Hello,

when looking for (ultimate) justifications / final reasons, one comes across the Münchhausen trilemma:

1) One can always ask for a new reason for what has just been founded -
So ends up in an infinite regress.
2) You turn in a circle and list as a justification what was previously listed as too be justified - a circle.
3) The chain of reasons is arbitrarily broken off at one point - break off / dogmatic start.

Now the trilemma itself is an assertion that is subject to the trilemma
and leads to a self-contradiction.
(There is no final reason for the trilemma? ...)

But there is another resolution:
For the formulation of the trilemma the classical logic is used,
and the trilemma in particular could show that this logic sometimes reaches its limits.

An extension of the propositional logic to the (new) layer logic enables a new approach
with this alternative logic:
To this end, a parameter is added to each statement, the layer.
(With possible values ​​0, 1, 2, 3, ...)
The statements now only get truth values ​​in connection with layers.

For example, statement A is true in layer 1 and false in layer 2.
(Such changes of the truth value with the layers are probably rare,
otherwise we would have discovered the layer logic a long time ago ...)

The layerss are created hierarchically, i.e. in higher levels truth values ​​and properties
from lower layerss can be known,
but for the same layer and higher layers they are "blind".

The lowest layer 0 has a special role,
there all statements are "indefinite".
Now we can analyze reasons again:
The reason (or cause) must always belong to a lower layer in the layer logic
than the justified (or the effect).

Regarding 1) Since the layer is reduced with every justification,
the smallest layers 1 and 0 are reached in a finite number of steps.
Infinite recourse is therefore not possible.

Regarding 2) What is to be justified cannot become a justification and thus a circle,
since the layer has to be reduced, i.e. the same layer does not recur.

To 3) An arbitrary termination is not necessary with layer logic.
As described in 1) you can justify until you have reached the smallest layers 1 and 0.
Then it is canceled for formal reasons - and not arbitrarily.

With the additional parameter layer (and the three truth values)
the layer logic is somewhat more complex than the classical logic (Ockhams razor),
but it offers new and mostly simpler solutions to many problems:

E.g. on the liar sentence, Cantor's diagonalization, the halting problem in computer science.
By means of the hierarchy of layers, self-references can be eliminated without antinomies
(and they are possible and allowed – other than in Type hierarchy).
They get under control by using layers without them having to be banned.

In the set theory of layers there is only one infinity, the countable sets and the set of all sets is a set.

The time doesn't seem to be ripe for such a new logic
because also the reflection logic of Professor Ulrich Blau,
who invented a somewhat more restricted layer logic twenty years before me
had little response.

If you want to discuss the layer logic,
here links with more detailed information:
www.researchgate.net/post/Is_this_a_new_valid_logic_And_what_does_layer_logic_mean
In German:
www.ask1.org/threads/stufenlogik-trestone-reloaded-vortrag-apc.17951/#post-492741
About Professor Ulrich Blau:
https://ivv5hpp.uni-muenster.de/u/rds/blau_review.pdf

In German:
https://link.springer.com/chapter/10.1007/978-94-017-1456-3_20

https://books.google.de/books?id=9x...kQAQ#v=onepage&q=reflexionslogik blau&f=false

I am also interested in how one can otherwise deal with the Münchhausen Trilemma?


Yours
Trestone