Hello Mark Nyquist,

yes, I am using here two (similar) theories:
A new logic, called „layer logic“ that helps to avoid contradictions
(by putting „true“ and „false“ to different layers)
and a „layer theory“, that the propositions of the (mental and physical) objects
of our world are also organized in layers,
what I use to construct a new model for body and mind.

Important: In both theories the "layers" are not physical but part of a new logic dimension
(a little like a new dimension of time, connectected to cause and effect).

Yes, the problem that my cycle times of body and mind are much shorter than human reaction times should be considered.

A solution could be, that many cycles (and layers) work together for a reaction.

Yours
Trestone

Layer logic and a model for body and mind:

Hello,

I have already indicated here on various occasions that my new layer logic
can handle (apparent) contradictions well and can usually even resolve them
with different layers.

So it is not surprising that this also applies to body and mind,
who face each other with very different characteristics.

Baruch Spinoza (1632–1677) believed that there is only one substance (God)
which in the different perspectives, namely appears in "thinking" as spirit
and as "expansion" as body,
my basic idea for this (except for the layer logic) already anticipated.

The layers of the layer logic can be seen as perspectives,
from which an object can have very different properties.
(Although partly hierarchically dependent on one another,
the layers can be seen as separate worlds with their own rules.)

So if the "object" is the liar sentence LS
("This statement LS is true in layer k + 1 if it is not true in layer k, otherwise false)
it is true in odd layers and false in even layers.
There has been an experience since ancient times that is expressed as follows:
“Natura non facit saltus” (“Nature doesn't make jumps”).
This originally refers to the physical / body world, but we also experience
our spiritual/minds world mostly without leaps.

Nevertheless, I propose a model for body and mind,
which even has an extremely large number of jumps,
however, these are hardly noticeable.

The simple idea is that body and mind properties are combined alternating in the layers, like the truth in the liar:
In the odd levels 1,3,5,7, ... objects would have body / physical properties,
in the even levels 2, 4, 6, 8, ... mind qualities. (or the other way around).

In the interaction between body and mind, therefore, no energy would have to be transferred, because e.g. a pain neuron could be activated in layer 2k-1
and a feeling of pain occurs in layer 2k.

But this is possibly an incomplete view:
According to layer logic, the contents of a layer k can depend on the contents of
all smaller layers, i.e. not just on the previous layer.

I had already considered that layer increases could be triggered (globally)
by (local) interactions.
Since the Big Bang, that's roughly 10 to the power of 120,
so a lot and extremely short layer changes.
Why don't we notice that?

- The body layers probably have no perception, so when we perceive
we are always in a mind level.
- The spirit/mind layers are also not outside / above the layers,
can only perceive the inside of the mind.
- In the mind layers the (very) short changes to the physicals layers can not be noticed.

- Successive mind layers are very similar, therefore nature does not “jump” for us.

How is human mind / consciousness explained?
Spinoza already saw God as the general spirit, in which the human "consciousnesses" appeared as parts.

In my model one can also accept God (or something similar) as a universal spirit/mind and human consciousnesses / minds parallel to every human nervous system.
The universal body would be the physical universe.

Important: No subsequent layer (mind or body) is only an image of the previous layer, because the properties of an object in one layer are made up of properties of the object and properties of the layer (Greetings to Immanuel Kant) together.

With layer theory we do not have mind and body:
We have a rapid succession of mind and body
both reflections of an hidden object in different layers.

So neither realism nor idealism.
With layer theory we would be "citizens of a world with two sides",
which seems also to be close to our everyday experience.

Yours
Trestone

Hello,

In my model, the mind can either act targeted via its coupled body
or act on the world in an untargeted manner that cannot be shielded via gravity.

The fact that gravitation cannot be shielded could be due to the infinite layer of the mind.
With a gravitational interaction there is no layer increase,
therefore it cannot be shielded.

A mind that is not coupled to a body (= dark matter) can therefore probably
not actively affect the world,
but is "passively at the mercy of gravity",
so very similar to the classic matter.

The coupled body is not a “prison” for the mind (as Plato says)
but rather a “free space”, that allows free decisions for the mind.

But the existence as "dark matter" or an animated pure spirit, completely incapable of action,
I would not wish my worst enemy, that seems deeply unfair to me.

Perhaps the mind-body connections can be broken in the long run
and new pairings are made.
Candidates for this would be black holes and a big bounce,
i.e. a return to the big bang in layer 0 and the coupling in layer 1.

But whether my moral ideas play a role in the construction of the world remains questionable,
what speaks for that idea is that I am part of this world,
on the other hand, what speaks against it is
that our morals hardly fit for the human world ...


Yours
Trestone

Hello,

Here again a summary of what happens from the point of view of the layer logic
to mind-body has revealed:


If you look at the universe and the Big Bang,
so it begins with an "apeiron" (everything physical / physical is indefinite)
in level 0
and parallel to it with the mind (which is particularly subject to gravity)
in the infinite level.

These two types of objects come together in level 1,
there, in particular, the first physical objects and bundles of energy are created.

In doing so, the mind objects are forming depending on their gravitational properties
suitable physical partner objects.

So to a mind object with an electron mass an electron is formed/connected,
to a mind object with proton mass a proton etc.

