Hi Joseph,

> On 31 May 2018, at 17:28, Joseph Brenner <joe.bren...@bluewin.ch> wrote:
> Stan,
> Good, but things can also run in the opposite direction. How about variety 
> (plus more energy) generating more variety, more possibilities and allowing 
> new ‘information’ to emerge? Standard logical analysis is inadequate because 
> it cannot handle this picture.

Is not a simple counting algorithm, in base greater than 2, generating all 
information (in Shannon sense)?

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, etc.

Of course, this does not generate 01, of 001, but they appear as easy 
subsequence like in 101 or 1001. You can also directly generate all finite 

Then a universal dovetailer, which is a program generating all programs (in 
some fixed programming language), and execute them on all input do much more, 
as it generates all information, and all ways all machine reacted to such 
information, and, assuming mechanism, that generates (in some sense) also their 
thoughts and experiences in that process (i.e, the information in the cognitive 
first person private sense). This is already less trivial than a counting 
algorithm which can be shown to be NOT Turing universal.

But this will never generate any physical realities. On the contrary, as I 
explain in my papers, the physical will have to be retrieved through a sum on 
all computations (which exists in arithmetic) below my substitution level, 
going through my states, and this can be used to show that physics has to be, 
fundamentally, a statistics, even a quantum-like statistics on all computations.

So, the arithmetical reality contains the seed of your varieties, I think, 
which generates all information(s). Now, to get physics from there, we need to 
structure that information space by using the canonical machine theory of 
self-reference, by Gödel, Löb, Solovay. That would be too long to describe here 
and now, but ask any question, as I do think this is relevant in this list, and 
especially in this thread on the nature of information, and, I add, on the 
nature of matter.


PS Please, take your time to answer, as this was my second post of this week. I 
will comment your possible remarks next week.

> Joseph
> From: Fis [mailto:fis-boun...@listas.unizar.es 
> <mailto:fis-boun...@listas.unizar.es>] On Behalf Of Stanley N Salthe
> Sent: jeudi, 31 mai 2018 16:21
> To: Burgin, Mark; fis
> Subject: Re: [Fis] Is information physical? A logical analysis
> Mark -- What Shannon referred to as 'entropy' was 'variety'. 'Information' 
> per se was achieved by way of a reduction or winnowing of this variety of 
> possibilities, leaving 'information' to survive. 
> On Wed, May 30, 2018 at 10:24 PM, Burgin, Mark <mbur...@math.ucla.edu 
> <mailto:mbur...@math.ucla.edu>> wrote:
> Dear Loet,
> Only one remark. There is no Shannon-type information but there is Shannon's 
> measure of information, which is called entropy. 
> Sincerely,
> Mark
> On 5/23/2018 10:44 PM, Loet Leydesdorff wrote:
>> Dear Mark, Soren, and colleagues,
>> The easiest distinction is perhaps Descartes' one between res cogitans and 
>> res extensa as two different realities. Our knowledge in each case that 
>> things could have been different is not out there in the world as something 
>> seizable such as piece of wood.
>> Similarly, uncertainty in the case of a distribution is not seizable, but it 
>> can be expressed in bits of information (as one measure among others). The 
>> grandiose step of Shannon was, in my opinion, to enable us to operationalize 
>> Descartes' cogitans and make it amenable to the measurement as information. 
>> Shannon-type information is dimensionless. It is provided with meaning by a 
>> system of reference (e.g., an observer or a discourse). Some of us prefer to 
>> call only thus-meaningful information real information because it is 
>> embedded. One can also distinguish it from Shannon-type information as 
>> Bateson-type information. The latter can be debated as physical.
>> In the ideal case of an elastic collision of "billard balls", the physical 
>> entropy (S= kB * H) goes to zero. However, if two particles have a 
>> distribution of momenta of 3:7 before a head-on collision, this distribution 
>> will change in the ideal case into 7:3. Consequently, the probabilistic 
>> entropy is .7 log2 (.7/.3) + .3 log2 (.3/.7) =  .86 – .37 = .49 bits of 
>> information. One thus can prove that this information is not physical.
