• Trestone
    60
    Hello,

    since Aristoteles some alternatives to classic logic have been constructed,
    but other than in physics classic logic still seems to be the leading theory and practice.

    That did not prevent me from looking for a new logic,
    especially for philosophy and mathematics.

    What disturbed me in philosophy were the problem of free will, the problem of body and mind,
    the problem of consciousness, the problem of ultimate foundation
    and the problem of cause and effect or first cause and - last not least - the liar sentence.

    In mathematics I did not like the diagonal proofs of Cantor, the irrational numbers, Goedel´s incompleteness theorems and the halting problem of informatics.

    In all these themes we use logic to argue or to prove something (mostly impossibilities).
    My hope: With a new logic we could perhaps come to new results.

    Of course the new logic should not be trivial ( like „all is true“)
    and should fit to our reality.
    That looks difficult, but it was surprisingly easy to find a promising approach.

    I combined ideas of Russell (type hierarchy), the complex numbers („a new parameter“)
    and quantum theory („only by measuring a property gets a defined value, else it is undefined“).

    After some tries I got layer logic from this ingrediences.
    I learned later, that professor Ulrich Blau in Munich, Germany, had some ten years earlier
    constructed a similiar logic called „the logic of reflection“.

    Link to the logic of Ulrich Blau:
    https://ivv5hpp.uni-muenster.de/u/rds/blau_review.pdf

    His logic is not for all kind of proposals, mainly for reflective ones.
    So he can handle the liar sentence, but not most of the other problems from above.
    Interestingly he seems to be the only logician with a similar approach to mine.
    So layer logic could in most parts be a really new logic (but I do not know all kind of logics).
    But for me its more important if it helps to solve my problems.

    Layer logic uses three truth values: true, false and undefined (t,f,u).
    But the main new part are the layers 0,1,2,3,4,5,... (not the natural numbers but an inductive set)

    Proposals to not have truth values any more,
    but only proposals in connection with a layer have a truth value.
    And every proposal has a truth value in every layer simultanously.

    If we have a proposal p it has a truth value T(p,k) in every layer k=0,1,2,3,4,5,...
    So truth of a proposal p now is a kind of infinite vector: ( T(p,0), T(p,1), T(p,2), … )

    And a layer logic proposal p (or sentence) is well defined only if we give the truth value T(p,k)
    for every layer k.
    We can do this directly or mostly by recursion.

    If we observe the hierarchy of the layers, we so get proposals, that are free of inconsistencies or paradoxes.
    Hierarchy of layers means: layers are blind to themself an higher layers, in a lyer only values of lower layers are accessible.

    In layer 0 all proposals are undefined (For all p: T(p,0)=u) (symmetrical start) .

    The liar statement here has the following form:

    L:= For all k= 0,1,2,3,... : T(L,k+1) = true if ( T(L,k) is not true ) else T(l,k+1) = false

    As all statements are u=undefined in layer 0,
    we get for layer k=0:

    For k= 0: T(L,0+1) = true if ( T(L,0) is not true ) else T(l,0+1) = false
    T(L,1) = true if ( u is not true ) else T(l,1) = false
    Therefore T(L,1) = true

    With this we get for k=1:
    For k= 1: T(L,1+1) = true if ( T(L,1) is not true ) else T(l,1+1) = false
    Therefore T(L,2) = false

    We see: The liar statement L is undefined in layer 0, true in layer 1,3,5,7,...
    and false in layer 2,4,6,8,...
    The truth vector of L is (u,t,f,t,f,t,f,...)

    So the truth-value is alternating with the layers.
    A classical statement would have only one truth-value in all layers 1,2,3,4,5,...,
    so we can see, that L is a non-classical statement.
    In layer logic it is not paradox, but an ordinary statement.

    Layer logic is a little bit cumbersome,
    but has amazing advantages:'

    Nearly all paradoxes can be solved similiar to the liar.
    With layer logic a "layer set theory" can be defined,
    where the diagonalization proof of Cantor is no longer valid
    and where the Russell set and the set of all sets are ordinary sets.
    Even natural numbers and an arithmetic can be defined.
    A small set back: The prime factorisation of natural numbers could differ in layers.
    But on the other hand it is probable, that the proofs of Gödel`s incompleteness theorems are valid no more.
    (Perhaps someone may prove or disprove this in a dissertation?)

