[Fis] Fis Digest, Vol 118, Issue 38

Thu Jan 16 06:37:24 CET 2025

" I dare say that maths themselves may participate of this scheme: various entities or objects (variables) experiment actions (operations) that transform the expression in an = one, with renewed variables and operations. Maths somehow externalize our inner processes of thought in world observation-action and make them more universal and abstract, though far more schematic and deprived of the intrinsic far richer "cognit" connectivity. But the result is an uncanny efficiency (as Eddington put: "The Unreasonable Effectiveness of Mathematics in the Natural Sciences”).”

There is almost always a set of prejudices in these discussions about “abstraction” being artificial in some way. This is probably because we do not remember how we began learning from the universal to the particular.
How could you keep remembering that everything downstairs was a “tick-tock” since the demarcation of upstairs from downstairs was an old grandfather clock? Or that your uncle’s new car you called a “wheelbarrow” since you had that term from actual wheelbarrow to anything with wheels. The patterns of mathematics, like the number two, are big conceptions of simpler worlds. And it is quite something to count down from complexity to …3 , 2 , 1 , 0 ,    .

> On Jan 15, 2025, at 11:47 AM, Pedro C. Marijuán <pedroc.marijuan at gmail.com> wrote:
> 
> Dear Lou and List,
> 
> May I enter some dissonance? Human cognition, not necessarily being "neurocentric" as Kate says, is well grounded (partially) by following the Action-Perception Cycle, or perception-action cycle.
> Starting with an interesting abstract (The Pragmatic Turn: Toward Action-Oriented Views in Cognitive Science, MIT Press 2016--with several editors, and a bunch of brilliant contributors):
> "Experts from a range of disciplines assess the foundations and implications of a novel action-oriented view of cognition. Cognitive science is experiencing a pragmatic turn away from the traditional representation-centered framework toward a view that focuses on understanding cognition as “enactive.” This enactive view holds that cognition does not produce models of the world but rather subserves action as it is grounded in sensorimotor skills. In this volume, experts from cognitive science, neuroscience, psychology, robotics, and philosophy of mind assess the foundations and implications of a novel action-oriented view of cognition. Their contributions and supporting experimental evidence show that an enactive approach to cognitive science enables strong conceptual advances, and the chapters explore key concepts for this new model of cognition. The contributors discuss the implications of an enactive approach for cognitive development; action-oriented models of cognitive processing; action-oriented understandings of consciousness and experience; and the accompanying paradigm shifts in the fields of philosophy, brain science, robotics, and psychology..."
> 
> Nowadays there is plenty of literature along these lines, starting with Gibson's ecological approach to vision. The basic claim is that the perceiver's ability to perceive is constituted (in a fundamental part) by sensorimotor knowledge. Even in our own languages we would find a sort of mirror image of the underlying cognizing engine: in a sentence, for instance, there is a subject/object (perception or meta-perception of an entity) that connects with a verb (action, or meta-motor transformation) forming a minimal cognitive episode, which is extended to connect with further episodes.  I dare say that maths themselves may participate of this scheme: various entities or objects (variables) experiment actions (operations) that transform the expression in an = one, with renewed variables and operations. Maths somehow externalize our inner processes of thought in world observation-action and make them more universal and abstract, though far more schematic and deprived of the intrinsic far richer "cognit" connectivity. But the result is an uncanny efficiency (as Eddington put: "The Unreasonable Effectiveness of Mathematics in the Natural Sciences").
> 
> Better if I leave my further criticisms on autopoiesis for a next occasion.
> Best--Pedro
> 
> El 15/01/2025 a las 17:42, Louis Kauffman escribió:
>> See my previous email. I assert that human consciousness cannot be encompassed by any single formal system.
>> This goes beyond set theory. I assert the validity of arguments such as those given in Penrose books Emporer’s New Mind, but state these arguments in my way
