Why People who Try to Argue with Penrose on Godel's Theorem are Wrong
Why (At Least Some of the) People who Try to Argue with Penrose's Interpretation of Godel's Theorem and the Brain are Wrong in one short sentence.
From a common refutation of Penrose's proofs summed up @ http://www.1729.com/consciousness/godel.html
"Let us make the following assumptions:
Ummmm. Try predicting the position for a quantum particle with certainty. (If that doesn't satisfy you, invoke Bell's theorem.) I rest my case. :)
Even if we neglect this obvious problem, later on things get even more silly: "If we tell the mathematician that F is the program determining their mathematical ability, then we are giving them extra information, and that is what enables them to state that G(G) is non-terminating, apparently going beyond the capability determined by F. We can just as easily program a robot mathematician to accept claims made by trustworthy parties about things that the robot does not already know, for example that a function F is the function that determines that robot's mathematical ability. But the moment that the robot accepts that information, F goes out of date as a description of that robot's mathematical ability."
WHAT? Who says a "program" determines mathematical ability? This is tantamount to the following assumption: If Penrose is wrong, and the source of human consciousness is entirely computable, then PENROSE IS WRONG AND THE HUMAN BRAIN IS COMPUTABLE! WOOHOO!"
Furthermore, how can "we" tell the mathematician anything? We CAN'T. We ARE the mathematician. We're trying to prove or disprove -- from WITHIN the system, that there is a program F that determines mathematical ability. We cannot ASSUME it or hand ourselves information from the outside.
Basically, the man is saying, "If only humans had a programmer [someone to feed us predetermined info from the outside], we would be a program." But we're assuming there is no programmer. If there is a programmer the info about F has not been fed to us.
From a common refutation of Penrose's proofs summed up @ http://www.1729.com/consciousness/godel.html
"Let us make the following assumptions:
- Human beings operate according to the laws of physics.
- The laws of physics are computable, i.e. the behaviour of all physical systems can be predicted using algorithmic calculations"
Ummmm. Try predicting the position for a quantum particle with certainty. (If that doesn't satisfy you, invoke Bell's theorem.) I rest my case. :)
Even if we neglect this obvious problem, later on things get even more silly: "If we tell the mathematician that F is the program determining their mathematical ability, then we are giving them extra information, and that is what enables them to state that G(G) is non-terminating, apparently going beyond the capability determined by F. We can just as easily program a robot mathematician to accept claims made by trustworthy parties about things that the robot does not already know, for example that a function F is the function that determines that robot's mathematical ability. But the moment that the robot accepts that information, F goes out of date as a description of that robot's mathematical ability."
WHAT? Who says a "program" determines mathematical ability? This is tantamount to the following assumption: If Penrose is wrong, and the source of human consciousness is entirely computable, then PENROSE IS WRONG AND THE HUMAN BRAIN IS COMPUTABLE! WOOHOO!"
Furthermore, how can "we" tell the mathematician anything? We CAN'T. We ARE the mathematician. We're trying to prove or disprove -- from WITHIN the system, that there is a program F that determines mathematical ability. We cannot ASSUME it or hand ourselves information from the outside.
Basically, the man is saying, "If only humans had a programmer [someone to feed us predetermined info from the outside], we would be a program." But we're assuming there is no programmer. If there is a programmer the info about F has not been fed to us.