On 22 Aug 2012, at 12:17, benjayk wrote:

Bruno Marchal wrote:On 22 Aug 2012, at 00:26, benjayk wrote:meekerdb wrote:On 8/21/2012 2:52 PM, benjayk wrote:meekerdb wrote:On 8/21/2012 2:24 PM, benjayk wrote:meekerdb wrote:"This sentence cannot be confirmed to be true by a humanbeing."The ComputerHe might be right in saying that (See my response to Saibal). But it can't confirm it as well (how could it, since we as humans can't confirm it and what he knows about us derives from what we program into it?). So still, it is less capable than a human.I know it by simple logic - in which I have observed humans to be relatively slow and error prone. regards, The ComputerWell, that is you imagining to be a computer. But program anactualcomputer that concludes this without it being hard-coded into it. All it could do is repeat the opinion you feed it, or disagree with you, depending on how you program it. There is nothing computational that suggest that the statement is true or false. Or if it you believe it is, please attempt to show how. In fact there is a better formulation of the problem: 'The truth- value of this statement is not computable.'.It is true, but this can't be computed, so obviously no computercanreach this conclusion without it being fed to it via input (which is something external to the computer). Yet we can see that it is true.Not really. You're equivocating on "computable" as "what can be computed" and "what a computer does". You're supposing that a computer cannot have the reflexive inference capability to "see" that the statement is true.No, I don't supppose that it does. It results from the fact that we get a contradiction if the computer could see that the statement is true (since it had to compute it, which is all it can do).A computer can do much more than computing. It can do proving, defining, inductive inference (guessing), and many other things. You might say that all this is, at some lower level, still computation,Sorry, but the opposite is the case. To say that computers do proving,defining, guessing is a confusion of level, since these areinterpretationof computations, or are represented using computations, not thecomputationsitself. If we encode a proof using numbers, then this is not the proofitself, but its representation in numbers. Just as "Gödel's proof"is notGödel's proof just because I say it represents Gödel's proof. Or just as I say computers the word computers don't compute anything.

`That is why when I say that a computer dreams, or that a number`

`dreams, it is a shorthand for a computer having an activity supporting`

`a dream, or a number involved in an arithmetical realization of a dream.`

This makes sense in the comp theory.

`In arithmetic too we already make the distinction between a number`

`representing a proof and the proof itself, which is the sequence of`

`distinct formula verifying some conditions.`

Computers do that distinction.

`PA use numbers as language like German use the German language, but`

`both the Germans and PA will distinguish what they talk about and the`

`syntactical terms used to denote them.`

Imagine a computer without an output. Now, if we look at what thecomputeris doing, we can not infer what it is actually doing in terms ofhigh-levelactivity, because this is just defined at the output/input. Forexample, novideo exists in the computer - the data of the video could be otherdata aswell. We would indeed just find computation. At the level of the chip, notions like definition, proving, inductiveinterference don't exist. And if we believe the church-turingthesis, theycan't exist in any computation (since all are equivalent to acomputation ofa turing computer, which doesn't have those notions), they would bemerelylabels that we use in our programming language.

`All computers are equivalent with respect to computability. This does`

`not entail that all computers are equivalent to respect of`

`provability. Indeed the PA machines proves much more than the RA`

`machines. The ZF machine proves much more than the PA machines. But`

`they do prove in the operational meaning of the term. They actually`

`give proof of statements. Like you can say that a computer can play`

`chess.`

`Computability is closed for the diagonal procedure, but not`

`provability, game, definability, etc.`

That is the reason that I don't buy turings thesis, because itintends toreduce all computation to a turing machine

`... to a Turing machine activity (as defined in math, I don't mean`

`physical activity).`

just because it can berepresented using computation. But ultimately a simple machine can'tcomputethe same as a complex one, because we need a next layer to interpretthesimple computations as complex ones (which is possible). That is,assemblerisn't as powerful as C++, because we need additional layers toretrieve thesame information from the output of the assembler.

`That depends how you implement C++. It is not relevant. We might`

`directly translate C++ in the physical layer, and emulate some`

`assembler in the C++.`

`But assembler and C++ are computationally equivalent because their`

`programs exhaust the computable function by a Turing universal machine.`

You are right that we can confuse the levels in some way,

`Better not to confuse the levels ever, except when using fixed point`

`theorem justifying precisely how to fuse levels.`

basically because there is no way to actually completely seperate them.

When we look at an unknown machine, yes.

But in this case we can also confuse all symbols and definitions, in effect deconstructinglanguage. So as long as we rely on precise, non-poetic language itis wiseto seperate levels.

OK. I agree with this. Bruno

Bruno Marchal wrote:but then this can be said for us too, and that would be a confusionoflevel.Only if we assume we are computational. I don't. Bruno Marchal wrote:The fact that a computer is universal for computation does not imply logically that a computer can do only computations. You couldsay that a brain can only do electrical spiking, or that moleculescanonly do electron sharing.You have a point here. Physical computers must do more thencomputation,because they must convert abstract information into physical signals(whichdon't exist at the level of computation).But if we really are talking about the abstract aspect of computers,I thinkmy point is still valid. It can only do computations, because all wedefinedit as is in terms of computationl. benjayk -- View this message in context: http://old.nabble.com/Simple-proof-that-our-intelligence-transcends-that-of-computers-tp34330236p34333663.html Sent from the Everything List mailing list archive at Nabble.com. --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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