[Fis] Brenner and Lupasco logic

Mon Dec 12 19:31:47 CET 2016

On 09 Dec 2016, at 15:50, tozziarturo at libero.it wrote:

> Dear Joseph,
>
> Hi!
>
> I quote your 2010 manuscript (by the way, compliments! yours is a  
> noteworthy paper! Furthermore, you were also able to make the  
> unreadable Lupasco very clear!) that the FISers can find here:
>
> http://apcz.pl/czasopisma/index.php/LLP/article/viewFile/LLP.2010.009/967
>
>
>
> "The key postulate, as formulated by Lupasco, is that every real  
> phenomenon, element or event e is always associated with an anti- 
> phenomenon, anti-element or anti-event non-e, such that the  
> actualization of e entails the potentialization of non-e and vice  
> versa, alternatively, without either ever disappearing completely.  
> The logic is a logic of an included middle, consisting of axioms and  
> rules of inference for determining the state of the three dynamic  
> elements involved in a phenomenon (“dynamic” in the physical  
> sense, related to real rather than to formal change, e.g. of  
> conclusions).
>
> 4.2. Axioms
>
> The three fundamental axioms of classical logic, in one version, are  
> the following:
>
> 1. The axiom of identity: A is (or =) A.
>
> 2. The axiom of non-contradiction: A is not (or 6=) non-A.
>
> 3. The axiom of the excluded middle: there exists no third term  
> ‘T’ (‘T’ from third) that is at the same time A and non-A.
>
>
That is the principle of non-contradiction. That is:  non (A and non A).

The axiom of the excluded middle is: A or non-A.

In classical logic they are equivalent, but when you throw out the  
axiom of the excluded middle, then they are no more equivalent, and  
all logics (intutionistic, quantum) keep up the principle of non  
contradiction. Intuitionist logic abandon the axiom of the excluded  
middle, but most quantum logics keeps the axiom of the excluded  
middle. They weakened p -> (q -> p) instead (eenough to lose the  
distributivity axioms.

When a machine introspect itself, it discovers five ways to see "truth":

p
justify p
know p   ((justify p) and p)
observe p ((justify p) and (consistent p))
feel p   ((justify p) and (consistent p) and p)

which can be shown to define arithmetical interpretation of many non  
classical logics. We get quanta as particular qualia, as should be  
expected from some thought experiences. In that case p is restricted  
to the sigma_1 arithmetical proposition (which emulates the  
computations).

I feel you assume a physical reality, but with computationalism, the  
only way to solve the mind-body problem consists in deriving the  
statistical appearance of the physical by the true (not necessarily  
provable by the machine in question) ((justify p) and (consistent p)  
and p), but with p sigma_1 (= shape is "it exists x such that P(x)",  
they obey "p -> justify p") we get already a quantum logic for the  
knower ([]p & p).

It is the Gödel-Löb incompleteness theorems which prevents those  
logics to collapse. Incompleteness introduces all the Parmenidian  
nuances of "the one".

I am not sure to follow what you explain next. I don't and can't  
assume a (primary) physical reality, as digital mechanism is my  
hypothesis in cognitive science, and space-time dynamics is obtained  
by a statistics on first person view related to some sheaf of  
computations. Arithmetic contains a differentiating universal  
consciousness flux (assuming mechanism).