>> Best,
>> Loet
>> Loet Leydesdorff
>> Professor emeritus, University of Amsterdam
>> Amsterdam School of Communication Research (ASCoR)
>> l...@leydesdorff.net  <mailto:l...@leydesdorff.net>; 
>> http://www.leydesdorff.net/ <http://www.leydesdorff.net/> 
>> Associate Faculty, SPRU,  <http://www.sussex.ac.uk/spru/>University of 
>> Sussex; 
>> Guest Professor Zhejiang Univ. <http://www.zju.edu.cn/english/>, Hangzhou; 
>> Visiting Professor, ISTIC,  
>> <http://www.istic.ac.cn/Eng/brief_en.html>Beijing;
>> Visiting Fellow, Birkbeck <http://www.bbk.ac.uk/>, University of London; 
>> http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en 
>> <http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en>
>> ------ Original Message ------
>> From: "Burgin, Mark" <mbur...@math.ucla.edu <mailto:mbur...@math.ucla.edu>>
>> To: "Søren Brier" <sbr....@cbs.dk <mailto:sbr....@cbs.dk>>; "Krassimir 
>> Markov" <mar...@foibg.com <mailto:mar...@foibg.com>>; "fis@listas.unizar.es" 
>> <mailto:fis@listas.unizar.es> <fis@listas.unizar.es 
>> <mailto:fis@listas.unizar.es>>
>> Sent: 5/24/2018 4:23:53 AM
>> Subject: Re: [Fis] Is information physical? A logical analysis
>>> Dear Søren,
>>> You response perfectly supports my analysis. Indeed, for you only the 
>>> Physical World is real. So, information has to by physical if it is real, 
>>> or it cannot be real if it is not physical.
>>> Acceptance of a more advanced model of the World, which includes other 
>>> realities, as it was demonstrated in my book “Structural Reality,” allows 
>>> understand information as real but not physical.
>>>    Sincerely,
>>>    Mark
>>> On 5/17/2018 3:29 AM, Søren Brier wrote:
>>>> Dear Mark
>>>> Using ’physical’ this way it just tends to mean ’real’, but that raises 
>>>> the problem of how to define real. Is chance real? I Gödel’s theorem or 
>>>> mathematics and logic in general (the world of form)? Is subjectivity and 
>>>> self-awareness, qualia? I do believe you are a conscious subject with 
>>>> feelings, but I cannot feel it, see it, measure it. Is it physical then?? 
>>>> I only see what you write and your behavior. And are the meaning of your 
>>>> sentences physical? So here we touch phenomenology (the experiential) and 
>>>> hermeneutics (meaning and interpretation) and more generally semiotics 
>>>> (the meaning of signs in cognition and communication). We have problems 
>>>> encompassing these aspects in the natural, the quantitative and the 
>>>> technical sciences that makes up the foundation of most conceptions of 
>>>> information science.
>>>>   Best
>>>>                           Søren
>>>> Fra: Fis <fis-boun...@listas.unizar.es> 
>>>> <mailto:fis-boun...@listas.unizar.es> På vegne af Krassimir Markov
>>>> Sendt: 17. maj 2018 11:33
>>>> Til: fis@listas.unizar.es <mailto:fis@listas.unizar.es>; Burgin, Mark 
>>>> <mbur...@math.ucla.edu> <mailto:mbur...@math.ucla.edu>
>>>> Emne: Re: [Fis] Is information physical? A logical analysis
>>>> Dear Mark and FIS Colleagues,
>>>> First of all. I support the idea of Mark to write a paper and to publish 
>>>> it in IJ ITA.
>>>> It will be nice to continue our common work this way.
>>>> At the second place, I want to point that till now the discussion on 
>>>> Is information physical?
>>>> was more-less chaotic – we had no thesis and antithesis to discuss and to 
>>>> come to some conclusions.
>>>> I think now, the Mark’s letter may be used as the needed thesis.
>>>> What about the ant-thesis? Well, I will try to write something below.
>>>> For me, physical, structural and mental  are one and the same.
>>>> Mental means physical reflections and physical processes in the Infos 
>>>> consciousness. I.e. “physical” include “mental”.
>>>> Structure (as I understand this concept) is mental reflection of the 
>>>> relationships “between” and/or “in” real (physical) entities as well as 
>>>> “between” and/or “in” mental (physical) entities.
>>>> I.e. “physical” include “mental” include “structural”.
>>>> Finally, IF  “information is physical, structural and mental” THEN simply 
>>>> the  “information is physical”!