>> And without speculation about what kind of physics goes beyond Turing.
>> 
>> As I said before, such arguments are hard for some people to take. The assertion really is that if you accept the original Goedelian argument, then it tells you that a human cognizer reasoning about 
>> a formal system can do more than the formal system on its own. If you accept this, then you cannot be such a formal system without being inconsistent. I do think that people find this annoying.
>> But there it is. And maybe you find it annoying because it is proving what you already knew.
>> 
>> NotTuring
>> LK
>> 
>> 1. We prove Goedel’s Theorem as follows: 
>> Let T be a formal system that is consistent 
>> and contains at least the Peano axioms for number theory.
>> I examine T as a mathematical object and produce (via Goedel coding) 
>> a sentence G that declares its own unprovability in T. 
>> This declaration has an external meaning and it is 
>> devised so that a proof of G in T would lead to a contradiction. 
>> 
>> Thus, since T is consistent, G cannot be proved in T. 
>> But G states the non-provability of G in T. 
>> Thus G is true but not provable in T. 
>> We have proved, from outside T, that G is true. 
>> This proof is a mathematical proof of the statement G 
>> and it does not contradict T’s unprovability inside T, 
>> since we work in the larger system of 
>> reasoning about formal systems, including T.
>> 
>> 2. Could I be identical with T as above? 
>> Certainly not. 
>> For I have proved G. 
>> So if I = T, then T has proved G. 
>> I have shown that T cannot prove G.
>> Thus if I = T, then T is inconsistent. 
>> We have assumed that T is consistent. 
>> Therefore I am not identical with T as a mathematical reasoner.
>> 
>> 3. Could I be a Turing machine T, 
>> consistent and rich enough to contain Peano Arithmetic? 
>> Suppose it is so and 
>> go to 1. and 2. above 
>> to arrive at the conclusion that 
>> this is not possible.
>> 
>> 4. Go back to 1. 
>> and note that I have the capacity to take T as an object of study. 
>> The discussion in 2. and 3. leads to the 
>> ancient questions about whether a person can know themselves. 
>> 
>> In the mathematical context, 
>> if I do stand outside my own processes of reasoning 
>> and then reason about these processes, 
>> this is a practical capacity that I have.
>> 
>> The history of mathematics and logic is 
>> a long spiral of such self-examination. 
>> In order for it to spiral as it does, 
>> the whole process can not be encompassed in a single formal system. 
>> 
>> This is the import of Goedel’s theorem 
>> and it actually applies to the entities 
>> that we call persons, 
>> individual reasoners with understanding. 
>> The individual reasoners are not single formal systems 
>> (to the extent that they are consistent).
>> 
>> 
>>> On Jan 15, 2025, at 7:09 AM, Stuart Kauffman <stukauffman at gmail.com <mailto:stukauffman at gmail.com>> wrote:
>>> 
>>> Hello to All, 
>>> 
>>> in support of Lou, I attach two references that say the becoming of the world, including, presumably, human consciousness, is beyond any mathematical formulation based on set theory.
>>> 
>>> Kind wishes, 
>>> 
>>> Stu
>>> 
>>> Kauffman, S. and Roli, A. (2021) The World Is Not A Theorem” Entropy vol 23, issue 11 
>>> 
>>> Kauffman, S. and Roli, A. (2022), What is Consciousness? Biological Journal of the Linnean Society,_ _2022
>>>    
>>> 
>>> 
>>> 
>>>> On Jan 15, 2025, at 3:38 AM, Marcus Abundis <55mrcs at gmail.com <mailto:55mrcs at gmail.com>> wrote:
>>>> 
>>>> <  I am sympathetic with mathematical and formal modeling of “cognitive processes” but feel that it should be clear that formal models will not capture the whole phenomenon. >
>>>> 
>>>> For *myself*, while I accept an essential truth lies in this statement . . . I am ALSO inclined to think 'surrendering' prematurely is a lack of scientific imagination ('heavy lifting') – where 'science' is SUPPOSED to be in the business of continually reinventing itself. That said, I also accept that many do not see science as an actual/active creative process. For me, it is different. I think the core issue here is “cognitive processes = psychology”, a notoriously . . . .uhhh, I am not sure of the best word to use here, so I will just say 'difficult topic'.
>>>> 
>>>> And thanks for the lovely taoist imagery . . . taoism being the last word in Natural Psychology.
>>>> 
>>>> Marcus
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