    Indirect proofs are allowed in layer logic, but only within a layer.
    As in most classic proofs there are different layers involved if transformed to layer logic,
    those indirect proofs are mostly not valid any more.

    Most of my mathematical and logical problems are solved or nearly solved with layer logic.
    (If layer logic is consistent, what I have not formally proved, perhaps a diploma thesis?)

    The philosophical problems are a bit harder, there I just discovered first steps of a maybe long journey.

    Up to now layer logic is only discussed in laymen forums (english and german),
    but if a real logician wants to engage in or against it,
    I would welcome him or her.

    But the opinions or comments of laymen are welcome as well,
    for most times my postings remain without reply,
    perhaps my layer logic is too technical or too exotic?
    And classical logic is the hand that feeds us ...

    Link to more details of "layer logic" "Trestone"
    (You may also search in the net,
    in German further material with „Stufenlogik“ „Trestone“):
    https://www.researchgate.net/post/What_do_you_think_of_layer_logic-and_the_use_of_a_new_dimension_to_come_around_contradictions


    Yours
    Trestone
  • Trestone
    60
    Hello,

    imagine, there´s a new kind of logic,
    but nobody has a look ...

    Yours,
    Trestone
  • alan1000
    175
    Trestone,

    You present too much argument at the beginning. State your main point in a short paragraph, in terms which are plausible and provocative, and wait for the feedback. Then you can present your detailed arguments.
  • alan1000
    175
    PS don't say that you reject an argument because "you don't like it". You must have a rational counter-argument. If some amateur in an internet forum says he rejects Cantor's Diagonal Argument because he "doesn't like it", after a whole century of talented mathematicians trying and failing to prove it wrong, who do you think is going to listen to you?
  • Trestone
    60


    Hello alan1000,

    thanks for giving feed back.

    To be precise, I did not prove Cantor´s Diagonal Argument to be wrong.
    I just changed the rules and constructed a logic and a set theory
    where it can not be proved any more.

    Yours
    Trestone
  • Pippen
    80
    I think layer logic is pretty much a meta-linguistic-system where you just don't allow sentences (language) to mix up with their truth values (meta-language). You solve the Paradoxes by basically making them disappear. E.g. in Trestone's layer logic the Liar sentence can't be formulated the way it is meant, because originally it wants to say: This statement is (fully) false, but in Trestones' layer logic the Liars sentence becomes: This statement is (partially) false (depending on the layer). I'd claim that is not the Lair sentence anymore and thus a different problem.
  • Trestone
    60


    Hello Pippen,

    as layer logic is a new kind of logic with a new kind of truth all propositions about truth are different to classic propositions.
    Therefore you are right, the liar sentence in layer logic is not the same as the classic liar sentence.

    On the other side layer logic helps us to speak about self refering propositions without contradictions.
    If we would switch to layer logic the classic propositions would not be important anymore.

    Even I am not that radical, I see layer logic as an interesting alternative that shows us,
    that things could be quite different ...

    Yours
    Trestone
  • Pippen
    80
    I agree with you, and told you so in a german forum already. :) The problem is that with this kind of logic the language becomes not closed anymore and that is unsatisfying for many philosophers. For instance what would be the status of your Liar sentence in layer logic? You couldn't tell, just for a particular layer which by definition just describes a tiny fraction of the Liar sentence. So the Lair sentence as a whole would be as "paradox" as in classical logic, jumping between true and false. Your logic merely "visualizes" this back-and-forth-jumping.
  • Trestone
    60
    Hello Pippen,

    For instance what would be the status of your Liar sentence in layer logic? You couldn't tell, just for a particular layer which by definition just describes a tiny fraction of the Liar sentence. So the Lair sentence as a whole would be as "paradox" as in classical logic, jumping between true and false. Your logic merely "visualizes" this back-and-forth-jumping.

