<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">" 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 <em class="">Effectiveness</em> of <em class="">Mathematics</em> in the Natural Sciences”).”<div class=""><br class=""></div><div class="">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.</div><div class="">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 , .</div><div class=""><br class=""></div><div class=""><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Jan 15, 2025, at 11:47 AM, Pedro C. Marijuán <<a href="mailto:pedroc.marijuan@gmail.com" class="">pedroc.marijuan@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" class="">
<div class="">
<div class="moz-cite-prefix">Dear Lou and List,</div>
<div class="moz-cite-prefix"><br class="">
</div>
<div class="moz-cite-prefix">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.<br class="">
</div>
<div class="moz-cite-prefix">Starting with an interesting abstract (<i class="">The
Pragmatic Turn: Toward Action-Oriented Views in Cognitive
Science, </i>MIT Press 2016--with several editors, and a bunch
of brilliant contributors):<br class="">
</div>
<div class="moz-cite-prefix"><i class="">"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..."</i></div>
<div class="moz-cite-prefix"><br class="">
</div>
<div class="moz-cite-prefix">Nowadays there is plenty of literature
along these lines, starting with Gibson's ecological approach to
vision. <span class="ILfuVd BxUVEf" lang="en"><span class="hgKElc">The basic claim is that the perceiver's ability
to perceive is constituted (in a fundamental part) by
sensorimotor knowledge. Even </span></span>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: <span class="">"The Unreasonable <em class="">Effectiveness</em> of
<em class="">Mathematics</em> in the Natural Sciences").</span></div>
<div class="moz-cite-prefix"><br class="">
</div>
<div class="moz-cite-prefix">Better if I leave my further criticisms
on autopoiesis for a next occasion.</div>
<div class="moz-cite-prefix">Best--Pedro</div>
<div class="moz-cite-prefix"><br class="">
</div>
<div class="moz-cite-prefix">El 15/01/2025 a las 17:42, Louis
Kauffman escribió:<br class="">
</div>
<blockquote type="cite" cite="mid:D98184CD-067B-43E1-89ED-389280CA2911@gmail.com" class="">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" class="">
See my previous email. I assert that human consciousness cannot be
encompassed by any single formal system.
<div class="">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</div>
<div class="">And without speculation about what kind of physics
goes beyond Turing.</div>
<div class=""><br class="">
</div>
<div class="">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 </div>
<div class="">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.</div>
<div class="">But there it is. And maybe you find it annoying
because it is proving what you already knew.</div>
<div class=""><br class="">
</div>
<div class="">
<div class="">
<div class="">NotTuring</div>
<div class="">LK</div>
<div class=""><br class="">
</div>
<div class="">1. We prove Goedel’s Theorem as follows: </div>
<div class="">Let T be a formal system that is consistent </div>
<div class="">and contains at least the Peano axioms for number theory.</div>
<div class="">I examine T as a mathematical object and produce (via
Goedel coding) </div>
<div class="">a sentence G that declares its own unprovability in T. </div>
<div class="">This declaration has an external meaning and it is </div>
<div class="">devised so that a proof of G in T would lead to a
contradiction. </div>
<div class=""><br class="">
</div>
<div class="">Thus, since T is consistent, G cannot be proved in T. </div>
<div class="">But G states the non-provability of G in T. </div>
<div class="">Thus G is true but not provable in T. </div>
<div class="">We have proved, from outside T, that G is true. </div>
<div class="">This proof is a mathematical proof of the statement G </div>
<div class="">and it does not contradict T’s unprovability inside T, </div>
<div class="">since we work in the larger system of </div>
<div class="">reasoning about formal systems, including T.</div>
<div class=""><br class="">
</div>
<div class="">2. Could I be identical with T as above? </div>
<div class="">Certainly not. </div>