The physical (elementary) objects form analog to the gravitational structure
of the elementary mind objects.

Since one never observes a physical object without gravity,
every physical object has a (suitable) mind partner.


The dark matter could be composed of mind objects without physical partners
(therefore only gravity is effective),
is therefore probably “pure mind”.

The missing physical partners of the mind objects in "dark matter"
could have three causes:

A) The gravitation is too big for elementary physical objects

B) The gravitation is too small for elementary physical objects

C) In stage 1, no physical partners could be bound for these mind objects.


The bond between the elemental mind objects and the elemental physical objects
seems to be extraordinarily strong
(may even hold in a black hole),
since one never observes isolated physical objects (without gravity).

I do not know what type of bond this is, perhaps the enormous vacuum energy indicates
(10 to the power of 120),
what order of magnitude it could be.
The model is a dualistic model, but with three special features:

1. The inclusion of levels (level infinite for the mind, levels 0, 1, 2, 3,…. K
for the body.

2. Gravitation is bound to the mind, the other three interactions to the body.

3. Spirit objects and body objects are strongly bound to each other from level 1 onwards.

Because of 3. (and 2.) one could even speak of objects
that unite all mind-body properties, only 1. contradicts this.

In the model, the mind is leading because it is the first to show structures
and the bodies are modeled accordingly from level 0.
Conversely, we can use the resulting physical structures
inferring analogous structures of the invisible mind
(e.g. nervous system).

Functionally complement and differ the physical and mental structures,
e.g. Qualia in the mind.

How overarching structures build up in the mind from the elementary structures
(e.g. Consciousness, Self) remains open.

The latter dissolve at death, but not the mind-body bonds on an elementary level.
The elementary spirit objects from the layer of infinity are probably timeless / eternal.

For an immortal soul (overarching spirit structure) the model offers
but few arguments.

It is true that a new mind can, for example, become one again
for a new human body,
but like the new body it probably has little to do with the old mind,
it is probably composed of a completely new combination of elementary mind particles.

After all, the model can explain well why the spirits of children
are similar to the parents and ancestors (how this can work with transmigration of souls, Lucretius had already asked himself):
Analogous to the body DNA, there is probably a coupled mind DNA,
whereby the inherited mind properties are of course somewhat different.
After all, the model strengthens a panpsychic approach from layer 1 on.

I had shown the possible interaction between mind and body with quantum selections
(and time-inverse virtual particles of possibility).

Presumably is a prerequisite for having coupled mind-body particles
when choosing, because we cannot use just any body with our mind
influence, but only our own (and possibly only through our nervous system).

Probably the model still needs to be adjusted,
since I definitely do not have an overview of all the problems
that have been raised.

Yours
Trestone

Hello,

if we also include gravity in the quantum layer model,
then the following could happen:

A particle travels on several possible paths from the start to possible destinations,
at the same time it is invisible as a virtual particle of possibility and on the same layer
like at the start.

Gravitation acts on all of these particles.

Then the virtual particles of possibility return inverse in time to the start.

At the start the situation is the same as it was before the swarming out
the particle of possibility, only that now (hidden) information
about the possible goals are available.

In particular, the gravitational effects are canceled again.

After selecting a target particle (or a target package if several paths are possible),
this particle receives a higher level and becomes real.

Gravitation then also acts for this particle and its path (and only for this).

But whether that fits with current quantum gravitational research
I can not judge.

Yours
Trestone

Hello MAYAEL,

layer logic and the ideas given here are theories.

It might take some years (probably some 100 years) until some of them can be proven by experiments
(I already gave hints how it could be done with computers for layer logic,
but it is not easy).

So for me the value of the ideas is to give alternative and uncommon theories and play with them,
but the theories should be possible within the new frame of layer logic.

Yours
Trestone

Hello MAYAEL,

I want to show, that the new logic (layer logic) that I have developed
can also be used to develop new models for other questions
like parts of quantum physics or body and mind and gravitation.

As I know well layer logic but not physics,
I hope to discuss here, if my models are possible
or what has to be changed.

Yours
Trestone

Hello,

admittedly, the model seems a bit awkward and complicated.

But that both also applied to the models of Ptolomew and Copernicus.

Whether the two new ideas apply
("There are finite layers and an infinite layer",
"Gravitation belongs to the mind"),
must remain open for the time being.


Yours
Trestone

Hello TonesInDeepFreeze,

there could be a closer connection between children and my math
than can be seen at first glance:
When Layer Logic spreads in 100 years
maybe children will have to learn it in school too
(and hate me).

Yours
Trestone

Hello,

Perhaps my mistake is, that I didn`t pretend enough
this work on Layer Logic is fun
and I didn´t wait for passers-by to offer me an apple
to replace me for some time ...

I also like the view of Pippi Longstocking:

"2 times 3 make 4
Widdewiddewitt and three makes nine
I’ll make the world
widdewidde the way I like it."

Yours
Trestone

Hello,

from a German philosophy TV discussion today I learned,
that ingeneering (= “ingenius engineering”) needs positive visions.
So maybe I should concentrate more on what new things are or could be possible
with Layer Logic than showing what no longer works.

Perhaps someone will help except saying “none”...

Yours
Trestone

Hello TonesInDeepFreeze,

Is it good or bad to be ridiculous?