    In layer logic the "status" or "truth value" of the Liar sentence is an infinite truth vector v=(u,t,f,t,f,t,f,...)
    and every proposition has an indefinite truth vector in layer logic.
    Only those with constant truth vectors can be related to a classic truth value,
    the liar sentence is not such a proposition.
    Of course it would be nice if there would always be a classical interpretation,
    but if we take layer logic seriously as a new logic with more possibilities for truth (vectors),
    it is not asthonishing that it allows new kinds of propositions.
    The "old" truth may become less important if we get used to the new.

    Yours
    Trestone
  • Terrapin Station
    13.8k
    In layer logic it is not paradox, but an ordinary statement.Trestone

    Or, someone could simply say that a paradox is a statement that has alternating truth values in "layer logic."

    And then you've got the same problem you had prior to layer logic.
  • Terrapin Station
    13.8k
    Sometimes this board seems like the philosophy equivalent of a physics board where people mostly present their "free energy" and "time cube" proposals.
  • Trestone
    60
    In layer logic it is not paradox, but an ordinary statement. — Trestone

    Or, someone could simply say that a paradox is a statement that has alternating truth values in "layer logic."
    And then you've got the same problem you had prior to layer logic.

    Hello Terrapin Station,

    to me layer logic is similar to complex numbers:

    If you keep thinking classic, you can say: "x*x=-1" has no real solution.
    And being unsolvable is almost equivalent
    to having a complex solution with an non-zero imaginary part..
    On the other side mathematicans would agree:
    From the point of view of complex numbers a lot of the classic problems
    (like the square root of -1) do not exist as problems anymore.

    Yours
    Trestone
  • Pippen
    80
    x*x = -1 has no solution in IR. IC doesn't change that. It doesn't solve the problem (solution for x*x=-1 in IR), it just solves a different problem (x*x=-1 for any possible number). Therefore I am thinking: Is the liar sentence in the layer logic still the "original" liar sentence or something different?

    Of course that doesn't take away anything, it just points out that those ideas mostly don't solve the original "real" problem.
  • Trestone
    60
    Is the liar sentence in the layer logic still the "original" liar sentence or something different?

    Hello Pippen,

    to me not only the liar sentence is different in layer logic but the whole world:

    Like with complex numbers there are more and new possibilities, new dimensions.

    Which of those worlds is more "real"?

    To me this is an open question.

    Of course we are more used to the classic logic and world,
    but how can we be sure that there are not additional layers and dimensions
    that we did not notice up to now?

    Yours
    Trestone
  • Trestone
    60
    Sometimes this board seems like the philosophy equivalent of a physics board where people mostly present their "free energy" and "time cube" proposals.

    Hello Terrapin Station,

    I now can present a kind of "time cube proposal", that was inspired by layer logic:

    Extension of time and evolution

    15 billion years is not enough for the kind of history I am thinking of.

    An easy way of expanting time is to propose a chronologically earlier parallel world.
    I.e. we suppose a further world parallel to our world, where (all) the time is prior to the time in our world.
    Both worlds could have their own big bang and evolution.

    If Informations of the older world could come to our world,
    our possibilities would increase immensly.

    Those informations would come from a very distant past,
    but this past could be more similar to our distant future
    than to our local past back to our big bang,
    where we mostly look for causes.

    This informations could perhaps be placed directly at a particular time in our world
    and would not have to go over our big bang,
    as any time in our world is later than any time in the previous world.

    This gives nice possibilities for directed panspermia:

    Our predecessors in evolution in the previous world
    could develop for billions of billions of years
    (perhaps up to shortly before the end of their world)
    until they send their „message in a bottle“ to our world
    (perhaps shortly before the developement of galaxies),

    We ( or our successors) could pay back by giving similar informations tio the next world.

    Wether this would be good or bad is propably a question of perspective (or layer) ...


    Yours
    Trestone
  • szardosszemagad
    150
    To be sure, your brief description is so scant, that I don't understand layer logic. I have few of its properties and the corollaries, but the whole thing escapes me. And I won't research it, because I am too old to learn new tricks. So this is what I gleaned from your posts:

    Trestone, I think your layer logic is a kind of notation, and as such, it can describe, for instance, paradoxes simpler.

    Mind you, this sort of notation is also present in some computer languages which we studied during my undergrad years, back a million years ago (make it 30) and which I have promptly forgot by now.

