Perhaps you need references? @GeorgeLakoff Philosophy is just a branch of Psychology. David Hestenes https://www.youtube.com/watch?v=ItGlUbFBFfc … . Any questions?
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Replying to @IntuitMachine @BobKerns and
Yes, I know their arguments. I don't think that they are convincing. You may have noticed that some (even good!) psychologists tend not to have a deep understanding of mathematics.
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I was referring to Lakoff's characterization of philosophy and Hestenes characterization of mathematics. The commonality here is the requirement for all thought be grounded. This is a principle that is no less convincing than the principle of parsimony.
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Replying to @IntuitMachine @BobKerns and
I think the intuition that drives you and Lakoff is that there must be an ultimate source of priors, "out there" in reality. But there are only patterns, all order must be mathematically constructed.
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Replying to @Plinz @IntuitMachine and
Basically, the same motive as Russell and Whitehead. The belief that reality itself is built from a handful of parts and we just have to find the right parts and then all knowledge follows as a logical consequence, by fitting them together in different ways.
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Replying to @BobKerns @IntuitMachine and
I don't think it is a belief. It is a hypothesis. Where it gets exciting: we can show that our descriptions of the universe must bottom out in finite automata (i.e. all constructive language is computational), and conversely, all observables can be produced by finite automata.
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Yes, that is the hypothesis of the universe and cognition are all fundamentally computation. Therefore that computation should be compatible with the laws of physics. Conjuring up infinities are just convenience methods.
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Replying to @IntuitMachine @BobKerns and
Of course we can make computational physics. But most current physics is hypercomputational, and some physicists like Penrose hope for extracomputational. However, even a mathematician cannot make a hypercomputer from scratch, it has to be postulated.
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Replying to @Plinz @IntuitMachine and
Can you point me to a resource to learn about the difference btw computation vs hyper vs extra? Would like to read about it.
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Replying to @DKedmey @IntuitMachine and
No, but you could read up on non-intuitionist constructivism in mathematics. Basically, computation with reals carrying infinite amounts of information can only be approximated, Pi is not a number but a function, etc.
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Hypercomputation could for instance be implemented by a theoretical geometrical machine operating at infinite resolution, but there is reason to believe that such a machine cannot exist in our universe, and perhaps in no other universe.
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Extracomputation is a term that I made up to describe Penrose's program (and that of others but terminologically more confused people like Don Hoffman) of identifying processes that can do "more than computation" (also including more than QM and infinite resolution machines).
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What are the keywords for mathematics and physics that study this area of limited precision mathematics? I've heard of areas like 'non-standard analysis' and 'symbolic dynamics', but what else is out there?
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