Yours
Trestone

Hello TonesInDeepFreeze,

about a month ago I wrote a fairytale about layer logic,
based on this story with The Emperor`s Clothes.

The role of the Emperor and the boy/child is played by other people in my version ...

Link to German fairytale:
https://www.leselupe.de/beitrag/der-logik-neue-kleider-146395/

In English:

The Logic´s New Clothes

Once upon a time there was an emperor who loved science.
He called many bright minds around him who were eagerly researching.

One day two logicians came and made their discipline palatable to him
with the following words: Our logic is not only two thousand years old,
it is also the basis of all science and only those who are stupid
and not suitable for true science cannot understand it, because it is very easy.

The Emperor did not understand why he needed this logic now,
and so he asked deserved statesmen and ministers what they thought of it.
They did not want to show any nakedness and emphasized the universal validity
and unquestionable truth of the new logic.

So the emperor dared to go to the streets with the new old logic.
Even when the root of 2 turned out to be irrational by means of logic,
one could suddenly find uncountable infinite sets and the arithmetic showed
that most true sentences could not be proven, this was seen and believed
as an indication of the sophistication of this logic.

"But the logic has no clothes on - it doesn't work!" finally called a little child.
Then they quickly threw logic a few layers over and ended the procession.

There is also a story where I compare myself with Kassandra,
the prophetess that nobody listens to.

German link:
https://www.leselupe.de/beitrag/die-logik-von-troja-146428/

In English:

The logic of Troy

Troy had withstood the siege of the Greeks for ten years.
The voices calling for Agamemnon to withdraw grew louder and louder.
Odysseus called for the carpenters and started one last trick.
The Greeks withdrew with all their ships and left behind on the beach
just a huge wooden horse.
It was supposed to grant Athena's blessing on the journey home
and was dedicated to her Logos.

With the Trojans, Laocoon and Kassandra warned against bringing
so calamity into the city.

But Laocoon and his sons were killed by a snake sent by Athena -
whoever kills is right, that is the logic of the Greeks and Trojans!

And although Kassandra always prophesied the truth, no one believed her anymore,
because Apollo, who had been rejected by her, had cursed her gift of vision this way.

"Do you really want to break down the walls of common sense for this Danaer gift?" -
They did it with joy and had a feast.

The Greeks who crawled out of the horse's belly late at night,
then celebrated an orgy of a completely different kind,
opened the gates for the returning warriors and slaughtered Troy with fire and sword.

And since nobody listens to Kassandra's calls for alternatives even today,
we still use the captivatingly simple logic of the Greeks and Trojans ...

Yours
Trestone

Hello,

maybe it helps if we try imagination:

First we add a layer (0,1,2,3,...) to every statement with a truth value.
For example “The liar statement is false – in layer 2” and
“The liar statement is true – in layer 3”.

All statements in layer 0 will have the value “undefinded”,
and in all higher layers every statement has exactly one of the values
“true”, “false” or “undefined”.

Then we define truth values of statements by using higher layers
for the defined values and lower layers for the defining ones.
For example “Statement LL is true in layer k+1, if LL is not true in layer k
and LL is false in layer k+1 else.“

And fourth we use classic 2-valued logic and statements as meta logic
if we talk about layer logic, especially if we talk about layers or truth values
(like in the rules above).

And last we imagine a world where we all live in the same invisible layer
that grows with time.

What consequences would all this have for logic and math?

I believe there would be fewer contradictions
and there could be a rather simple set theory.

Yours
Trestone

Hello TonesInDeepFreeze,

you remind me of the border guard
who demanded the TAO-TE-KING from Laotse.
(Again a comparison to a famous person ...)

Unfortunately, I am unable to write down my ideas in 1000 lines
of beautiful Classical Chinese.

Therefore, here a short poem by me in German and English
and quotations from the beginning of the TAO-TE-KING.

Logeric
Es pendelte ein Philosoph mit der Bahn
nahm sich dabei der Logiklücken an
verhedderte sich in Stufen
denn die Geister die er gerufen
verlachen Logik als Wahn.

A philosopher commuted by train
took care of logic gaps there in vain
tangled up in layers
called spirits in his prayers
that laught at logic in wane.

TAO TE KING (Laotse, Geman by Richard Wilhelm)
Der Sinn, der sich aussprechen läßt,
ist nicht der ewige Sinn.
Der Name, der sich nennen läßt,
ist nicht der ewige Name.
"Nichtsein" nenne ich den
Anfang von Himmel und Erde.
"Sein" nenne ich die Mutter der Einzelwesen.
...
Des Geheimnisses noch tieferes Geheimnis
ist das Tor, durch das alle Wunder hervortreten.

TAO TE CHING (Laotse, English by Stephen Mitchell)
The tao that can be told
is not the eternal Tao.
The name that can be named
is not the eternal Name.
The unnamable is the eternally real
Naming is the origin
of all particular things.
...
Darkness within darkness.
The gateway to all understanding.

Yours,
Trestone

Hello EricH,

originally the Layer Logic was only a theory and a new logic system
like others.
So I handled truth values with Layer Logic but I did not bother what truth really was.

Later I noticed, that I could descripe cause and effect with layers,
and now all measured properties are described by me with layers.
Here I am near to Factual Statements.
But why would we need the real physical world for "This sentence is false"?
It is a logical proposition to me and so part of the logical world
(but I can not decide wether it is true or false).

