Actually Penrose's argument is quite simple he starts off with statements or computations where a computer or a machine will never halt or will run forever.
For example:
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Find a natural number which is not a sum of powers of 2.
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Find an even number greater than 2 which is not the sum of two primes. (Goldbach's conjecture)
We know that the first computation will never halt and we are not sure whether the second computation will halt or not but according to the conjecture the computer will never halt. Now based on such computations where a machine will never halt Penrose speculates if there is an underlying algorithm or a procedure that we humans are using to deduce whether a given computation performed on a natural number halts or not.
Penrose takes us through a series of arguments where he proves that such an sound halting algorithmic procedure encompassing all known computations known to human beings if it exists will fail to stop for one given computation when we actually know that the computation in fact does not stop. This is a contradiction the algorithmic procedure
A encompassing all known computations was assumed to be the underlying procedure used by human beings to ascertain whether a computation will halt or not but as we have just now proved there exists a computation where we know that the computation will not halt but the procedure fails to halt and therefore
A cannot be the underlying procedure used by human beings.
This proof is known as the Penrose's version of the Godel-Turing theorem. His proof is quite obvious for anyone to see and its an very important proof for mystics like me who holds on to the position,
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D. Awareness cannot be explained by physical, computational or any other scientific terms.
When the whole scientific community sidelined the most fundamental question facing biologists which is,
What is consciousness? hats off to Sir Roger Penrose for defending that a Theory Of Everything must incorporate or explain at least some aspects of Conscious understanding in scientific terms and he has been right on the money that conscious thinking is non-computable and its not something which can be explained with in the current physics as we know of.
Its been long known to Indian traditional scholars that mind and brain are two different things and that dualism or Platonic dualism is a fact and I congratulate and appreciate Sir Roger Penrose for being a mathematical physicist and intuitively arriving at a conclusion on a similar lines.
Mind and Brain are two different things. If this is not true Indian philosophy will collapse like a house of cards. I will convert to an atheist and go and hide myself if it is shown that mind and brain are not two different things. Dualism of mind and body is albeit necessary for Indian philosophy to succeed as described in the
Samkhya school of Indian philosophical system. This dualism of mind and body should not be confused with Cartesian dualism where the mind and body are made up of entirely different substances.
By including mind in the realm of matter, Samkhya avoids one of the most serious pitfalls of Cartesian dualism, the violation of physical conservation laws. Because mind is an evolute of matter, mental events are granted causal efficacy and are therefore able to initiate bodily motions.
Eugene Wigner was a strong proponent of mind-body dualism and he argued that mind-body dualism will again be acceptable in the mainstream sciences. Mind-Body dualism or the Many-Minds problem is also at the heart of the Measurement problem in Quantum mechanics.
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but rather that machines are not limited to what is designed in alogrithm. Therefore your rebuttal fails.
