Re: bruno list
On Sun, Jul 31, 2011 at 7:14 AM, Craig Weinberg whatsons...@gmail.com wrote: The China brain can't simulate the interior sense of a neuron. It's just a dynamic sculpture. Maybe the same is true of brains. Just because something behaves as if it has feelings and understanding doesn't mean that it really has feelings and understanding. Besides, the very notion that a carbon-based construct could be conscious is clearly ridiculous! http://www.terrybisson.com/page6/page6.html http://www.youtube.com/watch?v=gaFZTAOb7IE -- Stathis Papaioannou -- 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: bruno list
On Jul 31, 7:07 am, Stathis Papaioannou stath...@gmail.com wrote: On Sun, Jul 31, 2011 at 7:14 AM, Craig Weinberg whatsons...@gmail.com wrote: The China brain can't simulate the interior sense of a neuron. It's just a dynamic sculpture. Maybe the same is true of brains. Just because something behaves as if it has feelings and understanding doesn't mean that it really has feelings and understanding. Besides, the very notion that a carbon-based construct could be conscious is clearly ridiculous! http://www.terrybisson.com/page6/page6.html http://www.youtube.com/watch?v=gaFZTAOb7IE Nice. You're making my point though. We would have no clue that our brains could think by the exterior behavior of the neurons it's made of. It's only because we are our brains that we know it is the case that groups of neurons do think and feel. Therefore, designing something based upon only what our brain appears to us to be doing (not much... just another interesting organ in the body doing it's cell/organ things) doesn't mean that the thinking and feeling is going to show up by itself. If we could modify our own minds first to be able to see and feel the thoughts and feelings of another brain, then we would be more likely to be able to tell whether we were on the right track in designing a deep AGI. Without that sense, we're like blind people comparing the beauty of the pictures we've painted - insisting that if it feels like the Mona Lisa to touch then there's no reason why it couldn't look exactly like the Mona Lisa. You need the right brushstrokes, definitely, but if you can't see the color of the paint and do it all in black it doesn't much matter. -- 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.
Math Question
Reblogging myself here, but curious to see what you think of the idea that 1 cannot be proven greater than 0. Someone’s comment on the previous chart mentioned the difficulty (impossibility?) of proving that 1 0. It’s an interesting kernel there, and it reminds me of the whole “time does not physically exist” realization. On one level, I can think of zero as having no different relation to 1 than it has with any other number. Zero does the same thing to any number as it does to one and should be thought of more properly as the hub of the decimal spiral. I’m no mathematician, but I suppose that 0 is also formally defined as an integer between 1 and -1 or something. Still it exposes the question of whether the elemental underpinnings of our ability to count is really anchored in anything at all other than our own anthropological conventions of counting. Beyond numbers themselves, it appears that the whole quantitative notion - of greater than or less than, and of ‘equal’ is nothing but a figment of our feelings about order. There may not be any inherent moreness to something than the absence of something. If it’s the same thing, it actually seems more palatable to see the absence of something being a condition predicated upon the things’ a priori presence, no? Even if we want to get into quantum atopoietic craziness where things come out of nothing, rendering such a possibility discretely seems to threaten the whole notion of mathematical coherence. If any or all quantities, variables, and formulas can be generated arbitrarily from 0, then 0 would seem to be the same thing as ∞, and greater than 1 or any other arithmetic expression. Anthrodeximal Numberline Maybe it’s time to create a new numberline, without all of the repetitive decimal numerals. Instead there could be a Wiki of new quantitative symbols and names which anyone can add to and own as a permanent vector in the schema. It would be easy to translate them to and from Arabic numerals online and some interesting possibilities for informal encryption and unanticipated mathematic-linguistic synchronicity. By removing the aspect of repetition, we would unmask the semantic bias of the math logos and arrive at a pure generic linear calibration defined only in it’s own idiosyncratic a-signifying terms. Sort of like breaking the mantra of math, it’s trance-like rhythms that disguise it’s human neurological origin from us. By adding more unique qualitative sense to the thing, the quality-flattening power drains out and the system seems to disqualify itself. -- 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: bruno list