Transferred to Layer Logic the liar LL has different events/objects in different layers:
„For all k=0,1,2,3,...: This proposition LL is true in layer k+1, if LL is not true in layer k
and LL is false in layer k+1 else.“

The definition of the truth value of LL in layer k+1 only depends on values of layer k.
This values are like events/objects in layer k (here logical and not physical).

As I showed this definitions lead to alternating truth values u,t,f,t,f,t,...,
and there are no problemds with the truth v alues any more).

The idea with Layer Logic is to use a classic logic (like L3 of Łukasiewicz)
and add layers 0,1,2,3,4,... to it – for every time a truth value is determined.

Using the layers hierarchical when defining propositions,
most paradoxes and antinomies can be avoided.
And proofs that use contradictions are mostly valid no more,
as true in one layer and false in annother layer are allowed truth values.
So the Layer Logic helps at much more problems than only the liar.

The use of self references is explicitely allowed in Layer Logic,
it is only not allowed within a layer.

LL is a sentence that makes perfect sense in Layer Logic,
it is an example of a sentence with changing truth values with different layers.
Classic logical sentences would have a constant truth value in all layers,
except in layer 0 where all layerr statements have the value “undefined”.

But there is a more factual use / interpretation of Layer Logic:

if an object in physics has a measured proposition,
whe can apply a layer to this measurement:Objekt O has proposition p in layer k
(= when measured in layer k).

Now I think that if there is a physical interaction (not gravity) around O,
the layer in the sourrounding will increase (say to k+1).

As there are physical interactions all the time,
we only have to wait a very short time to get a new and higer layer
(for example in a computer).

So if we have a property, that changes from layer k to layer k+1,
we just have to wait untill both layers are reached one after the other.
Such a property could be the prime decompensation of a large number n.

And so we could see in a physical experiment that there are layers
(or something other strange).

Yours
Trestone

Hello jgill,

in my eyes you do not have to install Layer Logic on a computer:
It`s already there.
(Of course this is only a daring hypothesis of me.)

It is the same as with the General Theory of Relativity,
Eddington had not to install it to the sun andf the light rays,
it was already part of the world (if it was true).

In everyday life we do not notice that we have Layer Logic instead of classic logic,
as most propositions are not layer dependent.
But prime decompositions of very large numbers could be.

I assume that the the change of layers is very easy in everyday life
(and in computers):
we just have to wait for some time.

(More exact: We have to wait for the next physical interaction
(not by gravity) in our environment.
And with every evaluation a computer has to use a new layer)

As usually propositions do not change with layers,
we do not notice this change of layers in our surroundings.

But the layers could be there all the time ...

Yours
Trestone

Hello TonesInDeepFreeze,

there are two problems:

First, even having studied mathematics 30 years ago,
I never liked the formalisms.
And when studying philosophy, my feeling was,
that the (formal) approach to logic was not good.

In oppsition to all this I developed my new logic
using and developing my own notations over almost twenty years –
in (mostly German) discussions and not in a very systematic way.

Over the years less and less reactions came to my writings,
so now I am used to being “a voice crying in the wilderness”.

The second problem is, that meanwhile I can hardly take
the position of someone to whom Layer Logic is new.

To me all looks easy and clear – as I have lived with it for so long time.
Here questions can help, but point one is a problem.

And maybe unconsciously I want to be the only one
who understands Layer Logic,
so that I am the only one who can play with it ...

Yours
Trestone

Hello TonesInDeepFreeze,

in the German link to layer logic there are some more definitions.
Layer Logic in German at ask1.org

For example this to the natural numbers (here in English):

N1: Definition of successor function M+ for level set M
(for the construction of natural numbers):

Vt> 0: W (x e M+, t + 1): = W (x e M, t + 1) v W (x = M, 1)
Let us consider the 0: W (x e 0, t) = f for t> 0.
“Zero” is therefore empty from t = 1 (independent of the level).

1 = 0 +: W (x e 0+, t + 1) = W (x e 0, t + 1) v W (x = 0.1) = W (x = 0.1)
From t = 1, "one" contains exactly the one element "zero".

(Therefore 0 is not the same as 1).

General: n + contains exactly the elements n, n-1,…, 1 in level t> 0

The addition can now also be defined in the same way as the classic procedure:
W (xen + m+, t + 1): = W (xe (n + m)+, t + 1) = W (xe (n + m), t) v W (x = (n + m), 1 )

As natural numbers are layer sets in layer set theory,
I have to define what n>m means (and to be more exact, what it means in layer k).

I propose, that a natural number set n is greater than a number set m in layer k,
if n has more elements than m in layer k.
As x always has the same elements as x in layer k>0
we can say, that in all layers k>0 there is no x that is a layer natural number
and that fulfills x>x.

Yours
Trestone

Hello TonesInDeepFreeze,

thank you for still answering me!

I do not think that we will in near time agree on the main points of Layer Logic,
but to have a look from different sides helps me to understand,
where open questions and points might be.