>>>> Friendly greetings
>>>> Krassimir
>>>> From: Burgin, Mark <mailto:mbur...@math.ucla.edu>
>>>> Sent: Thursday, May 17, 2018 5:20 AM
>>>> To:  <mailto:fis@listas.unizar.es>fis@listas.unizar.es 
>>>> <mailto:fis@listas.unizar.es>
>>>> Subject: Re: [Fis] Is information physical? A logical analysis
>>>>    Dear FISers,
>>>>    It was an interesting discussion, in which many highly intelligent and 
>>>> creative individuals participated expressing different points of view. 
>>>> Many interesting ideas were suggested. As a conclusion to this discussion, 
>>>> I would like to suggest a logical analysis of the problem based on our 
>>>> intrinsic and often tacit assumptions.
>>>>    To great extent, our possibility to answer the question “Is information 
>>>> physical? “ depends on our model of the world. Note that here physical 
>>>> means the nature of information and not its substance, or more exactly, 
>>>> the substance of its carrier, which can be physical, chemical biological 
>>>> or quantum. By the way, expression “quantum information” is only the way 
>>>> of expressing that the carrier of information belongs to the quantum level 
>>>> of nature. This is similar to the expressions “mixed numbers” or “decimal 
>>>> numbers”, which are only forms or number representations and not numbers 
>>>> themselves.
>>>>   If we assume that there is only the physical world, we have, at first, 
>>>> to answer the question “Does information exist? “ All FISers assume that 
>>>> information exists. Otherwise, they would not participate in our 
>>>> discussions. However, some people think differently (cf., for example, 
>>>> Furner, J. (2004) Information studies without information).
>>>>    Now assuming that information exists, we have only one option, namely, 
>>>> to admit that information is physical because only physical things exist.
>>>>    If we assume that there are two worlds - information is physical, we 
>>>> have three options assuming that information exists:
>>>> - information is physical
>>>> - information is mental
>>>> - information is both physical and mental  
>>>> Finally, coming to the Existential Triad of the World, which comprises 
>>>> three worlds - the physical world, the mental world and the world of 
>>>> structures, we have seven options assuming that information exists:
>>>> - information is physical
>>>> - information is mental
>>>> - information is structural  
>>>> - information is both physical and mental  
>>>> - information is both physical and structural  
>>>> - information is both structural and mental  
>>>> - information is physical, structural and mental  
>>>> The solution suggested by the general theory of information tries to avoid 
>>>> unnecessary multiplication of essences suggesting that information (in a 
>>>> general sense) exists in all three worlds but … in the physical world, it 
>>>> is called energy, in the mental world, it is called mental energy, and in 
>>>> the world of structures, it is called information (in the strict sense). 
>>>> This conclusion well correlates with the suggestion of Mark Johnson that 
>>>> information is both physical and not physical only the general theory of 
>>>> information makes this idea more exact and testable.
>>>>    In addition, being in the world of structures, information in the 
>>>> strict sense is represented in two other worlds by its representations and 
>>>> carriers. Note that any representation of information is its carrier but 
>>>> not each carrier of information is its representation. For instance, an 
>>>> envelope with a letter is a carrier of information in this letter but it 
>>>> is not its representation.
>>>>    Besides, it is possible to call all three faces of information by the 
>>>> name energy - physical energy, mental energy and structural energy.
>>>>    Finally, as many interesting ideas were suggested in this discussion, 
>>>> may be Krassimir will continue his excellent initiative combining the most 
>>>> interesting contributions into a paper with the title
>>>>                                                                       Is 
>>>> information physical?
>>>>    and publish it in his esteemed Journal.
>>>>    Sincerely,
>>>>    Mark Burgin
>>>> On 5/11/2018 3:20 AM, Karl Javorszky wrote:
>>>>> Dear Arturo,  
>>>>> There were some reports in clinical psychology, about 30 years ago, that 
>>>>> relate to the question whether a machine can pretend to be a therapist. 
>>>>> That was the time as computers could newly be used in an interactive 
>>>>> fashion, and the Rogers techniques were a current discovery.
>>>>> (Rogers developed a dialogue method where one does not address the 
>>>>> contents of what the patient says, but rather the emotional aspects of 
>>>>> the message, assumed to be at work in the patient.)
