# Re: Turing Machines

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On 18 Aug 2011, at 19:05, meekerdb wrote:```
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```On 8/18/2011 7:24 AM, Bruno Marchal wrote:
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I agree with that sentiment. That's why I often try to think of consciousness in terms of what it would mean to provide a Mars Rover with consciousness. According to Bruno the ones we've sent to Mars were already conscious, since their computers were capable of Lobian logic.
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I don't remember having said this. I even doubt that Mars Rover is universal, although that might be serendipitously possible (universality is very cheap), in which case it would be as conscious as a human being under a high dose of salvia (a form of consciousness quite disconnected from terrestrial realities). But it is very probable that it is not Löbian. I don't see why they would have given the induction axioms to Mars Rover (the induction axioms is what gives the Löbian self-referential power).
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You didn't say it explicitly. It was my inference that the computer's learning algorithms would include induction.
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Yes, and that makes them universal. To make them Löbian, you need them to not just *do* induction, but they have to believe in induction.
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Roughly speaking. If *i* = "obeys the induction rule", For a UM *i* is true, but that's all. For a LUM is is not just that *i* is true, but *i*is believed by the machine. For a UM *i* is true but B*i* is false. For a LUM we have both *i* is true, and B*i* is true.
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Of course the induction here is basically the induction on numbers(*). It can be related to learning, anticipating or doing inductive inference, but the relation is not identity.
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(*) The infinity of axioms: F(0) & for all n (P(n) -> P(s(n)) ->. for all n P(n). With F any arithmetical formula, that is a formula build with the logical symbol, and the arithmetical symbols {0, s, +, *}.
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Brent

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http://iridia.ulb.ac.be/~marchal/

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