**From:** Marc Geddes (*marc_geddes@yahoo.co.nz*)

**Date:** Sat Oct 09 2004 - 01:16:58 MDT

**Next message:**Marc Geddes: "'The Next Really Big Enormous Thing' by Robin Hanson"**Previous message:**Ben Goertzel: "RE: Human mind not Turing computable according to Eliezer?"**In reply to:**Christian Szegedy: "Re: Human mind not Turing computable according to Eliezer?"**Next in thread:**Christian Szegedy: "Re: Human mind not Turing computable according to Eliezer?"**Reply:**Christian Szegedy: "Re: Human mind not Turing computable according to Eliezer?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

--- Christian Szegedy <szegedy@or.uni-bonn.de> wrote:

*> Bill Hibbard wrote:
*

*>
*

*> >But his argument depends on a property of Turing
*

*> machines, namely
*

*> >the ability to do arithmetic with arbitrary
*

*> integers, not shared
*

*> >by finite state machines. So his argument fails by
*

*> assuming a
*

*> >capability that humans do not have.
*

*> >
*

*> No, he does not assume any capability. He
*

*> *exhibits* a capability:
*

*> that you can decide something you are not supposed
*

*> to be able to.
*

*>
*

*> His argument is based on a proof by contradiction.
*

*> It goes by:
*

*>
*

*>
*

*> 1) Assume that your brain can be modeled by a Turing
*

*> machine
*

*> (This is true even if it is a finite state
*

*> machine)
*

*>
*

*> 2) Let us consider the following problem that this
*

*> TM cannot
*

*> solve.
*

*>
*

*> 3) But, you can clearly solve it => Contradiction!!!
*

*>
*

*> 4) Since we had a contradiction, your brain cannot
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*> be modelled by a TM.
*

*>
*

*>
*

*> You cannot refute this line of argumentation by
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*> saying that our brain is
*

*> an FSM
*

*> changing his proof and say that the modified proof
*

*> is flawed.
*

*>
*

*> You must refute the *original proof*.
*

*>
*

*>
*

One of the most irritating things about Penrose and

his arguments is that whilst most people agree that

he's wrong, the reasons that his critics as to *why*

Penrose is wrong are all different to one another ;)

I agree that Finite State Machines are not the issue.

What *is* the issue is the empirical fact that as far

as we know, there is no such thing as an uncomputable

finite physical process. That is, we think that all

finite physical processes are computable.

But empirical issues aside, what is logically wrong

with the Penrose argument summarized above?

My answer:

There is an ambiguity in the word 'solve'. Look at

(2) again:

*> 2) Let us consider the following problem that this
*

*> TM cannot
*

*> solve.
*

All the Godel Theorem shows is that there is no

algorithmic procedure for *solving* certain classes of

problem WITH 100% ACCURACY

So in other words, Penrose is using a very limited

definition of the word 'solve'. By 'solve' he means

reach a conclusion that we can be 100% of.

If we drop the requirement that we have to limit

oursleves to axiomatic reasoning yielding certain

conclusions, then the Godel Theorem no longer limits

us.

You see that Penrose's argument now falls apart.

There is no reason why a computer cannot make guesses,

approximations and draw probablistic conclusions about

any of the so-called 'uncomputable' problems. Take

any 'uncomputable' function. There is no reason why a

computer could not compute this to say 99% accuracy.

All 'uncomputable' means is that no finite algorithm

can be 100% accurate.

You see that Penrose's argument now falls apart.

Penrose is trying to con us into thinking that humans

can draw infallible conclusions about maths truths.

But there is no reason for thinking this is the case

at all. Humans *can't* reach infallible answers about

uncomputable functions, any more than computers can.

Humans simply GUESS at the answers to 'uncomputable'

problems, using statistical (Bayesian) reasoning to

draw probabilistic conclusions. The point is that we

are NOT in fact certain that arithmetic is consistent.

We humans simply GUESS that it is (or at least we

assign some probability which is less than 100%).

So there is nothing special about human reasoning.

There is nothing to Penrose's arguments at all. He is

just plain flat wrong.

=====

"Live Free or Die, Death is not the Worst of Evils."

- Gen. John Stark

"The Universe...or nothing!"

-H.G.Wells

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**Next message:**Marc Geddes: "'The Next Really Big Enormous Thing' by Robin Hanson"**Previous message:**Ben Goertzel: "RE: Human mind not Turing computable according to Eliezer?"**In reply to:**Christian Szegedy: "Re: Human mind not Turing computable according to Eliezer?"**Next in thread:**Christian Szegedy: "Re: Human mind not Turing computable according to Eliezer?"**Reply:**Christian Szegedy: "Re: Human mind not Turing computable according to Eliezer?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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