<div class="">For I have proved G. </div>
<div class="">So if I = T, then T has proved G. </div>
<div class="">I have shown that T cannot prove G.</div>
<div class="">Thus if I = T, then T is inconsistent. </div>
<div class="">We have assumed that T is consistent. </div>
<div class="">Therefore I am not identical with T as a mathematical
reasoner.</div>
<div class=""><br class="">
</div>
<div class="">3. Could I be a Turing machine T, </div>
<div class="">consistent and rich enough to contain Peano Arithmetic? </div>
<div class="">Suppose it is so and </div>
<div class="">go to 1. and 2. above </div>
<div class="">to arrive at the conclusion that </div>
<div class="">this is not possible.</div>
<div class=""><br class="">
</div>
<div class="">4. Go back to 1. </div>
<div class="">and note that I have the capacity to take T as an object
of study. </div>
<div class="">The discussion in 2. and 3. leads to the </div>
<div class="">ancient questions about whether a person can know
themselves. </div>
<div class=""><br class="">
</div>
<div class="">In the mathematical context, </div>
<div class="">if I do stand outside my own processes of reasoning </div>
<div class="">and then reason about these processes, </div>
<div class="">this is a practical capacity that I have.</div>
<div class=""><br class="">
</div>
<div class="">The history of mathematics and logic is </div>
<div class="">a long spiral of such self-examination. </div>
<div class="">In order for it to spiral as it does, </div>
<div class="">the whole process can not be encompassed in a single
formal system. </div>
<div class=""><br class="">
</div>
<div class="">This is the import of Goedel’s theorem </div>
<div class="">and it actually applies to the entities </div>
<div class="">that we call persons, </div>
<div class="">individual reasoners with understanding. </div>
<div class="">The individual reasoners are not single formal systems </div>
<div class="">(to the extent that they are consistent).</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
</div>
<blockquote type="cite" class="">
<div class="">On Jan 15, 2025, at 7:09 AM, Stuart Kauffman
<<a href="mailto:stukauffman@gmail.com" class="moz-txt-link-freetext" moz-do-not-send="true">stukauffman@gmail.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<meta http-equiv="content-type" content="text/html; charset=UTF-8" class="">
<div style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hello to All,
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">Kind wishes, </div>
<div class=""><br class="">
</div>
<div class="">Stu</div>
<div class=""><br class="">
</div>
<div class="">
<div style="margin: 0in; font-size: inherit; font-family: "Times New Roman", serif;" class="">Kauffman, S. and Roli, A. (2021) The World
Is Not A Theorem” Entropy vol 23, issue 11 <o:p class=""></o:p></div>
<div style="margin: 0in; font-size: inherit; font-family: "Times New Roman", serif;" class=""><br class="">
</div>
<div style="margin: 0in; font-size: inherit; font-family: "Times New Roman", serif;" class=""><u class=""><span style="font-size: 9pt; font-family: Helvetica; color: blue;" class="">Kauffman,
S. and Roli, A. (2022), What is Consciousness? </span></u><i class=""><span style="font-size: 8pt; color: rgb(33, 29, 30);" class="">Biological Journal of the Linnean
Society</span></i><span style="font-size: 8pt; color: rgb(33, 29, 30);" class="">,_ _2022<o:p class=""></o:p></span></div><p class="MsoNormal" style="margin: 0in; font-size: inherit; font-family: "Times New Roman", serif;"><span style="font-size: 8pt; color: rgb(33, 29, 30);" class=""> </span></p>
<div style="margin: 0in; font-size: inherit; font-family: "Times New Roman", serif;" class=""><span style="font-size: 8pt; color: rgb(33, 29, 30);" class=""><br class="">
</span></div>
<div style="margin: 0in; font-size: inherit; font-family: "Times New Roman", serif;" class=""><br class="">
</div>
<div class=""><br class="">
<blockquote type="cite" class="">
<div class="">On Jan 15, 2025, at 3:38 AM, Marcus
Abundis <<a href="mailto:55mrcs@gmail.com" class="moz-txt-link-freetext" moz-do-not-send="true">55mrcs@gmail.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div dir="ltr" class="">
<div dir="ltr" class="">
<div style="font-size:large" class="gmail_default">< 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.
