On Sunday, November 4, 2018 at 12:18:48 PM UTC-6, John Clark wrote:
> On Sun, Nov 4, 2018 at 9:19 AM Mark Buda <her...@acm.org <javascript:>> 
> wrote:
> *> Information is only processed in minds, not in physical systems,*
> A brain is a physical system. Mind is what the brain does. I think our 
> fundamental disagreement is you think "Mark Buda" is a noun but I think 
> you're a adjective, you're the way atoms behave when they're organized in a 
> Markbudaian way.
> * > unless you can show that minds are physical systems. *
> Before I can do that I need to know just what you mean by that term.  A 
> racing car is a physical system, what a racing car does is go fast. Is 
> "fast" a physical system? It is certainly produced by one but whether it 
> itself is a physical system is a matter of philosophical interpretation of 
> no operational difference as far as I can see. 
>> > I believe minds are mathematical objects, as are physical systems,
> Turing did more than prove the Halting Problem has no solution, with his 
> machine he also showed us exactly how the laws of physics could produce 
> arithmetic. However nobody has shown how arithmetic could produce the laws 
> of physics or even come close to doing so.
> *> and that minds are a particular kind of mathematical object.*
> Then why is it that if I change the physical object that is your brain 
> your mind changes and when you change your mind your brain changes? The 
> function F(x)=x^2 is a mathematical object and it remains the same 
> regardless of what I do to your brain, but your mind doesn't. 
>> * > I strongly suspect that the particular kind of mathematical object 
>> that minds are is called a lawless choice sequence.*
> The lawless choice sequence was invented by the mathematician L.E.J. 
> Brouwer and he was also the founder of intuitionism, a philosophy of 
> mathematics that says mathematics is not fundamental is just the product of 
> the human mind. I don't know that I'd go as far as Brouwer because I 
> think ET of a AI or any mind would eventually come us with something 
> similar to our mathematics, but only because mathematics is the best 
> language to use when describing how the laws of physics work.
> John K Clark

Brouwer, followed by Heyting, ... produced modern type theory, the 
foundation of programming language theory.


*- Brouwer rejected the idea that the meaning of a mathematical proposition 
is its truth value.*
*- Mathematical propositions do not exist independently of us *[alternative: 
*- We cannot say that a proposition is true without having a proof of it.*

(when "us" or "minds" is replaced by "languages")

- pt 

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