Hi Craig, Sorry for having take some time to comment your posts. I will be busy the two next weeks, so be patient for possible comments. I comment all your 3 posts addressed to me in one mail. On 30 Jul 2011, at 15:50, Craig Weinberg wrote: Chipping away at it.. more later. On Jul 29, 3:51 pm, Bruno Marchal marc...@ulb.ac.be wrote: On 28 Jul 2011, at 17:41, Craig Weinberg wrote: A machine cannot have an experience, it is the container, it is that which is experienced, No. The machine itself is not experienced. The experience of the machine is experienced, and it may, or not, refer to some representational level. Fair enough. From a truly objective perspective though, how could the experience of the machine NOT refer to some phenomenological level. Of course. To say that it is representational is to conflate the referent and the signifier. Not at all. It is a bet on the invariance of our subjective experience on a substitution level. Biology illustrates already the idea in the language of chemistry. Comp does not imply that everything is representational, nor that Turing machine can simulate everything. On the contrary, some machine's attributes are not Turing emulable. In order for the machine to STOP, there doesn't automatically need to exist a 1p experience of a red sign. It depends on the machine. In the case of human, there usually are 1p experience. I assume comp. In our 1p, we see a red stop sign as a qualitative image, we understand it as a symbolic text, we interpret it as a pragmatic condition that motivates us to respond with motor commands to our body to push the brake, the brake stops the car. Yes. But that is not an argument that some machine cannot do that. In the comp theory, there is no need to eliminate the 1p experience. Don't confuse the comp theory, and its misuse by materialists. Through our interpretation we re-present the signifier, which is a representation-neutral experience of presented color, shape, size, and context. As the machine is a reverse engineered logic, we have no reason to presume that our signifier - the red light or sign, is presented just because a command is sent to the processor queue to stop the car when the ccd in the camera encounters electromagnetic changes of a particular sampled configuration. You are right, but this only means that we fail on the correct substitution level. If we are machine, we cannot know which machine we are, nor really which computations go through, but we still face something partially explainable. It's going to stop the car whether there is an experience of a sign or not. I say that there is an experience, but it's likely not remotely like a human signifier and would compare as one piano note compared to an entire symphony, if not the sum of hundreds of symphonies filtered through different molecular, cellular, physiological, neurological, and psychological audiences. My point works even if you decided that your generalized brain (the part of reality I need to emulate to get your consciousness preserved) is given by the quantum rational Heisenberg matrix, of the whole cluster of galaxies, at the level of strings. but it has no capacity to experience anything as an abstract design. What is abstract? What is concrete? An abstraction is an ideal teleological signifier, having no relevant physical qualities itself but the capacity to be used as a template to inform both physical and ideal forms. Concrete is the opposite, a material referent which exists physically as an objective phenomena which is subject to the teleonomy of physical, chemical, biological consequences. That seems quite abstract to me. I don't buy that there is necessarily a given physical universe. It is only an Aristotelian rumor, based on a gross extrapolation on our animal experience. But it fails, both on mind *and* matter. I hear what you're saying, and I agree in the sense that from the absolutely objective 0/∞p perspective there is no special difference between physical and non-physical phenomena, You miss the point. Comp shows and makes it possible to illustrate the needs to explain how the physical arises or is build from conceptually simpler non physical notions, already well known, which are the mathematical relations. but in SEE, the idea is that existence is a relation of essential phenomena confronting it's tail, I think that you might confuse existence with consciousness. I think a scientist does not commit himself ontologically, beyond the terms of its theory. through the involution of time-space characteristics. This does not help. In this sense both mind and matter the notions of mind and matter lose all absolute character of abstract or concrete - it is only through perceptual relativity which the tail is assigned material qualities from the 1p of it's 'head'. Perceptual relativity bundles the individual piano notes of
Re: Math Question
On 31 Jul 2011, at 14:15, Craig Weinberg wrote: Reblogging myself here, but curious to see what you think of the idea that 1 cannot be proven greater than 0. In which theory? The notion of proof is theory and definition dependent. (contrary to computability, which is absolute, by Church thesis). If you agree to define x y by Ez(z+x = y)E = It exists. I assume classical logic + the axioms: x+0 = x x+s(y) = s(x+y) 0 denotes the number zero, and s(x) denotes the successor of x, often noted as x+1. Cf the whole theory I gave last week. I use only a subset of that theory here. So we have to prove that 0 s(0). By the definition of above, we have to prove that Ez(z + 0 = s(0)) But s(0) + 0 = s(0) by the axiom x + 0 = x given above. So Ez(0 + z = s(0)) is true, with z = s(0). (This is the usual use of the existence rule of classical logic). Of course we could have taken the theory with the unique axiom 