 # Trestone

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## Everything posted by Trestone

1. ## layer logic - alternative for humans and aliens?

Hello studiot, I do not know all about layer logic and layer arithmetics, as I just made some definitions to have a layer atrithmetic - but I have no practice in using it. I looked if with layer logic a solution for your Chinese problem would be possible with natural numbers (and different layers) - but I do not know enough of layer arithmetics. Within one layer the solution is the same as in classical arithmetic and we get three integer fractions as solutions, but we learn nothing about layers this way, as there are the same rules for arithmetics within one layer as in classical arithmetic. Yours Trestone
2. ## layer logic - alternative for humans and aliens?

Hello, I found a link on English to Prof. Ulrich Blau´s work (numbers, paradoxes and relexion logic) (there are not many): (It is formally more correct then my work, but really "hard stuff", most about regions of infinity that my layer logic no longer needs) https://books.google.de/books?id=Xg6QpedPpcsC&pg=PA311&lpg=PA311&dq=Reflexion+logic+Ulrich+Blau&source=bl&ots=HZNNGnEARu&sig=ACfU3U2Hunv0FZTcdq9T5TDfVa7XArq9VA&hl=de&sa=X&ved=2ahUKEwjf9ZSVnczpAhVERxUIHXhHAp44ChDoATALegQICBAB#v=onepage&q=Reflexion%20logic%20Ulrich%20Blau&f=false Yours Trestone
3. ## layer logic - alternative for humans and aliens?

Hello studiot, it is ok to be puzzled by layer logic. I myself was puzzled for years and still am in some questions. When constructing propositions like the layer liar, the connection between layers is easy and clear. And the use of recursions helps to connect truth values of different layers. (And layer logic helps with induction/recursion, as there is always a "free" start with "all propositions have truth value undefined in layer 0") But I am not sure if we have such connections between layers for all propositions. If there are layers in the (logical) world, they could be also independent from each other. So a layer could be like a world of its own. There is a hierarchy with the layers, but this does not mean, that a truth value in a higher layer is “more true” or “more important” than a truth value of a lower level. All “exist” simultanously and equally. As we all perceive a similar world and do seldom discuss if there is an object or not (for example because of different properties in different layers) we all seem to live in the same layer, at least with our perception. As layers increase with cause and effect, this layer is dynamic. That was one of the reasons why I believed, that there is one layer for the whole universe, and that it increases with every interaction (except gravitation) of objects in it. I have learned to give a layer to every observer frame system. But here we have left the reign of pure logic and changed to human perceiption and physics. In your chinese problem I do not see the “12 layers”? If a solution in natural numbers is looked for, the last line could be connected to layer logic: 4y + 8 z = 39 . Classical the left side is even, the right side not. In the arithmetic of layer logic, a number can be even in one layer and not even in another, so there could be a layer were there exists a solution in natural numbers. (But I do not know numbers, that are even and not even in layers – and I have not solved the puzzle.) All in all layer logic is in some respects similar to the “ Many World Theory”, but I hope not too much, as I like this theory not at all. Yours Trestone Hello Dord, I think parts of classical logic were developed in ancient Greek for speaking at court and searching for truth. As there is not “one truth” in layer logic (but one for each layer), it could help to be more open minded and to tolerate even contradictory statements. But I do not think that layer logic will help us in real live with witnesses at court: I believe, that all humans are “in” the same layer when perceiving, so the differences do not come by different layers but different people. And humans are a greater mystery then logic... Yours Trestone
4. ## layer logic - alternative for humans and aliens?