With the two examples with the “~” I made a mistake, as you noticed:
I thought the “~” refered only to the next sign, and not to the whole term.
~0=1 Trestone: true in layer math and
~Ex (x is a natural number & x>x) Trestone: true in layer math

Perhaps this is exemplary: If we are not used to the language of the other,
even small misundestandings can create totally wrong interpretations.
(And probably most times I am wrong).

Looked upon only as a theory, it is not nice, that natural numbers might have
different prime decompositions in different layers.

But it could help my theory without being fully formalized:
If (perhaps in 100 years) we handled big enough numbers (with computers),
the following could happen:
On one day we get for a number n the prime decomposition P1.
One week later we get on the same computer with the same program for n
another prime decomposition P2 (and similar disturbing results with other computers).

(After a speculation of me, there are layers in the real (physical) world,
and they increase with every physical interaction (except gravity).
So to increase layers we only have to wait a little time.)

Most probably this will be handled as computer bugs
and nobody will remember Layer Logic.

But by chance somebody might check even old articles -
and Layer Logic could be one of the candidates to explain the surprising effect.

As I can not tell how large n and the layers have to be,
I can not say how long we will have to wait for an Arthur Stanley Eddington.
(Yes, now I have compared myself with Albert Einstein,
but he is already part of my nickname)

So “sit and wait” is maybe not the worst strategy to develop Layer Logic ...

Yours
Trestone

Note: In my previous posts, anywhere I mistakenly wrote 'level' I meant 'layer', as I guess would be obvious anyway.

↪Trestone


In ordinary mathematical logic, contradictions are syntactical, not requiring assignment of truth values. Meanwhile, as far as I can tell, your layer logic is described primarily semantically in terms of truth values; I don't know the syntax of whatever proof system you have in mind, so I can't evaluate the means by which you would prevent (syntactical) contradictions. You could assert that provability entails soundness, but we need to prove that, not just assert it, and you can't prove it without first stating what the proof system is. — TonesInDeepFreeze

Trestone: I do not fully understand, as I do not know the technical terms (syntax?, proof system?).
For me a contradiction is, if the same statement is shown as true and not true.
In layer logic the statement has to be in the same layer,
as being true in one layer and being false in another layer is allowed and no contradiction.
That stands without your response.

I would guess that layer logic does disprove contradictions. That is, layer logic disproves all formulas of the form 'P & ~P' (where they "reside" (or\e whatever way you say it) in the same level [should be layer]). — TonesInDeepFreeze
Trestone: No, only when there are different layers used.
In most classical proofs that are indirect or by contradiction,
different layers are used, if they are transferred to layer math,
so many are disproved, but not those in the same layer.

Is my guess correct?

And does layer math prove the following?:

~0=1 Trestone: false in layer math

and

~Ex (x is a natural number & x>x) Trestone: false in layer math

And you admit that layer math does not prove the fundamental theorem of arithmetic. So layer math would not seem to offer much as a mathematical foundation anyway.
Trestone: It is not so good for multiploikation and primes - b ut what if the real worl is so?

what you say is that there are three truth values and that statements are evaluated at different levels [should be layers]. You haven't given even the starting point: description of evaluation of truth and falsehood for atomic sentences, compound sentences, and quantificational sentences. — TonesInDeepFreeze
Trestone: In many cases it helps, that in layder 0 all sentences have truth value "undefined".
That often can be used for starting. More I have not looked upon yet.

That stands without your response.

how I handle the proof of the halting problem — Trestone


You begin with:

with layer logic we have to add layers if a program has to give a value/result:
A given program halts or not in layer k for given input data. — Trestone


But no axioms or rules of inference by which to claim that.

So to follow along with you in your layer math, one just has to accept the arbitrary lines in your arguments as given by you personally (there is no objective codification). You do not provide one with a way to check whether the lines you put forth are axioms or theorems of layer math but instead one must rely solely on your dicta as to what constitutes a valid line or inference in an argument.

Trestone: Yes, I have not developed a full layer informatics, I just added layers to programms,
that give a result. That was enough to abandon the Halting problem and
create Non-Turing algorithms.

my earlier handling of Cantor´s diagonalization and proof in layer logic — Trestone


You begin with:

(t marks the layers, W(x,t) ist the truth value of x in layer t, -w stands for „not true“ or „false“
ther value „undefined“ I left out to make things easier).
Be M a set and P(M) its power set and F: M -> P(M) a bijection between them (in layer d)
Then the set A is defined with W(x e A, t+1) = w := if ( W(x e M,t)=w and W(x e F(x),t)=-w ) — Trestone


In ordinary logic, truth values apply to sentences. It seems that had previously been the case in your discussion of layer logic too. Here you mention the truth value of x, So I take it that x ranges over sentences there. But then we find x ranging over prospective members of the set A. So which is it? x ranges over sentences or x ranges over prospective members of sets? So far, what you've given is pseudo-math or gibberish dressed up with undefined math/logic-sounding verbiage.

Trestone: x is a member of a layer set and therefore itself a layer set.

Also, you mention things (which I guess are sentence) as being true or false in layers, but now here we find that functions too are things in layers. But you've not stated what a layer sis or what kinds of things can be in layers or, as I mentioned earlier, how it is determined a given atomic, compound, or quantificational sentence is true or false in a layer.

Trestone: Yes, I am not very precise. Everything where you can ask if it has a truth value
(is it true, falser or undefined?) needs a layer in layer logic/math.