1 is greater than 0. For all proposition we can always find a theory which proves it. The interesting thing consists in proving new fact in some fixed theory, and change only a theory when it fails to prove a fact for which we have compelling evidences. Bruno Someone’s comment on the previous chart mentioned the difficulty (impossibility?) of proving that 1 0. It’s an interesting kernel there, and it reminds me of the whole “time does not physically exist” realization. On one level, I can think of zero as having no different relation to 1 than it has with any other number. Zero does the same thing to any number as it does to one and should be thought of more properly as the hub of the decimal spiral. I’m no mathematician, but I suppose that 0 is also formally defined as an integer between 1 and -1 or something. Still it exposes the question of whether the elemental underpinnings of our ability to count is really anchored in anything at all other than our own anthropological conventions of counting. Beyond numbers themselves, it appears that the whole quantitative notion - of greater than or less than, and of ‘equal’ is nothing but a figment of our feelings about order. There may not be any inherent moreness to something than the absence of something. If it’s the same thing, it actually seems more palatable to see the absence of something being a condition predicated upon the things’ a priori presence, no? Even if we want to get into quantum atopoietic craziness where things come out of nothing, rendering such a possibility discretely seems to threaten the whole notion of mathematical coherence. If any or all quantities, variables, and formulas can be generated arbitrarily from 0, then 0 would seem to be the same thing as ∞, and greater than 1 or any other arithmetic expression. Anthrodeximal Numberline Maybe it’s time to create a new numberline, without all of the repetitive decimal numerals. Instead there could be a Wiki of new quantitative symbols and names which anyone can add to and own as a permanent vector in the schema. It would be easy to translate them to and from Arabic numerals online and some interesting possibilities for informal encryption and unanticipated mathematic-linguistic synchronicity. By removing the aspect of repetition, we would unmask the semantic bias of the math logos and arrive at a pure generic linear calibration defined only in it’s own idiosyncratic a-signifying terms. Sort of like breaking the mantra of math, it’s trance-like rhythms that disguise it’s human neurological origin from us. By adding more unique qualitative sense to the thing, the quality-flattening power drains out and the system seems to disqualify itself. -- 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 . 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: COMP refutation paper - finally out
Bruno Marchal wrote: On 24 Jul 2011, at 22:08, benjayk wrote: OK. Remember the goal, to find the, or a, TOE. What I suggest, at least, is that with comp, any first order logical specification of any universal machine, will do. Well, okay. I just get the feeling that a TOE doesn't really exist. You just have a theory that manages to state this very clearly, and logically. You might try to take literally what I say. I was saying that each universal numbers (like FORTRAN, Conway's game of life, LISP, prolog, Robinson arithmetic, etc.) are TOE. To fix the things I have chosen Robinson Arithmetic. The theory of everything is basically a bit of classical logic and the axioms: 0 ≠ s(x) s(x) = s(y) - x = y x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Another one is mainly Kxy = x Sxyz = xz(yz) That gives rich ontologies in which internal observers project realities. With comp we have to embed the mathematician (the little ego!) in arithmetics, and the laws of mind and matter does not depend on the choice of the first initial universal system. All computations contains all computations by all universal systems, that is why the tehological matter (including physics) does not depend on the initial choice. It does not mean that there is no TOE. Only a lot, which are equivalent for the fundamental matter. They lead all to the same hypostases, once you accept the classical theory of knowledge (Theaetetus). We can debate the terms. I think calling universal systems a TOE is a bit of a stretch. The notion of a TOE usually is used in a reductionist sense, as a theory that can be used to predict everything. I don't think this can be done through universal systems. It appears to me COMP allows for uncomputable, and therefore unpredictable phenomena. I am critical of the very notion of a TOE. It doesn't make much sense. Even current physics clearly shows that results of experiments can't be predicted precisely. So is the TOE supposed to give a perfect probability distribution? But what is this even supposed to mean? COMP shows, as you said, that there are unbridgeable gaps, which really means there is something left unexplained, and unexplainable. So no theory can explain everything. But we can show the necessity of there being a gap. -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164031.html Sent from the Everything List mailing list archive at Nabble.com. -- 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: COMP refutation paper - finally out