Hello, in my definitions for layer logic a statement does not belong to a layer, but is independent of all layers. The statements have a truth value in each layer (sometimmes different in layers) and are mostly defined by recursion. An example is the (layer) liar L: For all t= 0,1,2, ...: The liar L is true in layer t+1 if it is not true in layer t – and false in layer t+1 else. The layer truth vector of a layer statement is an infinite vector for t=0,1,2,3,... . For the liar L it is (undefined, true, false, true, false, ...) The same is with layer algorithems or programms P, they are independent or comprehensive of layers - and can stop in one layer t and not stop in an other t+1. It is possible, that a Halting programm H exists, that gives a true in layer t+1 for every layer programm P, if P stops in layer t with input X. (Important: The same H will give a true ore false for P and X for layer t+2). So I think that there are not infinite Halting programms in layer logic. (But of course I do not have H explicitely) Yours Trestone Hello studiot, in the TAO-TE-CHING (Lao Tzu) is the saying: “A journey of a thousand miles begins with one step”. May be layer logic and “layer model' in computing have this one step together. But then the journey in my eyes goes different ways: In layer logic I have infinite layers (0,1,2,3,...) and a strict hierarchy of layers: In a lower (or equal) layer no information of a higher layer is accesible, they are “blind” for all above. And the truth values in the layers are recursivly used to define the truth values of a layer statement for all layers, so layer statements are independent of layers (= defined for all layers). And mainly of course it is a logic. Layer logic has four fathers: - Classic proposional logic (at least 65 % are the same) - Three-valued logic (Łukasiewicz logic) (using three truth values, 5%) - The Logic of reflection by Prof. Ulrich Blau (using layers, only for reflecting proposals, 10%) - Layer Logic of Trestone (expanding layers to all proposals, layer set theory, 20%) It can be used very similar to classical logic: For logic itself, for doing set theory and math, for computer science, for philosophy, for physics and other science (or here for fiction). Yours, Trestone
5. ## layer logic - alternative for humans and aliens?

Hallo strange, my proof is finished at the line: “So there could be a holding program H with layer logic.” Your quote " The next processing layer ... It would be labeled t + r (t)." is part of later speculations. I did not solve the Halting problem but proofed, that with layer logic the proof of the Halting problem is no longer valid. In logical and mathematical layer logic I only use finite layers. The infinite layer (with layer logic there is only one infinity) I use for philosophy and there as layer of the mind. How nature and math are connected (for example pickets and natural numbers) I do not know, but some kind of connection there seems to be. And a logic that would have no connection to our reality/nature would be a strange and not very useful thing. (Sorry for my unclear and clumsy notation, but my university time is past more than 30 years). Yours Trestone
6. ## layer logic - alternative for humans and aliens?

