to serve them a soup of the gods.

But Loki wouldn´t have been Loki if he thereby did not plot some tricks:

He added three hairs to the soup, which became eatable only if all were found and removed.

1) The first hair was discovered by Pythagoras and Euclid: “ The square root of two is irrational”,
i.e. it is not representable as a fraction of two integers -
and there is a infinite amount of such numbers.

As they could not remove this hair, the humans got used to swallow this irrational lumps in their soup
for over two thousand years.

2) The second hair was detected by Georg Cantor: “The cardinal number of the power set is higher than that of the set”
i.e. it has a greater kind of infinity and we can build a never ending sequence of infinities.

He could not remove this hair, but a lot of mathematicians are pleased, that so the soup will never be spooned up.
About one hundred years later this is a bit boring and some would like to know what is waiting at the bottom of the soup – instead of spooning forever.

3) The third hair of Loki was discovered by Kurt Gödel in 1931, it is named “Gödel's incompleteness theorem”:
In every axiomatic system including arithmetic there are true propositions which are not provable in this system.
(And there are much more true propositions than proofs).

This hair was difficult to find, up to now it is also not removeable.
If we imagine the provable propositions swimming on top of the soup,
we are just skinning the soup with our proof-spoons and never come to deeper regions.

 

There is a solution key as always in fairy tales:

With the soup Loki gave a spoon called “logic” to the humans and they liked to use it.
With this spoon they could eat a little of the soup, but the hairs could not be removed with it.

Who wants to get to the bottom of the soup has to carve a new one.
A first try which helps to handle the first and the second hair provides a search with “layer logic Trestone”.

The third hair being a little more complicated, the help of a mathematician would be welcome,
but chances are good.

If the soup is empty (all hairs removed) I have to find more details
for what is to be found at the bottom of this super bowl …


Yours
Trestone