Bruno Marchal wrote: On 24 Jul 2011, at 22:08, benjayk wrote: OK. Remember the goal, to find the, or a, TOE. What I suggest, at least, is that with comp, any first order logical specification of any universal machine, will do. Well, okay. I just get the feeling that a TOE doesn't really exist. You just have a theory that manages to state this very clearly, and logically. You might try to take literally what I say. I was saying that each universal numbers (like FORTRAN, Conway's game of life, LISP, prolog, Robinson arithmetic, etc.) are TOE. To fix the things I have chosen Robinson Arithmetic. The theory of everything is basically a bit of classical logic and the axioms: 0 ≠ s(x) s(x) = s(y) - x = y x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Another one is mainly Kxy = x Sxyz = xz(yz) That gives rich ontologies in which internal observers project realities. With comp we have to embed the mathematician (the little ego!) in arithmetics, and the laws of mind and matter does not depend on the choice of the first initial universal system. All computations contains all computations by all universal systems, that is why the tehological matter (including physics) does not depend on the initial choice. It does not mean that there is no TOE. Only a lot, which are equivalent for the fundamental matter. They lead all to the same hypostases, once you accept the classical theory of knowledge (Theaetetus). We can debate the terms. I think calling universal systems a TOE is a bit of a stretch. The notion of a TOE usually is used in a reductionist sense, as a theory that can be used to predict everything. I don't think this can be done through universal systems. It appears to me COMP allows for uncomputable, and therefore unpredictable phenomena. I am critical of the very notion of a TOE. It doesn't make much sense. Even current physics clearly shows that results of experiments can't be predicted precisely. So is the TOE supposed to give a perfect probability distribution? But what is this even supposed to mean? COMP shows, as you said, that there are unbridgeable gaps, which really means there is something left unexplained, and unexplainable. So no theory can explain everything. But we can show the necessity of there being a gap. -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164032.html Sent from the Everything List mailing list archive at Nabble.com. -- 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: COMP refutation paper - finally out
Bruno Marchal wrote: On 24 Jul 2011, at 22:08, benjayk wrote: OK. Remember the goal, to find the, or a, TOE. What I suggest, at least, is that with comp, any first order logical specification of any universal machine, will do. Well, okay. I just get the feeling that a TOE doesn't really exist. You just have a theory that manages to state this very clearly, and logically. You might try to take literally what I say. I was saying that each universal numbers (like FORTRAN, Conway's game of life, LISP, prolog, Robinson arithmetic, etc.) are TOE. To fix the things I have chosen Robinson Arithmetic. The theory of everything is basically a bit of classical logic and the axioms: 0 ≠ s(x) s(x) = s(y) - x = y x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Another one is mainly Kxy = x Sxyz = xz(yz) That gives rich ontologies in which internal observers project realities. With comp we have to embed the mathematician (the little ego!) in arithmetics, and the laws of mind and matter does not depend on the choice of the first initial universal system. All computations contains all computations by all universal systems, that is why the tehological matter (including physics) does not depend on the initial choice. It does not mean that there is no TOE. Only a lot, which are equivalent for the fundamental matter. They lead all to the same hypostases, once you accept the classical theory of knowledge (Theaetetus). We can debate the terms. I think calling universal systems a TOE is a bit of a stretch. The notion of a TOE usually is used in a reductionist sense, as a theory that can be used to predict everything. I don't think this can be done through universal systems. It appears to me COMP allows for uncomputable, and therefore unpredictable phenomena. I am critical of the very notion of a TOE. It doesn't make much sense. Even current physics clearly shows that results of experiments can't be predicted precisely. So is the TOE supposed to give a perfect probability distribution? But what is this even supposed to mean? COMP shows, as you said, that there are unbridgeable gaps, which really means there is something left unexplained, and unexplainable. So no theory can explain everything. But we can show the necessity of there being a gap. -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164033.html Sent from the Everything List mailing list archive at Nabble.com. -- 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: Math Question