Hello Strange, my main point is, to imagine, that classical logic may be not the real logic for our world and to construct an alternative. I found layer logic as a good possiblity. Of course it is very similar to classic logic (that sufficed for 2000 years), and as the meta logic of layer logic I still use classical logic. But with one parameter more (the layers), I can avoid almost all classical logical paradoxes and most indirect proofs are valid no more, even as layer logic does allow indirect proofs (within one layer). Math and computing science are still possible, but they are different in some points. Here a short analysis of the holding problem from computer science and on "layer algorithms" from the view of my “layer logic”: In the layer logic, a new parameter is added to the programs, layer t. A hierarchy applies: If a program wants to evaluate / use a value from another program from layer t, it can only do so at level t + 1 or higher (= t + r). We are looking for a (layer) program H that decides on each program P with (string) input X in layer t + r, whether this ever stops in step t or runs endlessly (e.g. due to a continuous loop). Definition / basic property H (P, X, t + r): The following applies to all programs P and inputs X: IF P (X, t) stops THEN H (P, X, t + r): = true ELSE H (P, X, t + r): = false In this case, r> = 1 must be selected, since layer t (at P) is used when calculating H. More precisely, the next universal layer t + r (t) is to be set (see below). We can now try to understand the classic counter-proof of the existence of H (P, X) and have to add the levels: Suppose H (P, X, t + r) exists with the property required above. (This is a hypothesis!) Then we use H to construct a "strange" program S: Definition S (P): The following applies to all P: S (P, t + r + k): = IF H (P, P, t + r) = true THEN loop ELSE S (P, t + r + k) = true; STOP (In contrast to the meta / colloquial formulation at H, S (P) can be written as a real program if the code of H is available. "loop" stands for a continuous loop) Here k> = 1 should be selected, since the layer t + r (at H) is used when calculating S. More precisely, the next universal layer t + r (t) + k (t + r (t)) has to be applied (see below). S therefore uses the result of the holding program when applying a program P to its own source code as input. Now we consider the self-application of S, i.e. we take the code for S as input for S S (S, t + r + k) = IF H (S, S, t + r) = true THEN loop ELSE S (S, t + r + k) = true; STOP Since H (S, S, t + r) = true exactly when S (S, t) stops, it is no longer paradoxical or contradictory: S (S, t + k + r) loops when S (S, t) stops and stops when S (S, t) does not stop! The following applies: t + k + r is not equal to t, i.e. two different layer calls from S. So S is a program with different values at different layers, but not necessarily paradoxical. S and H can therefore exist. So there could be a holding program H with layer logic. Why have I left r and k indefinite and not chosen 1 each? Now I suspect that the layer of step programs does not only depend on the subroutines called (they must be larger in each case), but also of the interactions in the universe (= the “layer of the universe " or at least of the “layer of the reference system”😞 My speculation: Every interaction (except through gravitation) increases the layer counter in the universe (also in computers) simultaneously, therefore the layers grow constantly and very quickly (and unfortunately hardly controllable). The next processing layer for layer t can only be narrowed down (at least 1 higher), but do not determine exactly. It would be labeled t + r (t). And we couldn't call computer programs twice with the same parameters ("don't go into the same river twice"), because the universal step counter “flows” constantly, and we cannot enter the step t, but we find it again and again (and higher). (Maybe it could be possible in the event horizon of a Black hole.) If the layer logic applies, then today's computer programs probably only work because they are limited to layer-independent programs, which is only a small part of the conceivable programs. Despite the problems outlined, this does not have to stay that way and maybe one or the other "layer" surprise is also possible in computer science ... E.g. one could refute the "Curch-Turing thesis" with layer computers: (i.e. calculate something new): If you implement an algorithm P (X) on a (normal) computer, the current layer t of the universe is implicitly used for each calculation, i.e. the computer calculates P (X, t). When P (X) is recalculated later, it calculates P (X, t + r). If P (X, t) is a step-dependent function, P (x, t) and P (X, t + r) could be different, although classically it should only be one value. Such a function P (X) could be the prime number decomposition of X, which could be layer-dependent for "large" X and t. However, the numbers would probably have to be so large that a practical review in this way is not yet possible. Maybe someone will try the experiment anyway or has an idea ... Yours Trestone
7. ## layer logic - alternative for humans and aliens?

Hello studiot, layer logic is an outsider (mine) theory to logic. About 15 years before me Ptrofessor Ulrich Blau in Munic had similar ideas, he called it “reflexion logic”. For him layers were the times we reflected about a sentence (like the liar L “this sentence is not true”. Layer 0: no reflection. L has the truth value “undefined”. Layer 1: We reflect, that L was undefined in layer 0, therefore it is true. Layer 2: We reflect on our reflection: L is false. Layer 3: L is true. And so on. I defined layers for all kind of logic sentences (proposals). But I do not know so exactly, what my layers are: Are they meta layers of logical speech, layers of causality or a new dimension or something else? Anyway as an idea they open a new look on logik and the world. And most famous proofs as by Cantor and Gödel or Turing are not valid with layer logic anymore. I see no connection to the “layer model” in computing except the name. But perhaps it is interesting for you, that a computer that would use layer logic would not be limitid by the Halting Problem. In the indirect proof we get different layers – and so there is no more a contradiction. Unfortunatelly I do not know how to built a layer computer, so layer logic is more a philosophical theory (and that was what i intended when I started it 15 years ago ...) Yours Trestone
8. ## layer logic - alternative for humans and aliens?

Hello, here my proof that Cantors diagonalisation ore different infinities are no more valid with layer logic. As All, the set of all sets, is a set in layer theory, it is no surprise, that the diagonalisation of cantor is a problem no more (I just give the main idea, more details in the link below) (t marks the layers, W(x,t) ist the truth value of x in layer t). 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 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 … More details at this link: https://www.scienceforums.net/topic/59914-layer-logic-a-new-dimension/?tab=comments#comment-627045 Yours Ttrestone
9. ## Interaction - a new non-local dimension?