>>>>> They then said, that in some cases it was indistinguishable, whether a 
>>>>> human or a machine provides the answer to a patient's elucidations. 
>>>>> Progress since then has surely made possible to create machines that are 
>>>>> indistinguishable in interaction to humans. Indeed, what is called 
>>>>> "expert systems ", are widely used in many fields. If the interaction is 
>>>>> rational,  that is: formally equivalent to a logical discussion modi 
>>>>> Wittgenstein, the difference in: "who arrived at this answer, machinery 
>>>>> or a human", becomes irrelevant. 
>>>>> Artistry, intuition, creativity are presently seen as not possible to 
>>>>> translate into Wittgenstein sentences. Maybe the inner instincts are not 
>>>>> yet well understood. But!: there are some who are busily undermining the 
>>>>> current fundamentals of rational thinking. So there is hope that we shall 
>>>>> live to experience the ultimate disillusionment,  namely that humans are 
>>>>> a combinatorial tautology. 
>>>>> Accordingly, may I respectfully express opposing views to what you state: 
>>>>> that machines and humans are of incompatible builds. There are hints that 
>>>>> as far as rational capabilities go, the same principles apply. There is a 
>>>>> rest, you say, which is not of this kind. The counter argument says that 
>>>>> irrational processes do not take place in organisms, therefore what you 
>>>>> refer to belongs to the main process, maybe like waste belongs to the 
>>>>> organism's principle. This view draws a picture of a functional biotope, 
>>>>> in which the waste of one kind of organism is raw material for a 
>>>>> different kind. 
>>>>> Karl 
>>>>> < <mailto:tozziart...@libero.it>tozziart...@libero.it 
>>>>> <mailto:tozziart...@libero.it>> schrieb am Do., 10. Mai 2018 15:24:
>>>>>> Dear Bruno, 
>>>>>> You state: 
>>>>>> "IF indexical digital mechanism is correct in the cognitive science,
>>>>>> THEN “physical” has to be defined entirely in arithmetical term, i.e. 
>>>>>> “physical” becomes a mathematical notion.
>>>>>> ...Indexical digital mechanism is the hypothesis that there is a level 
>>>>>> of description of the brain/body such that I would survive, or “not feel 
>>>>>> any change” if my brain/body is replaced by a digital machine emulating 
>>>>>> the brain/body at that level of description".
>>>>>> The problem of your account is the following:
>>>>>> You say "IF" and "indexical digital mechanism is the HYPOTHESIS".
>>>>>> Therefore, you are talking of an HYPOTHESIS: it is not empirically 
>>>>>> tested and it is not empirically testable.  You are starting with a sort 
>>>>>> of postulate: I, and other people, do not agree with it.  The current 
>>>>>> neuroscience does not state that our brain/body is (or can be replaced 
>>>>>> by) a digital machine.
>>>>>> In other words, your "IF" stands for something that possibly does not 
>>>>>> exist in our real world.  Here your entire building falls down.  
>>>>>> --
>>>>>> Inviato da Libero Mail per Android
>>>>>> giovedì, 10 maggio 2018, 02:46PM +02:00 da Bruno Marchal 
>>>>>> marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>:
>>>>>>> (This mail has been sent previously , but without success. I resend it, 
>>>>>>> with minor changes). Problems due to different accounts. It was my 
>>>>>>> first comment to Mark Burgin new thread “Is information physical?”.
>>>>>>> Dear Mark, Dear Colleagues, 
>>>>>>> Apology for not answering the mails in the chronological orders, as my 
>>>>>>> new computer classifies them in some mysterious way!
>>>>>>> This is my first post of the week. I might answer comment, if any, at 
>>>>>>> the end of the week.
>>>>>>>> On 25 Apr 2018, at 03:47, Burgin, Mark < 
>>>>>>>> <mailto:mbur...@math.ucla.edu>mbur...@math.ucla.edu 
>>>>>>>> <mailto:mbur...@math.ucla.edu>> wrote:
>>>>>>>> Dear Colleagues,
>>>>>>>> I would like to suggest the new topic for discussion
>>>>>>>>                                       Is information physical?
>>>>>>> That is an important topic indeed, very close to what I am working on. 