F: M -> P(M) a bijection — Trestone


Are you there asserting that there exists such an F? If you are, but without first proving the existence of such an F, it would seem to be question begging, since by supposedly refuting Cantor's theorem, you're claiming to prove that there does exist such an F.

Trestone: like in the proof of Cantor, I asume herre that such a F exists.

the proof about the power set can be similary be "unproofed" like the halting problem — Trestone


Just to be clear, these are all distinct:

(1) A proof of ~P in a given system..

(2) A meta-proof that P is not a theorem of given system.

(3) Pointing out a line in a purported proof of a given system that it is not actually an allowed line in that system (i.e. pointing out where a purported proof is not an actual proof).

(4) A meta-proof that P is false in a given model of a given theory.

So, letting P = Cantor's theorem, do you you claim either (1) or (2) regarding layer math? (I take it that you do claim (4) or something like it.)

Trestone: (5) I do not disprove the original P of Cantor,
but a transferred P2 in a new model, layer math.

His new world is pure nonsense and fantasy for the Cave people. — Trestone


That's question begging. One can just as well say you've not left your own cave, as you are not familiar with the logic and mathematics that has been explored by generations of logicians and mathematicians who have themselves studied alternatives including types, orders, levels in set theory, quantification over theories themselves, modalities, possible world semantics, topological semantics, and even para-consistency. — TonesInDeepFreeze

Trestone:
"You will know them by their fruits" (Matthew 7:15-20)
Even if Matthew warns here of bad people,
I am astonished what new fruits (not only in mathematics)
are in range with layer logic.

Yours
Trestone

Hello TonesInDeepFreeze,

I am sorry that I can not answer most your questions to formal details.
As I said, my studying math is over thirty years ago.

The idea with layer logic is, that all is as in classic (three valued) logic,
only that layers have to be added, if a truth value is used or looked upon.

Professor Ulrich Blau has done all the formal work for his reflexion logic,
so i assume the formal part for layer logic should be possible.

Now again to the proof of Cantor:

What is the first line in each of the below proofs that is not allowed in layer math?

Show: There is no function from a set onto its power set.

In layer math we have a different kind of sets, the layer sets.
And if something is "true" or "false" we have to give a layer.
So we look onto a proof were all terms are transferred to layer math - we are in the "new world".

Proof :

Let f be function from S to PS. Let d = {x | xeS & ~xef(x)}.

Now I transfer this to layer math: F is the layer function for f.
M is the layer set for S.
And A is the layer set for d.

Be M a set and P(S) its power set and F: M -> P(M) a bijection between them (in layer k)
Then the set A is defined by W(x e A, t+1) = w := if ( W(x e M,t)=w and W(x e F(x),t)=-w )
A is a subset of M and therefore in P(M).
A e P(M) (analog to d e PS).

If d is in range(f), then for some x in S we have d=f(x).

Transferred: If A is in range(F), then for some x0 in M we have A=F(x0).

If xef(x), then ~xed, so ~xef(x).

If ~xef(x), then xed, so xef(x).

Contradiction. So d is not in the range of f. So f is not a function from S onto PS.

Now comes the part, where layers make the difference:

So it exists x0 e M with A=F(x0).
First case: W(x0 e F(x0),t) = w , then W(x0 e A=F(x0), t+1) = -w
(no contradiction, as t and t+1 are different layers)

Second case: W(x0 e F(x0),t) = -w then W(x0 e A=F(x0), t+1) = w
(no contradiction, as t and t+1 are different layers)

So in layer math, the existence of F does not lead to a contradiction.
(And the set All with identity to P(All)=All even is an example in layer set theory).

I hope you have a little understanding for a "Columbus",
who accidently sailed to a new world, but is neither a governor nor a cartographer
and if asked where he was, tells something obscure about "India".
Nevertheless there could be a new world ...

Yours
Trestone

Hello,

I have found my earlier handling of Cantor´s diagonalization and proof in layer logic:

As All, the set of all sets, is a set in layer theory, it is no surprise,
that the diagonalization of Cantor is a problem no more (I just give the main idea):

 (t marks the layers, W(x,t) ist the truth value of x in layer t, -w stands for „not true“ or „false“
ther value „undefined“ I left out to make things easier).
Be M a set and P(M) its power set and F: M -> P(M) a bijection between them (in layer d)
Then the set A is defined with W(x e A, t+1) = w := if ( W(x e M,t)=w and W(x e F(x),t)=-w )
A is a subset of M and therefore in P(M).
So it exists x0 e M with A=F(x0).

First case: W(x0 e F(x0),t) = w , then W(x0 e A=F(x0), t+1) = -w
(no contradiction, as in another layer)

Second case: W(x0 e F(x0),t) = -w then W(x0 e A=F(x0), t+1) = w
(no contradiction, as in another layer)

If we have All as M and identity as Bijektion F we get for the set A:
W(x e A, t+1) = w := if ( W(x e All,t)=w and W(x e x),t)=-w ) = if ( W(x e x),t)=-w )
This is the layer Russell set R (I omitted the ´u´-value for simplification) -
and no problem.
 (R is a regular set in layer set theory).

So in layer theory we have just one kind of infinity – and no more Cantor´s paradise …

A important remark: I do not say that the classic proofs are false, they are perfectly right.