Hello joigus, the observer-dependency was not my invention, but is a consequence of relativity. From a physical view it is not relevant if observers are “amoebe” or “humans”, as long as they are in the same frame of reference. Of course it would be nice, if we could compute the differences between frames of refernce also for my interaction count – and what consequences this has. As I do not know most consequences of different counts, I am far away from this. (And I do not know, how an amoeba experiences the world). Yours Trestone
10. ## Interaction - a new non-local dimension?

Hello swansont, with layer logic math is different. The proofs of Cantor and Gödel are valid no more and also the proof, that the prime factoriztion is unique, as there could be different factorizations in different layers. More details at this link: https://www.scienceforums.net/topic/96134-layer-logic-alternative-for-humans-and-aliens/?tab=comments#replyForm (The parts about logic and math are more serious than this speculations about physics, but there nobody answered for a long time) Yours Trestone
11. ## Interaction - a new non-local dimension?

Hello Strange. You are right, relativity is a problem to my theory. Perhaps we can assume a universe for every observer. If the observer notices an interaction, the count is increased in his universe. If an other observer does not notice an interaction, the count stays unchanged. So we have a (universal) count for every observer. Wether this approach is working, I do not know. Yours Trestone Hello swansont, I don´t believe that my theory helps to tell electrons apart. Near to the end of my text I described a possible test: „We assume that our computers (with the exception of errors) work independently of time. So if we determine the prime factorization of a large number, the same result should be delivered yesterday, today and tomorrow. Now I was able to show that logic and mathematics may apply (layer logic), where the prime factorization could be layer-dependent, and where in reality the layer could correspond to the levels of the interaction counters. So it would be conceivable that if the computer tried again to determine the prime factors of a large number, would suddenly produce different results. Unfortunately, in this experiment we may have to wait until the end of the universe ...” Yours Trestone
12. ## Interaction - a new non-local dimension?

13. ## layer logic - alternative for humans and aliens?

Hello, in the meantime I developed layer logic further and tried to apply it to philosophical and physical questions. In German you cand find here most details: http://philo-welt.de/forum/thread.php?postid=458920 For example I found a solution of the mind - body problem by doing a special interpretation of quantum theory: If particels or quants have several possible ways from start to target, invisible "virtuel possible" particles will go all the ways to the target, and then (still invisible and virtuel) come back to the start, reverse in time, bringing back informations about the (future) target. As they are in the same layer as when started, this virtual informations can not be read by the start. Therefore in physical quantum movements, one of the returning particles has to be selected blindly, and this will become the real particle. So we unterstand quantum contingency better. We already learned that the physical world has a universal layer, that increases with every interaction (except gravitation). Now I assume, that the mind belongs to the infinite layer. If body and mind are onnected in the nervous system, the mind can "read" all quantum informations, especially the informations of the target. He therefore can choose "conciously" and not "blind". In this way the mind can act, but he can only choose possibilities, that the body also could have chosen by chance. Another point is to connect gravity (distortion in space-time) with the mind. As there is mostly a combination of body and mind, the gravity effects could be between minds (in the infinite layer). Dark matter could be "pure mind". But this all is rather speculative of course ... Yours Trestone
14. ## layer logic - alternative for humans and aliens?

Hello, more than a year has gone, but I am still exploring layer logic, mostly in German. Here an older link 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
15. ## Three hairs in Lokis soup (questions about logic)

Three hairs in Lokis 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
16. ## layer logic - alternative for humans and aliens?

Hello, merry Christmas and a new year 2017 (on earth) and 2022 (on your alien planet) full of peace to all reading this. Yours Trestone
17. ## layer logic - alternative for humans and aliens?

Hello ydoaPS, in most cases the truth values of propositions in a layer are defined using the truth values of propositions in lower levels. But it is possible to define the truth value of a proposition in some layers independently. As I do not see the similarity of layer logic to modal logic, can you give some details? Yours Trestone
18. ## layer logic - alternative for humans and aliens?