Bruno

PS second, and thus last message for this week.
>
>
> Based on his “antagonistic” worldview, according to Basarab  
> Nicolescu (see Nicolescu 1996),
>
> Lupasco “rewrote” the three major axioms of classical logic as  
> follows:
>
> 1. (Physical) Non-Identity: There is no A at a given time that is  
> identical to A at another time.
>
> 2. Conditional Contradiction: A and non-A both exist at the same  
> time, but only in the sense that when A is actual, non-A is  
> potential, reciprocally and alternatively, but never to the limit of  
> 100%.
>
> 3. Included Middle: An included or additional third element or T- 
> state (‘T’ for ‘tiers inclus’, included third).
>
>
>
> The evolution of real processes is therefore asymptotically toward a  
> non-contradiction of identity or diversity, or toward contradiction.  
> The mid-point of semi-actualization and semi-potentialization of  
> both is a point of maximum contradiction, a “T-state” resolving  
> the contradiction (or “counter-action”) at a higher level of  
> reality or complexity.
>
> Lupasco deserves the historical credit for having shown that a logic  
> of the included middle is a valid multivalent logic, with the  
> indicated terms. At a single level of reality, the second and third  
> axioms are essentially equivalent. In Nicolescu’s extension of the  
> logic, the T-state emerges from the point of maximum contradiction  
> at which A and non-A are equally
>
> actualized and potentialized, but at a higher level of reality or  
> complexity, at which the contradiction is resolved. His paradigm  
> example is the unification in the quanton (T) of the apparently  
> contradictory elements of particle (A) and wave (non-A). In contrast  
> to the Hegelian triad, the three terms here coexist at the same  
> moment of time. The logic of the included middle does not abolish  
> that of the excluded middle, which remains valid for simple,  
> consistent situations. However, the former is the privileged logic  
> of complexity, of the real mental, social and political world.
>
> The logic of the included middle is capable of describing the  
> coherence between levels of reality. A given T-state (which operates  
> the unification of A and non-A) is associated with another couple of  
> contradictory terms at its higher level (A^1, non-A^1), which are in  
> turn resolved at another level by T^1.
>
> According to Nicolescu, the action of the logic of the included  
> middle induces an open structure of the set of all possible levels  
> of reality, similar to that defined by Gödel for formal systems"
>
>
>
>
>
>
>
>
>
> Lupasco’s  “linguistic joke” (forgive me this expression, but,  
> in this context, is something positive, not negative!) is very  
> intriguing and well done, but the problem is always the same, as  
> every kind of logic (…including maths, to be honest…) is based on  
> axioms that stand just for who believe they are true.  I give you an  
> example, by examining Luparsco’s postulates.
>
>
>
> 1.       (Physical) Non-Identity: There is no A at a given time that  
> is identical to A at another time.
>
> It is not true: an atom of hydrogen today is identical to an atom of  
> hydrogen tomorrow.  I would also say that a square is always a  
> square, or in my mind a centaur is always a centaur, but I suppose  
> that you are talking in a physical, not mathematical or  
> psychological sense, therefore I prefer the example of the atom.   
> And do not say that the hydrogen atoms of today and of tomorrow are  
> two different atoms, because, according the definition of hydrogen  
> atom, I cannot distinguish the one from the other!
>
>
>
> 2.       Conditional Contradiction: A and non-A both exist at the  
> same time, but only in the sense that when A is actual, non-A is  
> potential, reciprocally and alternatively, but never to the limit of  
> 100%.
>
> Actual and potential reminds too much the scientifically untenable  
> Aristotle… How can you say what is potential and what is actual?   
> Actual and potential compared to what?  The bullet that killed John  
> Kennedy is actual when you think that it reached Kennedy, but is  
> potential if you think that it did not kill Jaqueline… Therefore,  
> your concept of actual and potential requires a subjective observer  
> who states what is actual and what is potential.  You may argue that  
> you are talking about Lagrangian and Hamiltonians, but it does not  
> help, in this case.  Indeed, the concept of energetic gradient  
> descent, for example in Fokker-Planck equations, this time, cannot  
> help you, because they do not talk of the EXISTENCE of  potentiality  
> of actuality, but just of an energetic path of a random walk towards  
> lesser energetic levels (on the other side, at which low energetic  
> level can you say that potentiality finish and actuality is present?).
>
>
>
> 3. Included Middle: An included or additional third element or T- 
> state (‘T’ for ‘tiers inclus’, included third).
>
>
>
> This axiom reminds me… the Borsuk-Ulam theorem!  Two antipodal  
> points (call it A and non-A) become a point T, when projected in a  
> different dimension… The only difference is that, according  
> Lupasco,  A and non-A become T in a dimension higher, while,  
> according the Borsuk-Ulam theorem, A and non-A become T in a  
> dimension lower…
>
>
>
>
>
>
> Arturo Tozzi
>
> AA Professor Physics, University North Texas
>
> Pediatrician ASL Na2Nord, Italy
>
> Comput Intell Lab, University Manitoba
>
> http://arturotozzi.webnode.it/
>
>
>
> ----Messaggio originale----
> Da: "Joseph Brenner" <joe.brenner at bluewin.ch>
> Data: 07/12/2016 15.15
> A: "fis"<fis at listas.unizar.es>
> Cc: <tozziarturo at libero.it>
> Ogg: Fw: [Fis] Fwd: R: Re: Who may proof that consciousness is an  
> Euclidean n-space ??? Logic
>
> 
> Dear Folks,
>
> Arturo wrote:
>
> "therefore logic, in general, cannot be anymore useful in the  
> description of our world. I'm sad about that, but that's all."
>
> The answer is to change logic from one of propositions (Lesniewski- 
> Tarski) or mathematics (Zermelo-Fraenkel) to one of the states of  
> real processes (Lupasco; Logic in Reality). Why this is not even  
> considered as an option for serious discussion is a great mystery to  
> me.
>
> Arturo also said:
>
> "The concepts of locality and of cause/effect disappear in front of  
> the puzzling phenomenon of quantum entanglement, which is  
> intractable in terms of logic."
>
> Here, I fully agree; Logic in Reality also does not apply to quantum  
> phenomena. It is limited to description of processes involving  
> thermodynamic change in which there is a mutual interaction between  
> elements as individuals, including people. I do not claim it allows  
> causal prediction, but logical inference.
>
> Arturo:
>
> "The same stands for nonlinear chaotic phenomena, widespread in  
> nature, from pile sands, to bird flocks and  to brain function. When  
> biforcations occur in logistic plots and chaotic behaviours take  
> place, the final systems' ouputs are not anymore causally  
> predictable."
>
> Here, I agree with Arturo but for a different reason. The non-linear  
> phenomena mentioned are too simple. In crowd behavior, individual  
> interactions are absent or meaningless - information_as_data. Brain  
> behavior of this kind is of lower complexity and interest, involving  
> mostly lower level functionalities, although they they may accompany  
> higher level cognitive functions.
>
> I look forward to point by point refutation of or agreement with the  
> above.
>
> Best wishes,
>
> Joseph
>
>
>
>
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