But with layer logic and layer set theory we are in a new world.
All terms have to be transferred into the layer world
and only there most of the proofs are valid no more.

It is a little like in Plato's allegory of the cave:
If someone has been out of the cave and seen the real world,
he has to learn new rules and the rules of the old shadow world
will no longer fit.
If someone returns from the sun to the cave,
nobody will listen to him or understand him.
“Speak within our shadow rules or be quiet.”
His new world is pure nonsense and fantasy for the Cave people.

Yours
Trestone

Hello,

the proof about the power set can be similary be "unproofed" like the halting problem
by adding layers and layer logic.

There is even a more simple "proof":
In layer set theory the set of all sets (called All) is a set.
The power set of All is All.
So there is a bjection from a set (All) to its powerset (All) : the identity x->x.

That is one of the things why I like the layer set theory.

Yours
Trestone

Hello,

here I will show how I handle the proof of the halting problem:
Here a classical proof of it (from https://wiki.c2.com/?HaltingProblemDiscussions):

"Assume I have a program P that can tell you whether any program halts or not for given input data.
I construct a program Q based on P which, if P says its input program doesn't halt, immediately halts, and if P says the program halts, goes into an infinite loop.
Feeding Q(Q) to P I can see that if P says it halts, it won't, and if P says it doesn't halt, it will.
Therefore I don't have any such program P and anyone else who says they do is full of it."

Now with layer logic we have to add layers if a program has to give a value/result:
A given program halts or not in layer k for given input data.
And the program P has to tell about the halting in layer k+1,
as only values oflower layers can be worked on.
Now when constructing Q, which if P says in layer k+1 its input programm
does not halt in layer k it immediately halts, that halt of Q will be in layer k+2,
as values of layer k+1 are needed.
And the infinite loop of Q in the other case will also be in layer k+2.
We feed now Q(Q) to P :
We look at Q in layer k. If P says in layer k+1 that Q halts on Q in layer k,
the construction of Q says, that Q goes to an infinite loop in layer k+2.

So Q halts in layer k and Q goes to an infinite loop in layer k+2.
That is no contradiction, as programms can have different outcomes in different layers.
(That is not the complete layer logic proof, but the main idea is given.)
Therefore it is possible, that a Halting programm H exists,
that gives a true in layer k+1 for every layer programm P,
if P stops in layer k with input X.

The layers make the difference.

Yours
Trestone

Hello TonesInDeepFreeze,

perhaps the formulation „indirect proof“ was misleading.
I better could say „proof by contradiction“.

The point is, however we call those proofs, the constructed contradiction in them
is not valid any more when we transfer the proofs to layer logic.

The reason is, that by constructing the contradictions we have to use different layers,
and different truth values in different layer are not a contradiction in layer logic.

And yes, all the proofs you named are valid no more
and probably also the uncompleteness sentences of Gödel
(I did not proof this completely with layer logic so far).

Yours
Trestone

Hello keystone,

the statement "x is an element of R if it is not an element of R in all layers"?
is not allowed as a layer theory statement, as there is no layer given
where "x is an element of R" should be true.
if we add an layer k, the "all layers" will break the rule, that in definitions only
smaller layers are allowed.
So the forbidding of statements is according to rules.

Yours
Trestone

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

Hello maytham naei,

I think the logic problems with „I always lie“ are similar to „This statement is not true“.
With classic logic they are true and false – what is not allowed.

In layer logic we would formulate for example:

LA is true in layer k+1 if LA:= „All I say“ is not true in layer k and LA is false else.

In layer 0 LA is undefined (as all layer logic propositions).

In layer 1:
LA is true in layer 0+1 if LA:= „All I say“ is not true in layer 0 and LA is false else.
Therefore LA is true in layer 1.

In layer 2:
LA is true in layer 1+1 if LA:= „All I say“ is not true in layer 1 and LA is false else.
Therefore LA is false in layer 2.

So “ I always lie“ or „All I say is not true“ in layer logic are allowed statements
that have alternating truth values „true“ and „false in the layers >0.

Yours
Trestone

Hello TonesinDeepFreeze,

as I left university some 30 years ago and have developed layer logic only as a hobby,
I have no systematic theory, I mostly developed it in (German) discussions in threads like this.

Most details in English can be found here:
Layer logic at researchgate

Some more details in German here:
Layer Logic in German at ask1.org

I would be glad if someone would start a systematic work on Layer Logic.

Yours
Trestone

Hello,

here some points about layer set theory and the Russell set,
so you can check for yourself what is being swept „under the rug“:

S1: Definition of layer sets
The (layer set) x is in layer t+1 an element of the (layer) set M if and only if
x has the property P(x) in layer t.
In formulas:
The truth value of „x e M“ in layer t+1
is the truth value of P(x) in layer t.
Vt >=0: Vx VM: W(x e M,t+1):= W(P(x),t)

S2: Layer sets to propositions:
For every layer logic proposition P(x) about any layer set x
there exists a layer set M which fulfills for all layers t=0,1,2,3,...
the element equation:
W(x e M, t+1) := W(P(x), t)
That means:
The truth value of „x e M“ in layer t+1 is the same as
the truth value of P(x) in layer t.

In layer set theory „x e M“ can have three values: true, false and undefined.