>>>>>>> My result here is that 
>>>>>>> IF indexical digital mechanism is correct in the cognitive science, 
>>>>>>> THEN  “physical” has to be defined entirely in arithmetical term, i.e. 
>>>>>>> “physical” becomes a mathematical notion.
>>>>>>> The proof is constructive. It shows exactly how to derive physics from 
>>>>>>> Arithmetic (the reality, not the theory. I use “reality” instead of 
>>>>>>> “model" (logician’s term, because physicists use “model" for “theory").
>>>>>>> Indexical digital mechanism is the hypothesis that there is a level of 
>>>>>>> description of the brain/body such that I would survive, or “not feel 
>>>>>>> any change” if my brain/body is replaced by a digital machine emulating 
>>>>>>> the brain/body at that level of description.
>>>>>>> Not only information is not physical, but matter, time, space, and all 
>>>>>>> physical objects become part of the universal machine phenomenology. 
>>>>>>> Physics is reduced to arithmetic, or, equivalently, to any 
>>>>>>> Turing-complete machinery. Amazingly Arithmetic (even the tiny 
>>>>>>> semi-computable part of arithmetic) is Turing complete (Turing 
>>>>>>> Universal).
>>>>>>> The basic idea is that:
>>>>>>> 1) no universal machine can distinguish if she is executed by an 
>>>>>>> arithmetical reality or by a physical reality. And,
>>>>>>> 2) all universal machines are executed in arithmetic, and they are 
>>>>>>> necessarily undetermined on the set of of all its continuations 
>>>>>>> emulated in arithmetic. 
>>>>>>> That reduces physics to a statistics on all computations relative to my 
>>>>>>> actual state, and see from some first person points of view (something 
>>>>>>> I can describe more precisely in some future post perhaps).
>>>>>>> Put in that way, the proof is not constructive, as, if we are machine, 
>>>>>>> we cannot know which machine we are. But Gödel’s incompleteness can be 
>>>>>>> used to recover this constructively for a simpler machine than us, like 
>>>>>>> Peano arithmetic. This way of proceeding enforces the distinction 
>>>>>>> between first and third person views (and six others!).
>>>>>>> I have derived already many feature of quantum mechanics from this 
>>>>>>> (including the possibility of quantum computer) a long time ago.  I was 
>>>>>>> about sure this would refute Mechanism, until I learned about quantum 
>>>>>>> mechanics, which verifies all the most startling predictions of 
>>>>>>> Indexical Mechanism, unless we add the controversial wave collapse 
>>>>>>> reduction principle.
>>>>>>> The curious “many-worlds” becomes the obvious (in arithmetic) many 
>>>>>>> computations (up to some equivalence quotient). The weird indeterminacy 
>>>>>>> becomes the simpler amoeba like duplication. The non-cloning of matter 
>>>>>>> becomes obvious: as any piece of matter is the result of the first 
>>>>>>> person indeterminacy (the first person view of the amoeba undergoing a 
>>>>>>> duplication, …) on infinitely many computations. This entails also that 
>>>>>>> neither matter appearance nor consciousness are Turing emulable per se, 
>>>>>>> as the whole arithmetical reality—which is a highly non computable 
>>>>>>> notion as we know since Gödel—plays a key role. Note this makes Digital 
>>>>>>> Physics leaning to inconsistency, as it implies indexical 
>>>>>>> computationalism which implies the negation of Digital Physics (unless 
>>>>>>> my “body” is the entire physical universe, which I rather doubt).
>>>>>>>> My opinion is presented below:
>>>>>>>>    Why some people erroneously think that information is physical
>>>>>>>>    The main reason to think that information is physical is the strong 
>>>>>>>> belief of many people, especially, scientists that there is only 
>>>>>>>> physical reality, which is studied by science. At the same time, 
>>>>>>>> people encounter something that they call information.
>>>>>>>>    When people receive a letter, they comprehend that it is 
>>>>>>>> information because with the letter they receive information. The 
>>>>>>>> letter is physical, i.e., a physical object. As a result, people start 
>>>>>>>> thinking that information is physical. When people receive an e-mail, 
>>>>>>>> they comprehend that it is information because with the e-mail they 
>>>>>>>> receive information. The e-mail comes to the computer in the form of 
>>>>>>>> electromagnetic waves, which are physical. As a result, people start 
>>>>>>>> thinking even more that information is physical.
