Re: free will and mathematics
On 19 Jun 2012, at 19:02, R AM wrote: On Wed, Jun 13, 2012 at 6:35 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 13 Jun 2012, at 10:44, R AM wrote: I know that you and Bruno are compatibilists. I'm not attacking your notion of free will. I agree that free will is a social construct. I'm going even further: free will doesn't even deserve a name. Deep down, free will is not something people have, but just a social definition of under what conditions or situations we will be considered responsible (and punishable). You can do that. But would *that* not be a reductionist view of reality? No, because I'm just exposing a false belief. You are saying that free-will does not exist because it is a higher level description of complex aggregations of simple processes. Not really, all I'm saying is that belief in free will is like belief in flat earth: false. And this is not based on physical reality being deterministic or random but on subjective experience: - Introspection shows that most of our thoughts and decisions are unconscious (try not to think on anything for 30 minutes and see what happens) - The idea of I could have done otherwise is silly. If you try to imagine yourself in exactly the same conscious situation, you will have to conclude that you would not have done otherwise (at least, not consciously). Otherwise, you would already have done it. Dan Dennett says most of these things much better than I could, here: http://www.youtube.com/watch?v=aKLAbWFCh1E I don't understand. You are using a false premise. We just cannot imagine ourself in exactly the same conscious situation, nor is free will based on the idea that I could have done otherwise. That would be nc-free-will, which is nonsense. But c-free-will remains sensical and a useful high level notion. If not you are on the slope of eliminativism, of free will, person if not consciousness. Dennett is on that slope, because he ignores that the physical reality is also a high level construct, and if we follow the eliminativism of high level notions, we can eliminate everything but the numbers. It would be like saying that energy does not exist. Such eliminativism seems to me a deny of facts to save at all price the aristotelian theology, which is refuted in the computationalist theories no matter what. c-free-will is not a social convention. It is real. It is based on a real intrinsic ignorance when the machine look at herself, and which can make it hesitating with respect to conscious decisions. It is a real epistemological construct, having a role in our life and in the evolution of life, even if entirely deterministic. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups 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.
Re: Autonomy?
On 19 Jun 2012, at 19:41, John Clark wrote: On Tue, Jun 19, 2012 at 6:01 AM, Bruno Marchal marc...@ulb.ac.be wrote: Unlike the proton and neutron nobody has found any experimental evidence that the electron has a inner structure, that it is made of parts. The primitive matter I talk about is the idea of primary matter in the Aristotle sense Aristotle was a great logician but a dreadful physicist. If I say that electron is not primitive, I don't mean it is made of part, almost the contrary, that it is a mathematical reality, or that it is reducible to a non physical mathematical or theological reality, an invariant in our sharable computations. I don't know what that means. What experiment would I need to perform, what would a electron need to do to prove it was primitive. The electron cannot do that, but my pet amoeba cannot prove they are unicellular, despite they are. It is just that if matter is primitive (not explainable from non material relation) then we have to make it infinite to singularize consciousness. With comp, we just abandon the idea of singularize consciousness in bodies, and then the bodies have to be explained in term of number relation. It is more easy to understand that reversal at the epistemological level. Physical concepts are not primitive means that we can reduce them to non physical concepts, like those coming from theoretical (mathematical) computer science. It means that physics is not the fundamental science. Exactly like we can reduce biology to physics, we can reduce physics to the study of machine dreams. To calculate the first 100 digits of Chaitin's constant you'd need to feed all programs that can be expressed in 100 bits or less into a Turing Machine and see how many of them stop and how many of then do not. Some of them will never stop but the only way to know how many is to wait a infinite number of years and then see how many programs are still running. So you'd need to be infinitely patient, in other words you'd need to be dead. Only to be sure of the decimals obtained. Well yeah, it's easy to calculate Chaitin's constant if you don't mind getting it wrong. After BB(100) computation steps, the decimals will be correct. I will not know it, but they are correct. If I relax that constraints, then I need only to be *very patient*. The non computable, but well defined Buzzy Beaver function (BB) bounds the time needed to wait. Of course it grows *very* fast. But I don't need an *infinite* time to get the 100 first digits correct. Any time bigger than BB(100) will do. If we wait a googoplex to the googoplex power years some 100 bit programs will still be running, some of them could be Busy Beaver programs but others could just be very long finite programs. And in the same 1962 paper where Rado introduced the idea of the beaver he proved that a general algorithm to tell if a program is a Busy Beaver or not does not exist. That is true for all programs. There is no algorithmic way to see if a program compute the factorial function. Again, this does not change anything in the argument. It's true that if you knew the numerical value of Chaitin's Constant then you would know that if a 100 bit program had not stopped after a Turing Machine had run n number of finite operations then it never will; but the trouble is you don't know Chaitin's Constant and never can, so you can never know how big n is. So even though they have been running for a googoplex to the googoplex power years one of those programs could stop 5 seconds from now. Not if I waited, by chance or whatever, a time bigger than BB(100). If a decimal change after that, then we got a computable function growing more quickly than BB. And a Busy Beaver program grows faster than any computable function but to my knowledge it has not been proven that all non-computable functions grow as fast as the Busy Beaver. That would be false. There are many non computable predicate, with non growing values. Lawrence Krauss in his book A Universe From Nothing says that someday something close to that might actually be possible. You mean? Deriving addition and multiplication from physics? No, Krauss talks about deriving physics from addition and multiplication, or at least from logic; he talks about proving that in the multiverse only certain fundamental laws of physics are logically self consistent. He even talks about the distant dream of showing that something is consistent but nothing is not. OK. Nice. That is impossible. I think both Krauss and I would give the same response to that, maybe. Why do you use gibberish to condemn free will, and not to condemn event without cause? Because the meaning of a event without a cause is clear and no circularity is involved. Cause is a fuzzy notion, and so non causal is even more fuzzy. Even the
Re: Autonomy?
On Wed, Jun 20, 2012 at 3:39 AM, Bruno Marchal marc...@ulb.ac.be wrote: It's true that if you knew the numerical value of Chaitin's Constant then you would know that if a 100 bit program had not stopped after a Turing Machine had run n number of finite operations then it never will; but the trouble is you don't know Chaitin's Constant and never can, so you can never know how big n is. So even though they have been running for a googoplex to the googoplex power years one of those programs could stop 5 seconds from now. Not if I waited, by chance or whatever, a time bigger than BB(100). Then it will never stop but you don't know it will never stop, so you'll still be looking to see if it stops in the next 5 seconds or the next 10 seconds or the next googoplex to the googoplex power years. Godel was a Platonist, he thought things were true or they were not he just said sometimes we can't know which, and Turing certainly believed all programs will come to a stop or they will not, but he was investigating if we can always obtain that one bit of information for any program and he proved we can not. Neither the Busy Beaver nor Chaitin's work on the Omega Constant changes that fact and is just more confirmation that Turing was right, not that more confirmation was needed, the proof is ironclad. If a decimal change after that, then we got a computable function growing more quickly than BB. As I've said if a program of a given size has not stopped by a certain finite number of operations it never will, but that fact does you no good at all because to know what that finite number is you'd have to know Chaitin's Constant and you don't know that and never will. John K Clark -- You received this message because you are subscribed to the Google Groups 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.