></div>
<div style="font-size:large" class="gmail_default"><br class="">
</div>
<div style="font-size:large" class="gmail_default">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<span class="gmail-Apple-converted-space"> =
psychology</span>”, a notoriously . . .
.uhhh, I am not sure of the best word to
use here, so I will just say 'difficult
topic'.</div>
<div style="font-size:large" class="gmail_default"><br class="">
</div>
<div style="font-size:large" class="gmail_default">And thanks for the
lovely taoist imagery . . . taoism being
the last word in Natural Psychology.</div>
<div style="font-size:large" class="gmail_default"><br class="">
</div>
<div style="font-size:large" class="gmail_default">Marcus</div>
</div>
</div>
_______________________________________________<br class="">
Fis mailing list<br class="">
<a href="mailto:Fis@listas.unizar.es" class="moz-txt-link-freetext" moz-do-not-send="true">Fis@listas.unizar.es</a><br class="">
<a class="moz-txt-link-freetext" href="http://listas.unizar.es/cgi-bin/mailman/listinfo/fis">http://listas.unizar.es/cgi-bin/mailman/listinfo/fis</a><br class="">
----------<br class="">
INFORMACI�N SOBRE PROTECCI�N DE DATOS DE
CAR�CTER PERSONAL<br class="">
<br class="">
Ud. recibe este correo por pertenecer a una
lista de correo gestionada por la Universidad de
Zaragoza.<br class="">
Puede encontrar toda la informaci�n sobre como
tratamos sus datos en el siguiente enlace:
<a class="moz-txt-link-freetext" href="https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas">https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas</a><br class="">
Recuerde que si est� suscrito a una lista
voluntaria Ud. puede darse de baja desde la
propia aplicaci�n en el momento en que lo desee.<br class="">
<a class="moz-txt-link-freetext" href="http://listas.unizar.es/">http://listas.unizar.es</a><br class="">
----------<br class="">
</div>
</blockquote>
</div>
<br class="">
</div>
</div>
</div>
</blockquote>
</div>
<br class="">
</div>
<br class="">
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre wrap="" class="moz-quote-pre">_______________________________________________
Fis mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Fis@listas.unizar.es">Fis@listas.unizar.es</a>
<a class="moz-txt-link-freetext" href="http://listas.unizar.es/cgi-bin/mailman/listinfo/fis">http://listas.unizar.es/cgi-bin/mailman/listinfo/fis</a>
----------
INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
Ud. recibe este correo por pertenecer a una lista de correo gestionada por la Universidad de Zaragoza.
Puede encontrar toda la información sobre como tratamos sus datos en el siguiente enlace: <a class="moz-txt-link-freetext" href="https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas">https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas</a>
Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de baja desde la propia aplicación en el momento en que lo desee.
<a class="moz-txt-link-freetext" href="http://listas.unizar.es/">http://listas.unizar.es</a>
----------
</pre>
</blockquote><p class=""><br class="">
</p>
</div>
_______________________________________________<br class="">Fis mailing list<br class=""><a href="mailto:Fis@listas.unizar.es" class="">Fis@listas.unizar.es</a><br class="">http://listas.unizar.es/cgi-bin/mailman/listinfo/fis<br class="">----------<br class="">INFORMACI�N SOBRE PROTECCI�N DE DATOS DE CAR�CTER PERSONAL<br class=""><br class="">Ud. recibe este correo por pertenecer a una lista de correo gestionada por la Universidad de Zaragoza.<br class="">Puede encontrar toda la informaci�n sobre como tratamos sus datos en el siguiente enlace: https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas<br class="">Recuerde que si est� suscrito a una lista voluntaria Ud. puede darse de baja desde la propia aplicaci�n en el momento en que lo desee.<br class="">http://listas.unizar.es<br class="">----------<br class=""></div></blockquote></div><br class=""></div></div></body></html>