Hello TonesInDeepFreeze,
Lenin is quoted with the following syaing:
“If these Germans want to storm a train station, they first buy a platform ticket!”
I am myself feeling like a German revolutionary / explorer.
But not so much as a scientist but more like Christopher Columbus:
I detected Layer Logic by chance as I am more on a philosophical than a logical journey.
My goal is to pass on the revolutionary intuition associated with the Layer Logic.
And the most important points thereby are not “platform tickets” or even Layer Logic,
but to open new ways of thinking besides classic logic,
Layer Logic itself to me looks not so complicated to understand,
but here some more explanations that might help:
The only new components are the layers.
Eight things are important about layers:
A) The layers are elements of an inductive set with elements 0,1,2,3, …
(multiplicative properties not needed)
B) All propositions P have truth values W only in combination with a layer k: W(P,k).
C) There are 3 possible truth values W(P,k): true (=t) , false (=f) and undefined (=u)
D) In layer 0 all Propositions P are undefined: For all P: W(P,0)=u
E) The truth value of a proposition P is the vector of all the truth values in all layers.
W(P) = (u, W(P,1), W(P,2), W(P,3), …)
F) A proposition P is well defined, if the truth values W(P,k) for all layers k
are well defined (one value for every layer).
G) When defining values for W(P,k+1) for proposition P all defined propostions and values
of smaller values (k or smaller) can be used - even W(P,k).
H) Layers and Propositions in layer k are „blind“ for this layer k and higher layers.
So when speaking about a property or using a value we have to change from layer k to k+1.
Analysis of most classical indirect proofs show, that with layer logic we have because of G) and H)
to use two different layers.
As true and false in different layers is allowed in layer logic there is no more
a contradiction and the indirect proofs are valid no more.
(Within a layer different truth values are still not allowed).
That is the revolutionary part of Layer Logic!
With all this formalization we still do not know what layers are
and why we did not notice them (or the new dimension) in the last 2000 years?
Well, I have already used and showed layers with the liar and with Russell`s set.
In everyday use most propably layers make no difference,
as properties may change with layers but they do not have to.
So layers mostly make a difference with infinity, selfreference and the start of cause - effect chains.
And in everyday life we all can be in the same layer that may change (simultanously)
with every physical interaction (besides gravitation) – but that is very speculative.
So that if two people look at an objekt at the same time,
they see the same propositions in the same layer.
But may be the main reason why we do not perceive layers could be,
that they don't fit into our view of the world ...
Prof. Ulrich Blau gave a more formerly definition of his reflexion logic
and his layers as „levels of reflection“ -
and he wrote a (German) book with about 1000 pages around it.
About Professor Ulrich Blau:
review about Prof. U. Blau
In German:
German Link 1 about Prof. Blau Reflexionslogik
German link 2 on Prof. Blau Reflexionslogik
His reflexion logic is only for a small part of all propositions, the reflective propositions,
where as Layer Logic treats all propositions in the new way –
as a full new logic with a new dimension, the layers.
By the way:
When I went to my first demonstration in 1989 UniMut in Berlin,
I actually bought a subway ticket before to get to the KuDamm,
where our students demonststration took place.
A revolutionary student theatre had agitated me.
Later I voted in Marburg against student strikes, but took a prominent part later.
With philosophy students and professors we performed a play of me
(“The death of Sokrates”) with also contained a (Sophistic) saying about logic:
“If logic does not apply, it can confidently continue to apply -
and that is also still thought of logically!”
So you see, I've been dealing with platform cards and logic for 30 years.
Unfortunately, my creativity and intuitions are dwindling
so I have to talk about my ideas from 30 years ago ...
Yours
Trestone