[Fis] Brenner and Lupasco logic. Emergent Simplicity

Sun Dec 11 17:29:48 CET 2016

Dear Arturo,

Thank you for your encouraging comment. Please see responses in blue.

You wrote:

“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.  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!

The key thing about my Logic in Reality is to understand to what it does not apply: it does not apply to simple single entities and to entities between which there is no interaction or none to all intents and purposes. The atom of hydrogen today and tomorrow are in a different position in space-time and so non-identical in this sense but so what.

<!    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.  

Again, your reference is to a catastrophic event, not a process. There are an infinite number of potential things, and you are right that an observer is needed, but this is not a drawback. The observer does not determine what is primarily actual and potential. But I see the actuality and potentiality of say, mutual understanding, as being as real as the actual and potential energy of a swinging pendulum. Aristotle is indeed untenable without the re-interpretation and extension possible today in terms of quantum physics.

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 or 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 is finished and actuality is present?).

a) I understand that the mathematics to which you refer does not apply, but that does not mean that an appropriate one might not be found. I have repeatedly asked people, without success, for a mathematical formulation of the Lupasco expression of his logic as a series of implications (of implications, etc.).

b) I am not talking about random walks, but interactive processes in which there is reciprocity of actuality and potentiality of both components in the interaction. Neither actuality nor potentiality is ever finished for the complex energetic processes I am talking about. I can show that any infinite regress is avoided since at a certain point no further information is provided by a further iteration.

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…

Fascinating!! Please tell me more, e.g. does this have macroscopic implications? Even better: can we discuss BUT in terms of complexity? In that case, BUT is a theory that may apply to EMERGENT SIMPLICITY! The Earth's orbit is simpler than the process it took to get the Earth in it. The thing to be sure of, for LIR to apply, is that the antipodal points are not isolated abstractions but parts of an interactive system. 

I look forward to your response and that of other FISers with great interest. 

Best wishes,

Joseph
----- Original Message ----- 
From: tozziarturo at libero.it 
To: Joseph Brenner ; fis at listas.unizar.es ; pcmarijuan.iacs at aragon.es 
Sent: Friday, December 09, 2016 3:50 PM
Subject: Brenner and Lupasco logic

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.

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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