3 ms·

Does your argument hold if you consider that input to the brain is limited to the reception of electromagnetic/mechanical waves through a set of sensors, being

Does your argument hold if you consider that input to the brain is limited to the reception of electromagnetic/mechanical waves through a set of sensors, being the fact that one can transmit speech (and Godel sentences) through those sensors is just a higher level abstraction? Put in another way: Couldn't I in principle define such a circumscribed system with all axioms and inference rules by including all of those sensors and all of their possible states into the system?

lisper 9y ago
Yes, of course you can. But if you are part of that system, then you can't Godelize it. In order to Godelize a system, not only does the system need to be circumscribed, but the thing doing the Godelizing has to be outside of the boundaries of the circumscription. Let's recall the original argument: "a mechanist formulates a particular mechanistic thesis by claiming, for example, that the human mind is a Turing machine with a given formal specification S. Lucas then refutes this thesis by producing S’s Gödel sentence, which we can see is true, but the Turing machine cannot. Then, a mechanist puts forth a different thesis by claiming, for example, that the human mind is a Turing machine with formal specification S’. But then Lucas produces the Gödel sentence for S’, and so on, until, presumably, the mechanist simply gives up." When you are presented with S there are two possibilities: either S includes you, or it doesn't. If S includes you, then you can't Godelize it. If S doesn't include you, then you might be able to Godelize it, but if you present your result to the thing that S is supposed to be a model of -- indeed as soon as you interact with that thing in any way -- then S is no longer an accurate model of that system because now it is interacting with something that, by assumption, was not part of the model.

lisper 9y ago

Yes, of course you can. But if you are part of that system, then you can't Godelize it. In order to Godelize a system, not only does the system need to be circumscribed, but the thing doing the Godelizing has to be outside of the boundaries of the circumscription. Let's recall the original argument: "a mechanist formulates a particular mechanistic thesis by claiming, for example, that the human mind is a Turing machine with a given formal specification S. Lucas then refutes this thesis by producing S’s Gödel sentence, which we can see is true, but the Turing machine cannot. Then, a mechanist puts forth a different thesis by claiming, for example, that the human mind is a Turing machine with formal specification S’. But then Lucas produces the Gödel sentence for S’, and so on, until, presumably, the mechanist simply gives up." When you are presented with S there are two possibilities: either S includes you, or it doesn't. If S includes you, then you can't Godelize it. If S doesn't include you, then you might be able to Godelize it, but if you present your result to the thing that S is supposed to be a model of -- indeed as soon as you interact with that thing in any way -- then S is no longer an accurate model of that system because now it is interacting with something that, by assumption, was not part of the model.