On Jul 31, 9:49 am, Bruno Marchal marc...@ulb.ac.be wrote: In which theory? The notion of proof is theory and definition dependent. (contrary to computability, which is absolute, by Church thesis). If you agree to define x y by Ez(z+x = y) E = It exists. I assume classical logic + the axioms: x+0 = x x+s(y) = s(x+y) 0 denotes the number zero, and s(x) denotes the successor of x, often noted as x+1. Cf the whole theory I gave last week. I use only a subset of that theory here. So we have to prove that 0 s(0). By the definition of above, we have to prove that Ez(z + 0 = s(0)) But s(0) + 0 = s(0) by the axiom x + 0 = x given above. So Ez(0 + z = s(0)) is true, with z = s(0). (This is the usual use of the existence rule of classical logic). Of course we could have taken the theory with the unique axiom 1 is greater than 0. For all proposition we can always find a theory which proves it. The interesting thing consists in proving new fact in some fixed theory, and change only a theory when it fails to prove a fact for which we have compelling evidences. How do we know that 0 has a successor though? If 0 x = x and x -0 = x then maybe s(0)=0 or Ezs(0)... Can we disprove the idea that a successor to zero does not exist? Sorry, I'm probably not at the minimum level of competence to understand this. -- 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: COMP refutation paper - finally out
On 31 Jul 2011, at 16:14, benjayk wrote: Bruno Marchal wrote: On 24 Jul 2011, at 22:08, benjayk wrote: OK. Remember the goal, to find the, or a, TOE. What I suggest, at least, is that with comp, any first order logical specification of any universal machine, will do. Well, okay. I just get the feeling that a TOE doesn't really exist. You just have a theory that manages to state this very clearly, and logically. You might try to take literally what I say. I was saying that each universal numbers (like FORTRAN, Conway's game of life, LISP, prolog, Robinson arithmetic, etc.) are TOE. To fix the things I have chosen Robinson Arithmetic. The theory of everything is basically a bit of classical logic and the axioms: 0 ≠ s(x) s(x) = s(y) - x = y x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Another one is mainly Kxy = x Sxyz = xz(yz) That gives rich ontologies in which internal observers project realities. With comp we have to embed the mathematician (the little ego!) in arithmetics, and the laws of mind and matter does not depend on the choice of the first initial universal system. All computations contains all computations by all universal systems, that is why the tehological matter (including physics) does not depend on the initial choice. It does not mean that there is no TOE. Only a lot, which are equivalent for the fundamental matter. They lead all to the same hypostases, once you accept the classical theory of knowledge (Theaetetus). We can debate the terms. OK. I think calling universal systems a TOE is a bit of a stretch. Just to be precise, the TOE is not the universal system, but some first order classical logic, with equality, extension of the chosen universal system. OK. (the UMs and the LUMs are more like hero and heroin in the dramas the TOE allows) The notion of a TOE usually is used in a reductionist sense, as a theory that can be used to predict everything. A TOE should do that, in principle at least. Of course it should be able to predict everything which is predictible, in the right condition. No one asks for a TOE which can predict things which are not predictible. No TOE can predict that you will feel to be, just after the duplication, in W or in M. I don't think this can be done through universal systems. It appears to me COMP allows for uncomputable, and therefore unpredictable phenomena. A lot. All surprises hide surprises. I am critical of the very notion of a TOE. It doesn't make much sense. Even current physics clearly shows that results of experiments can't be predicted precisely. So is the TOE supposed to give a perfect probability distribution? But what is this even supposed to mean? The exact contrary. Comp is not just a change in 'perspective' (Aristotle - Plato), but the discovery of a creative bomb (the UM). With comp we begin to know that we don't know what we are doing. We can (machines can) understand that by trying to control it, we make it less controllable. A bit like a mother with a baby. That is not something entirely new, but here it appears in the 3-theories. COMP shows, as you said, that there are unbridgeable gaps, which really means there is something left unexplained, and unexplainable. Absolutely so (assuming comp). comp = CT + yes doctor. CT subsumes arithmetic. So no theory can explain everything. But we can show the necessity of there being a gap. OK. You are right. I will abandon the label TOE, for TOAE. Theory of almost everything. But, you know, it is more than the necessity for a gap, it is the discovery that the gap 'kick back', it has a geometry, it is something and machines have access to it, they can point mathematical telescope on it, also. Comp leads to a generalization of Everett's idea to apply QM to the observer. Comp applies arithmetic and meta-arithmetic (a part of arithmetic by Post, Gödel, Kleene Co.) to the 'body' of the mathematician, or at least the one who say yes doctor to a doctor which serendipitously opts for the correct level, in a mathematical precise sense: in this case it inherits of the hypostases, and the logic of it determine the views you can have from inside. But the simplest thing you can say on those views is that they all make us more ignorant. The concrete relative Löbian machines get interesting on the border of the computable and non computable, where very deep sharable histories develop, in all case, from all views some mysteries subsists, and some key mystery, the gap, have a quasi life of its own. But *that* fact, that there are mysteries, is no more a mystery. And in that sense, comp provides, I think, the first coherent picture of almost everything, from God (oops!) to qualia, quanta included, and this by assuming only seven arithmetical axioms. And the point is not that this is true, but that this is testable. Comp, not so much unlike salvia perhaps, put you
