Classical mathematics is unfortunately timeless, so we want to narrow it down to constructionist mathematics, which happens to be identical to computation. Boolean algebra is simply one of the many automata that equivalently define universal computation. Even NAND is enough.
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Nand That's All, Folks!
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Nor this!
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The correct way to describe cognition is through physics. Mathematics is just a branch of physics. Just as philosophy is just a branch of psychology. All useful abstractions are grounded in reality.
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Replying to @IntuitMachine @BobKerns and
Ugh. I am not sure if I can understand what you get out of this kind of sloppy thinking.
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Perhaps you need references?
@GeorgeLakoff Philosophy is just a branch of Psychology. David Hestenes https://www.youtube.com/watch?v=ItGlUbFBFfc … . Any questions?1 reply 0 retweets 0 likes -
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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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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