<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="">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><div>NotTuring</div><div>LK</div><div><br class=""></div><div>1. We prove Goedel’s Theorem as follows: </div><div>Let T be a formal system that is consistent </div><div>and contains at least the Peano axioms for number theory.</div><div>I examine T as a mathematical object and produce (via Goedel coding) </div><div>a sentence G that declares its own unprovability in T. </div><div>This declaration has an external meaning and it is </div><div>devised so that a proof of G in T would lead to a contradiction. </div><div><br class=""></div><div>Thus, since T is consistent, G cannot be proved in T. </div><div>But G states the non-provability of G in T. </div><div>Thus G is true but not provable in T. </div><div>We have proved, from outside T, that G is true. </div><div>This proof is a mathematical proof of the statement G </div><div>and it does not contradict T’s unprovability inside T, </div><div>since we work in the larger system of </div><div>reasoning about formal systems, including T.</div><div><br class=""></div><div>2. Could I be identical with T as above? </div><div>Certainly not. </div><div>For I have proved G. </div><div>So if I = T, then T has proved G. </div><div>I have shown that T cannot prove G.</div><div>Thus if I = T, then T is inconsistent. </div><div>We have assumed that T is consistent. </div><div>Therefore I am not identical with T as a mathematical reasoner.</div><div><br class=""></div><div>3. Could I be a Turing machine T, </div><div>consistent and rich enough to contain Peano Arithmetic? </div><div>Suppose it is so and </div><div>go to 1. and 2. above </div><div>to arrive at the conclusion that </div><div>this is not possible.</div><div><br class=""></div><div>4. Go back to 1. </div><div>and note that I have the capacity to take T as an object of study. </div><div>The discussion in 2. and 3. leads to the </div><div>ancient questions about whether a person can know themselves. </div><div><br class=""></div><div>In the mathematical context, </div><div>if I do stand outside my own processes of reasoning </div><div>and then reason about these processes, </div><div>this is a practical capacity that I have.</div><div><br class=""></div><div>The history of mathematics and logic is </div><div>a long spiral of such self-examination. </div><div>In order for it to spiral as it does, </div><div>the whole process can not be encompassed in a single formal system. </div><div><br class=""></div><div>This is the import of Goedel’s theorem </div><div>and it actually applies to the entities </div><div>that we call persons, </div><div>individual reasoners with understanding. </div><div>The individual reasoners are not single formal systems </div><div>(to the extent that they are consistent).</div><div><br class=""></div><div><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="">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="">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>
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