Impact of Gödel's incompleteness theorems on a TOEby PhysDrew Tags: gödel, impact, incompleteness, theorems 

#307
Jan811, 12:54 PM

P: 1,667

Careful 



#308
Jan811, 12:56 PM

P: 497





#309
Jan811, 11:05 PM

P: 497

"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean – neither more nor less." It is precisely because of our ability to use symbols that our species has been able to achieve what it has. 



#310
Jan911, 03:21 AM

P: 1,667

i don't think there is much point in continuing the discussion; you seem to be unaware that your position is equally a (very unplausible) belief and moreover you seem to indulge yourself in the comfort that your view belongs to physics and mathematics while mine doesn't. I sharply disagree with that in the case of physics, in the case of mathematics I could be more forgiving. Physics is not appied mathematics. We agree that mathematics is relational; that why I tried to tell you cannot tell to a computer what the word forall means, something which he will need if he wants to prove that the function x > x is continuous. Therefore what I tried to tell you, and what Penrose tries to convey is that these undefinable qualities associated to meaning and understanding are necessary to do mathematics. Since we are a part of nature, a TOE should be able to discribe that as well, and it basically never ever will. I agree that symbolic language has been the main driver of human progress and knowledge but again the quality which manipulates this symbolic language cannot be defined in terms of it. Moreover, I am not trying to even say that this issue is the end mathematics and certainly not of physics as I understand it! On the contrary, I think the most basic laws of nature will be defined in terms of very general principles like general covariance and so on which by themselves cannot be defined accurately. It is a particular projection of them, by adding more relational context than necessary which will allow for study in terms of the language of mathematics. This is precisely what Einstein stressed throughout his whole life, if we can learn something of the old man, then it is this!
As a final comment, I would say that physicists and mathematicians should become more open for interdisciplinary study regarding the other sciences. They are also sciences and have meaningful aspects to communicate to us, the reductionist view will always fail and as a physicist/mathematician I have certainly not the pretense that my activities would somehow be better than the one of a biologist. Careful 



#311
Jan911, 04:45 AM

P: 497

But you're right, since the other issues that came up until we got to this point were side issues about which we have put down our respective arguments, we can either let other readers expand upon them or let this post finally come to an end. Cheers 



#312
Jan911, 06:38 AM

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#313
Jan911, 10:49 AM

P: 5

In a nutshell, Godel's ideas mean that we can only know stuff based on what we already know. If mathematics itself can never be a complete description of phenomena (due to its axioms not predicting every possible consequence of them) then it follows that we can only predict as much as our abilities allow us to predict, as a species. A TOE will also be subject to the same limitations so that what we define as 'knowledge' will always be parochial in nature, it cannot be otherwise. I suppose what I am really saying is that we may only define 'reality' within the constraints of our biological limitations. Who knows, perhaps some UFOs, for example, represent phenomena that we simply haven't the ability to define or comprehend!




#315
Jan911, 12:14 PM

P: 1,667




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