>>>>>>>>    However, letters, electromagnetic waves and actually all physical 
>>>>>>>> objects are only carriers or containers of information.
>>>>>>>>    To understand this better, let us consider a textbook. Is possible 
>>>>>>>> to say that this book is knowledge? Any reasonable person will tell 
>>>>>>>> that the textbook contains knowledge but is not knowledge itself. In 
>>>>>>>> the same way, the textbook contains information but is not information 
>>>>>>>> itself. The same is true for letters, e-mails, electromagnetic waves 
>>>>>>>> and other physical objects because all of them only contain 
>>>>>>>> information but are not information. For instance, as we know, 
>>>>>>>> different letters can contain the same information. Even if we make an 
>>>>>>>> identical copy of a letter or any other text, then the letter and its 
>>>>>>>> copy will be different physical objects (physical things) but they 
>>>>>>>> will contain the same information.
>>>>>>>>    Information belongs to a different (non-physical) world of 
>>>>>>>> knowledge, data and similar essences. In spite of this, information 
>>>>>>>> can act on physical objects (physical bodies) and this action also 
>>>>>>>> misleads people who think that information is physical.
>>>>>>> OK. The reason is that we can hardly imagine how immaterial or non 
>>>>>>> physical objects can alter the physical realm. It is the usual problem 
>>>>>>> faced by dualist ontologies. With Indexical computationalism we recover 
>>>>>>> many dualities, but they belong to the phenomenologies.
>>>>>>>>    One more misleading property of information is that people can 
>>>>>>>> measure it. This brings an erroneous assumption that it is possible to 
>>>>>>>> measure only physical essences. Naturally, this brings people to the 
>>>>>>>> erroneous conclusion that information is physical. However, measuring 
>>>>>>>> information is essentially different than measuring physical 
>>>>>>>> quantities, i.e., weight. There are no “scales” that measure 
>>>>>>>> information. Only human intellect can do this.
>>>>>>> OK. I think all intellect can do that, not just he human one.
>>>>>>> Now, the reason why people believe in the physical is always a form of 
>>>>>>> the “knocking table” argument. They knocks on the table and say “you 
>>>>>>> will not tell me that this table is unreal”.
>>>>>>> I have got so many people giving me that argument, that I have made 
>>>>>>> dreams in which I made that argument, or even where I was convinced by 
>>>>>>> that argument … until I wake up.
>>>>>>> When we do metaphysics with the scientific method, this “dream 
>>>>>>> argument” illustrates that seeing, measuring, … cannot prove anything 
>>>>>>> ontological. A subjective experience proves only the phenomenological 
>>>>>>> existence of consciousness, and nothing more. It shows that although 
>>>>>>> there are plenty of strong evidences for a material reality, there are 
>>>>>>> no evidences (yet) for a primitive or primary matter (and that is why, 
>>>>>>> I think, Aristotle assumes it quasi explicitly, against Plato, and 
>>>>>>> plausibly against Pythagorus).
>>>>>>> Mechanism forces a coming back to Plato, where the worlds of ideas is 
>>>>>>> the world of programs, or information, or even just numbers, since very 
>>>>>>> elementary arithmetic (PA without induction, + the predecessor axiom) 
>>>>>>> is already Turing complete (it contains what I have named a Universal 
>>>>>>> Dovetailer: a program which generates *and* executes all programs).
>>>>>>> So I agree with you: information is not physical. I claim that if we 
>>>>>>> assume Mechanism (Indexical computationalism) matter itself is also not 
>>>>>>> *primarily* physical: it is all in the “head of the universal 
>>>>>>> machine/number” (so to speak).
>>>>>>> And this provides a test for primary matter: it is enough to find if 
>>>>>>> there is a discrepancy between the physics that we infer from the 
>>>>>>> observation, and the physics that we extract from “the head” of the 
>>>>>>> machine. This took me more than 30 years of work, but the results 
>>>>>>> obtained up to now is that there is no discrepancies. I have compared 
>>>>>>> the quantum logic imposed by incompleteness (formally) on the 
>>>>>>> semi-computable (partial recursive, sigma_1) propositions, with most 
>>>>>>> quantum logics given by physicists, and it fits rather well.
>>>>>>> Best regards,
>>>>>>> Bruno
>>>>>>> _______________________________________________
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