O n Fri, Oct 2, 2015 at 10:21 AM, Bruno Marchal <marc...@ulb.ac.be> wr rote
> you seem to doubt that the existence of computation in arithmetic. Yes, I'm not dogmatic on the subject but I have grave doubts about the existence of computation in arithmetic; certainly nobody has ever seen even a hint of such a thing. > your argument relies on a notion of physical computation. Yes, I have no doubts whatsoever about the existence of computation in physics. > When I ask what that is, your definition seems to be "implementation of > computation (in the arithmetical sense) in a physical reality, > > which contradicts your statement that computation does not exist in > arithmetic. Arithmetical objects (like numbers) can be computed no doubt about , it but as far as we know not by arithmetic, only by physics. > > which contradicts your statement that computation does not exist in > arithmetic. There is no contradiction, a rithmetical objects can certainly be computed but the question is what is doing the computing, is physics doing it or is arithmetic doing it to itself? I think physics is more likely. > you persist in confusing what is a computation in the CHurch-Turing sense, If " computation in the C h urch-Turing sense " doesn't mean finding a particular solution to a particular arithmetical problem then " computation in the C h urch-Turing sense " INTEL would not find it interesting and neither would I. > > > none of those theories can perform calculations, no theory can, I agree Actually theory are not necessarily supposed to be able to do that, I agree. > > only machine (in the mathematical sense) can do that. O nl y a machine (in the PHYSICAL sense) can do that. > > Now, it happens that if a theory is sigma_1 complete, like RA and PA, they > can do that, because such theories are universal machine If you know how to do that then for God's sake stop talking about it and just do it, start the Sigma 1 PARA Hardware Corporation and change the world! > > Physical material can do that [computation] in the physical world Yes and only physical material can do that , and I have a explanation of why that is so. You do not. > but here we talk about the computation done in arithmetic. No , here we talk about the computation done *TO* arithmetical objects ( by physics). Arithmetic is unchanging, nothing can be done in it; if you want to actually DO something and not just define something physics is needed. > obviously, we cannot use them in any direct way, like we can do with a > physical machine. If mathematics is more fundamental than physics as you say then it's about as far from obvious as you can get to understand WHY we can't do calculations directly but must instead get our hands dirty and mess around with elements such as silicon. > > you accept comp, I do not accept "comp". > > All your post illustrates that you are a sort of comp believer. None of my posts illustrates that I am a "comp" believer. > Comp is put for computationalism. No it is not. Over the years I have heard you say hundred s maybe thousands of times "according to comp this and according to comp th a t", but I am still unable to form a coherent picture of what you're talking about ; but I have a very clear understanding of computationalism so I know that whatever "comp" is it certainly isn't computationalism. > > > > That computations exist in arithmetic (even in the small sigma_1 complete > part) is accepted by all experts And yet for some strange reason like you none of these experts have become filthy rich by starting a computer hardware company that doesn't need to manufacture hardware. I find that very odd. > Of course. But once Turing defined calculation/computation > [...] > If definitions could make calculations INTEL would make definitions instead of silicon microchips because making definitions is one hell of a lot easier than making physical objects. > > it has been proved that it exists in any model of arithmetic, a fortiori > in the standard model. Proofs are no more adept than definitions at making calculations. > > You need a physical reality only to implement a physical computation. But > that is trivial, Try telling the stockholders and scientists at INTEL it's trivial! >> if you want to know a particular solution to a particular problem in >> arithmetic because neither proofs nor theorems can make a calculation; for >> that you need physics. > > > Yes, but it happens that we are not interested in having a solution, but > only in their existence, Then you're not interested in computations . T here is no disputing matters of taste but I am interested in computations and so is INTEL. John K Clark > How could a universal Turing machine makes the difference between an implementation in arithmetic and an implementation in a physical reality? "I compute therefore I am physical", or even more fundamentally "I am not static therefore I am physica l". 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