Hello Strange, the fewer use layer logic has for humans and aliens the more free I am in my research. And as humans, aliens and layer logic are probably changing, it is not impossible that sometimes it will become usefiull ... Yours Trestone Hello Endy0816, layer logic uses three truth values, but that is not so important. More important is the use of layers. That layers give a new look on indirect proofs: If different layers are involved there are no longer contradictions. The diagonalization of Cantor does not work with layer logic. I have strong indications that Gödel´s incompleteness theorems are not valid with layer logic, but I did not proof this up to now (help welcome). Changing of logic means to change a lot of things … Yours Trestone
19. ## layer logic - alternative for humans and aliens?

Hello ydoaPs, Layer logic is more similar to (a modified) classical propositional logic than to modal logic. It does not handle modalities or possibilities. It uses three truth values „true“, „false“ and „undefined“. The most important feature are the layers. A propostion in layer logic does not have one truth value but has a truth value in every layer 0,1,2,3,... , and different truth values in different layers are allowed. So in a way every proposition has an infinite truth vector. The layers are like additional new dimensions and allow new handlings of contradictions. Yours Trestone
20. ## layer logic - alternative for humans and aliens?

Hello, it looks as layer logic is "too human for aliens and too alien for humans." I take this as an encouragement. Yours, Trestone.
21. ## layer logic - alternative for humans and aliens?

Hello endy0816, the main new idea of my logic is that truth has (or can have) different layers. Therefore a statement can be true in one layer and false in another. Or with another view: Properties can be layer dependent - in every layer we can have a different world. Of course we do not experience this layer differences in our everyday life and most things seem to be constant over layers and only one world. But with borderline phenomena like infinity, mind - body interaction, consciousness, etc. this could be different. The layers open a lot of possibilities to avoid contradictions which restrict classical logic. The main definitions I have given in my opening thread and the link at its end. Like with complex numbers we can sovle problems with layer logic, that can not be solved by classic logic (or other logics I know). For example Gödels incompleteness theorems are not valid any more, but natural numbers and a (in some parts different) arithmetics are definable. As my studying at university is about thitrty years ago, I can not give a representation of layer logic in modern state of the art, perhaps somebody will try this? Yours Trestone
22. ## layer logic - alternative for humans and aliens?

Hello studiot, thank you for asking! My question is, if layer logic is a consistent alternative to classic logic - or if there are some deeper faults or incomprehensible parts. The alien story is a kind of "advertising", as there seems to be little interest in discussing a new logic ... Yours Trestone
23. ## layer logic - alternative for humans and aliens?

Hello, I am back from a holidy in Finland at the polar circle. So I am refreshed and ready to answer your questions. P.S. You do not have to wait ten years with your answers ... Yours Trestone
24. ## layer logic - alternative for humans and aliens?

25. ## layer logic - alternative for humans and aliens?

Hello, perhaps some examples will help to show how layer logic works (and hopefully inspire somebody to answer or ask a question): 1) a perception statement A := „I see a red car“. This classical statement can be true or false: W(A)=w or W(A)=f. In layer logic this statement has a truth value in every layer t: W(A,t) = w or f or u. In practice we will not need different values in different layers for concrete perceptions (and we will not need the third value u). Therefore we have the spezial case in layer 0 as always: W(A,0)=u and W(A,t)=w or W(A,t)=f for all t>0. This is an explanation why we do not have to agree to a layer at concrete statements when determing a truth value. 2) Implicit undefined or self-referencing statement B:= „This statement is not true“ In classic logic this statement is neither true nor false. In layer logic we have to modify it slighty, as true is only valid with a layer: SB:= „This Statement ist true in layer t+1, if it is not true in layer t (and false else)“ It is W(SB,0)=u. Therefore W(SB,1) = W(W(SB,0) -= w,1) = w Therefore W(SB,2)= W(W(SB,1) -= w,1) = f , W(SB,3)= w, W(SB,4)= w etc. Here we have a dependency on layers. In practice the second kind of statements seems to be rather rare, therefore layers seemed to be unnecessary, and problems or paradoxes appeared only at the borders of the system. Wether a logic with layers and less problems or paradoxes is a worthwile proposition (at least for specialists) may be a matter of taste … Yours Trestone
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