If physicalism is a metaphysical position...
Stephen Hawking gave a talk at Google's Zeitgeist Conference in which he declared philosophy to be dead. In December, a group of professors from America's top philosophy departments, including Rutgers, Columbia, Yale, and NYU, set out to establish the philosophy of cosmology as a new field of study within the philosophy of physics. Here is a really interesting [a must read] conversation with Tim Maudlin about "cosmology, multiple universes, the nature of time, the odds of extraterrestrial life, and why Stephen Hawking is wrong about philosophy". Even if you don't agree, its still worth thinking about it.
"Hawking is a brilliant man, but he's not an expert in what's going on in philosophy, evidently. Over the past thirty years the philosophy of physics has become seamlessly integrated with the foundations of physics work done by actual physicists, so the situation is actually the exact opposite of what he describes [...] Look, physics has definitely avoided what were traditionally considered to be foundational physical questions, but the reason for that goes back to the foundation of quantum mechanics. The problem is that quantum mechanics was developed as a mathematical tool [...] Bohr and Heisenberg tried to argue that asking for a clear physical theory [in QM] was something you shouldn't do anymore. That it was something outmoded. And they were wrong, Bohr and Heisenberg were wrong about that. [...] Well, the questions never went away. There were always people who were willing to ask them. [...] If you think that mathematical objects are not in time, and mathematical objects don't change -- which is perfectly true -- and then you're always using mathematical objects to describe the world, you could easily fall into the idea that the world itself doesn't change, because your representations of it don't."
Of course, de Bruijn has done a lot more than that.
2. Both are impossible to realize in a physical system with finite volume and energy due to physical limits of computation
3. Therefore hypercomputation is impossible.
But not conceptually impossible ;-)
Likewise, almost all real numbers are not definable, but they are all conceptually possible (and pragmatically used).
I think hypercomputation might be related to the distinction of computable real numbers and the larger class of definable real numbers. Chaitin's number contains all information about the halting problem, it is definable but not computable.
I don't know whether all definable numbers are hypercomputable, but if not, and if there might also by hyperhypercomputable real numbers and so on, hypercomputation seems to be a very interesting concept.
A continuation of the long deceased comp.ai.philosophy in which logical people used to argue about the philosophical aspects of AI and philosophy of mind in general. Now that USENET has been shut down, long live ai-philosophy!
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