No, computations are required to finish after a finite number of steps. That's part of Turing's definition of computation and it's fundamental to comp...
The strings of symbols that represent recursion are finite. The simplest example is the intuition of the natural numbers 1, 2, 3, ... Those dots are f...
Yes, the work of modern set theory has consisted largely in trying out new axioms that might solve the Continuum hypothesis. I suppose you could say t...
These conversations always make me look things up. This is from his SEP entry. In his philosophical work Gödel formulated and defended mathematical Pl...
I don't know enough to say. As I mentioned, Gödel was a Platonist and he was pretty smart. There's a lot I don't know about Platonism. This conversati...
Not being a Platonist, I couldn't say. I can't imagine that there are mathematical sets that actually exist anywhere except as abstract ideas that beh...
One of these days I'll read Tegmark. I only know about his mathematical universe hypothesis and can't really respond to the point you are making about...
No, why? Perhaps you can explain your point of view to me. I didn't study much physics but I've studied functional analysis. Hilbert spaces aren't ver...
?Gödel was in fact a Platonist. He believed in mathematical truth. His incompleteness theorems show the limits of formal systems in finding that truth...
Indeed, historians have recently discovered a cache of previously unpublished letters between Gödel and Hilbert. I take the liberty of summarizing the...
Really? How do we know the laws of the physics are valid everywhere? We have a very small sample of local observations. And that's what makes them law...
Isn't that true of all physical law? The universality of gravity is an assumption for which we have no evidence. When we say all swans are white it's ...
Glad this is clear. I mention only in passing that I think this is a more general problem. I am not sure anything at all in the real world is subject ...
That's not how sentential logic works. A proposition P is true or false. There are no observers. I am not aware of any effort within physics to rewrit...
Just a general idle comment here. It's always struck me as interesting that when the God of the Christian Bible created he universe, he said, "Let the...
Point well taken. I'm aware of what inconsistency means in the context of the study of formal systems, ie axiomatics. Of course you and @Banno are cor...
Wait, that's not right. X believes P, and Y believes not-P. That's not a contradiction. A contradiction would be, X believes P and X believes not-P. A...
But they don't! They give approximately correct predictions, to the limits of our experimental apparatus. Newton wasn't correct, nor is Einstein. They...
ps -- Ok I went Googling. But as I said earlier, we're just talking Googling here, I'm not telling anyone anything they couldn't find with the same Go...
But I don't understand why I'm in this conversation. I originally said something that I thought was very innocuous. I'd sooner retract whatever it was...
You have the same access to Google that I do. If QM and relativity are consistent with each other then why have physicists been trying to hammer out a...
Ah, identity of indiscernibles. But "properties" are imposed by sentient observers. A thing would still be a thing even if there were no people around...
Yes I can see that might have been a better word. But "X is incompatible with Y" and "X is inconsistent with Y" seem to be a distinction without a dif...
Again you are claiming that a single inconsistent aspect of the universe implies denial of the law of identity. I have stated that I do not follow you...
Unprovable and evidence-free metaphysical claim. Already falsified, with your agreement. False as noted, reputable links supplied, and your agreement ...
So you agree with my point that we can (under certain circumstances) speak rationally about inconsistency. Which falsifies your claim that there can b...
This is a well-known topic. I'll refer you to Wikipidia, for example this. https://en.wikipedia.org/wiki/Unified_field_theory In physics, a unified fi...
I'm afraid I don't see that at all. As an example, suppose that our current physical theories turn out to be "true" about reality. In that case, quant...
Can't find a single theory that unifies quantum physics and gravity. Isn't this the most famous problem in physics? From Einstein to Witten and beyond...
Well there's no way to know. We do know that contemporary theories of physics can not be incorporated into a single noncontradictory framework. Past t...
Banno's been responding to me but I don't remember what you are referring to. Can you help me understand why you think I'm denying the law of identity...
I'm at a loss to understand why you would ask me that question based on anything I wrote in this thread. Care to explain? The validity of the law of i...
https://en.wikipedia.org/wiki/Paraconsistent_logic https://en.wikipedia.org/wiki/Law_of_excluded_middle#Criticisms People seem to think "logic" means ...
I admit to not reading the entire thread in detail. OP noted that there's a disconnect between classical sentential logic and the mysterious "here but...
You're the one claiming physics is based on sentential logic from 2000 years ago. Today we have paraconsistent logic, denial of the law of the exclude...
The axiomitization of physics is still an open problem. This supports my point. https://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem In particular:...
I would say logic is an abstraction. There's no evidence that classical Aristotelian logic is part of nature. And much evidence that it's not. Relativ...
One is a principle of classical logic; and the other is a principle of modern physics. It's like asking why you can't score touchdowns in basketball, ...
Have you looked at this? https://en.wikipedia.org/wiki/Feynman_diagram That would be the starting point for this discussion. One para of interest: Fey...
We can begin to think about this by considering the earliest humans. Subsistence living, short lifespans, unimaginable conditions. If they didn't repr...
Critics of psychiatry point out that if a patient has a physical brain condition, they need a neurologist. And if they don't, they need a psychologist...
Everybody believes that. The source vibrates the medium which vibrates the little hairs in your eardrum, generating a chemical signal interpreted by y...
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