S3: Empty layer set:
For the empty layer set 0 every set x is a Not-element,
that means „x e 0“ has the truh value false in all layers >0.
Vt>0: W(x e 0, t) := false and W(x e 0, 0) := undefined.

S4: The full layer set All:
For the full set All every set is an element in all layers >0.
Vt>0: W(x e All, t) := true and W(x e All, 0) := undefined.

Russel set with layers:
We define the Russell layer set R as follows:
x is element of R in layer t+1 if x is not element of x in layer t
and not an element in layer t+1 else.

Now we look on „R e R“ in different layers:

In layer 0 „R e R“ is undefined (as always in layer 0 in layer logic).
As undefined, R is not element of R in layer 0.
Therefore „R e R“ is true in layer 1 (=0+1).
Therefore „R e R“ is false in layer 2 (=1+1, not an element becaus of the „else“)
Therefore „R e R“ is true in layer 3.
Therefore „R e R“ is false in layer 4. And so on.

As alternating truth values in the layers are allowed in layer set theory,
the layer Russell set is an allowed set and not paradox.

Yours
Trestone

Hello keystone,

my motivation for developing Layer Logic was to look after the things „under the rug“.
Layer set theory is rather nice: It has only one kind of infinity, the Russell set
and the set of all sets are ordinary sets.
Layer Logic and layer set theory are not nescessary, but they offer a new perspective
for the things „under the rug“.

Yours
Trestone

Hello jgill,

Thank you for your comment.

To „Schrödinger`s cat“:
I have tried to apply layer logic on Quantum theory (for double slit and entanglement).
I constructed a nice model with inverse time for virtual particels
(because they move in an „invisible“ layer),
but as I am not a physicist it is mostly speculation.

Yours
Trestone

Hello keystone,

in Layer Logic I have to “disallow” only some meta statements.

If I would disallow the original liar's statement (and renounce layer logic)
I would loose a lot of new solutions and possibilities that come with Layer Logic:

Besides the liar for example Cantors Diagonalization, Russell`s Paradox,
probably also the Uncompleteness Sentences of Gödel
and the Halting Problem of Informatics.
And there are new possibilities for the philosophy of mind and probably for physics.

So the „little effort with the layers“ should be worth the effort ...

Yours Trestone

Hello keystone,

yes, I use my layers for all statements and their truth values.
For the layers I do not really need „numbers“, I only need a set that is inductive,
multiplication is not needed for the layers.

As the proof for Cantor´s diagonalization is valid no more with layer logic,
one kind of infinity (that of the natural numbers) is enough.

But the situation for mathematics is not all good:
As the proof for the uniqueness of the prime factorization is no more valid,
there might be different factorizations in different layers.
This could show a way to proof or falsicate layer logic experimentally,
but the needed numbers could be astronomically large.

Layer logic is selfrefertial as the truth value of statements can be defined with the help
of truth values of this statements.
But layer logic is not fully self referential, as statements are not allowed to use truth values
of the same (or higher) layers.
The exciting question is, if this layer selfreference is needed.
With layer logic I could define a set theory and natural numbers with arithmetics
that followed the rules of layer logic.

So the the approach carries further than I thought in the beginning ...

Yours
Trestone

Hello keystone,

here the definitions (AL and BL) for statements A and B in layer logic:
For all k=0, 1,2,3, …: Statement AL is true in layer k+1 if statement BL is true in layer k
and statement AL is false else.
Statement BL is true in layer k+1 if statement AL is not true in layer k
and statement BL is false else.

In layer 0 both AL and BL are „undefined“ (as always in layer 0).

Layer 1: Statement AL is true in layer 0+1 if statement BL is true in layer 0
and statement AL is false else.
Statement BL is true in layer 0+1 if statement AL is not true in layer 0
and statement BL is false else.
Therefore statement AL is false in layer 1 and BL is true in layer 1.

Layer 2: Statement AL is true in layer 1+1 if statement BL is true in layer 1
and statement AL is false else.
Statement BL is true in layer 1+1 if statement AL is not true in layer 1
and statement BL is false else.
Therefore statement AL is true in layer 2 and BL is false in layer 2.

So AL and BL have alternating truth values in the layers and are no problem.
As shown layer logic can also handle antinomies without direct selfreference.

Yours
Trestone

Hello,

here the link to layer logic in researchgate:
layer logic in researchgate

And here a thread to layer logic on The Philosophy Forum:
layer logic on The Philosophy Forum

Yours
Trestone

Hello TonesInDeepFreeze,

thank you for the information.

By the way: Compared to layer logic intuitionistic logic is almost classical ...

Yours
Trestone

Hello TheMadFool,

thank you for the argumentation around the Münchhausen trilemma.

„There are no good justifications“ is a result that is not satisfying to me.

That is one of the reasons why I have invented layer logic.
It offers new possibilities to argumentation, one is that the argumentation
for the Münchhausen trilemma is not true with this logic.

What layer logic is I have shown above and in more details in the links there.
As it is unusual and bulky I can understand that not many are going to study it,
but in my eyes the possible results – a new look on logic and the world - it is worth the effort.

Yours
Trestone

Hello GrandMinnow,

sorry, the citation at the beginning of my writing was an error and can be ignored.

Yours
Trestone