    Under layer logic, it seems to me, you don't use a different logic, but a different notation of events vs truth values. This is fine.

    The difference between layer logic and conventional logic is similar to the difference of function forms that describe the same function in a Cartesian coordinate system and in a circular coordinate system. The same function, which is complicated to the extent of unusability, becomes tame and useful in the other system.

    This I find fine too.

    What I don't find fine is how you keep saying "to me..."

    For example, in:

    to me not only the liar sentence is different in layer logic but the whole world:

    Like with complex numbers there are more and new possibilities, new dimensions.

    Which of those worlds is more "real"?

    To me this is an open question.
    Trestone
    What bothers me is the subjective value of "to me". Logic is the last vestige of the absolutists; it is unassailable, much like the flow of a chess game is unassailable. You can't make mistakes, and everything falls into place every time. So if logic is impartial, impersonal, and unbiassed; if it is the ultimate unchanging governing set of rules which can't be applied more than one way, ever, then why is layer logic not that? It is not that, because to you, Testosterone, it must be different than to others; it is different because "to me", that is, to you, it is different than "to someone not me" or to others. And bang, the absolutes of the logic system are crumbled.

    THIS I don't like. "To me."
  • Trestone
    60
    Hello szardosszemagad,

    you write that you are "too old to learn new tricks".
    My experiance is, that most younger ones also seem not to like to learn new tricks,
    especially that of my layer logic.

    I do not complain about this as I myself probably would not give layer logic a second glance
    if it was presented to me by someone else.

    So layer logic in the past ten years has become a rather personal thing to me.
    And although logic is the main subject, it were my wishes and discontentedness that startet the project.
    Of course I hoped and still am hoping to discover something of objective validity,
    But to handle logic as a tool that has (at least partly) to obey my wishes
    is one of the new aspects I have to offer.

    When I had selected some basic rules for my layer logic it started a life of its own.
    And as it is not easy to think consequently in a new logic,
    I often add that something is "my personal view or interpretation of layer logic"
    especially if it is a conclusion outside logic and mathematics.

    For in the end I hope to use my tool to solve (or start solving, or inspire others to start solving) philosophical problems like mind-body, free will and consciousness.

    Yours
    Trestone
  • szardosszemagad
    150
    When I had selected some basic rules for my layer logic it started a life of its own.
    And as it is not easy to think consequently in a new logic,
    I often add that something is "my personal view or interpretation of layer logic"
    especially if it is a conclusion outside logic and mathematics.
    Trestone
    Thanks for the explanation, Testosterone!! It makes sense to me now. I had this sort of pleasure in my life, too, albeit I was a child then: I played with Marklin Toy Trains, and revelled in building complex track structures. I had a lot of track. And as you probably well know, it is a three-track system, so creating track configurations that looped back into themselves was easy, effortless with this design.

    I was the king of my own domain, building the tracks. Now I see that you have similar sentiments, also building complexity, and trying out new stuff, on your own domain, and only you can tell yourself which way to go, what is right and what is wrong about it... wonderful experience.

    I am happy for you.
  • Trestone
    60
    Hello,

    two years are gone,

    but I am still exploring layer logic, mostly in German.

    Here an older link with many details for layer logic at a thread by Trestone at ResearchGate:

    https://www.researchgate.net/post/Is_this_a_new_valid_logic_And_what_does_layer_logic_mean

    Or you may search “the net” with “layer logic “Trestone”“
    or for more actual sides with “Stufenlogik Trestone” (in German).

    For example: https://www.ask1.org/threads/stufenlogik-trestone-reloaded-vortrag-apc.17951/


    Yours,
    Trestone
  • Trestone
    60
    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
  • Mark Nyquist
    744
    Trestone, I looked at this yesterday and again today and I'm not getting it. Could you clarify if its application is to solve logic problems or is it a model of how body/mind work.
    There seem to be some good principles of logic here but I don't see that it can model how the brain and mind work. For example the need to reset, readjust moment to moment, and mental reaction times(layers are too slow). I looked up human reaction times - a quarter second is common. It doesn't seem like a layered process is common but more of a special case.
  • Trestone
    60
    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
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