Re: Math Question
On 31 Jul 2011, at 17:08, Craig Weinberg wrote: On Jul 31, 9:49 am, Bruno Marchal marc...@ulb.ac.be wrote: In which theory? The notion of proof is theory and definition dependent. (contrary to computability, which is absolute, by Church thesis). If you agree to define x y by Ez(z+x = y)E = It exists. I assume classical logic + the axioms: x+0 = x x+s(y) = s(x+y) 0 denotes the number zero, and s(x) denotes the successor of x, often noted as x+1. Cf the whole theory I gave last week. I use only a subset of that theory here. So we have to prove that 0 s(0). By the definition of above, we have to prove that Ez(z + 0 = s(0)) But s(0) + 0 = s(0) by the axiom x + 0 = x given above. So Ez(0 + z = s(0)) is true, with z = s(0). (This is the usual use of the existence rule of classical logic). Of course we could have taken the theory with the unique axiom 1 is greater than 0. For all proposition we can always find a theory which proves it. The interesting thing consists in proving new fact in some fixed theory, and change only a theory when it fails to prove a fact for which we have compelling evidences. How do we know that 0 has a successor though? If 0 x = x and x -0 = x then maybe s(0)=0 or Ezs(0)... Can we disprove the idea that a successor to zero does not exist? No. 0 is primitive term, and the language allows the term s(t) for all term t, so you have the terms 0, s(0), s(s(0)), etc. The rest follows from the axioms For all x 0 ≠ s(x), s(x) = s(y) - x = y (so that all numbers have only one successor. So you can, prove, even without induction, that 0 has a unique successor, different from itself. Sorry, I'm probably not at the minimum level of competence to understand this. I look on the net, but I see errors (Wolfram's definition is Dedekind Arithmetic!)? On wiki, the definition of Peano arithmetic seems correct. You need to study some elementary textbook in mathematical logic. Most presentation assumes you know what is first order predicate logic. You can google on those terms. There are good books, but it is a bit involved subject and ask for some works. Peano Arithmetic is the simplest example of Löbian theory or machines or belief system. It is very powerful. You light take time to find an arithmetical proposition that you can prove to be true and that she can't, especially without using the technics for doing that. Most interesting theorem in usual (non Logic) mathematics can be prove in or by PA. And PA, like all Löbian machine, can prove its own Gödel theorem (if I am consistent then I cannot prove that I am consistent). The I is a 3-I. Bruno -- 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 . 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: COMP refutation paper - finally out
Bruno Marchal wrote: Arithmetic just happens to be powerful enough to point towards it. All other universal systems accomplish the same. So to say just number relations exist and all else is an epistemological view on that is a very narrow interpretation. Arithmetical truth contains fortranic truth, lispic truth, combinatoric truth, etc. It does not contains theological truth, nor physical truth, except in the 'epistemological' points of view of the creature they have all. How exactly do we know that these epistemological truths are secondary / not ontological? I don't really see how COMP does tell us that, as it could well be that the assumptions COMP makes (including consciousness exists, in order to say yes, doctor) are in some sense equivalent to the epistemological points of view whose existence we derive from the assumptions of COMP. I can't prove this (I don't think it can be proven), but for me it seems like this is the case. -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164556.html Sent from the Everything List mailing list archive at Nabble.com. -- 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: COMP refutation paper - finally out
On 31 Jul 2011, at 18:24, benjayk wrote: Bruno Marchal wrote: Arithmetic just happens to be powerful enough to point towards it. All other universal systems accomplish the same. So to say just number relations exist and all else is an epistemological view on that is a very narrow interpretation. Arithmetical truth contains fortranic truth, lispic truth, combinatoric truth, etc. It does not contains theological truth, nor physical truth, except in the 'epistemological' points of view of the creature they have all. How exactly do we know that these epistemological truths are secondary / not ontological? I don't really see how COMP does tell us that, as it could well be that the assumptions COMP makes (including consciousness exists, in order to say yes, doctor) are in some sense equivalent to the epistemological points of view whose existence we derive from the assumptions of COMP. I can't prove this (I don't think it can be proven), but for me it seems like this is the case. It is just that we don't need to assume them. It is like the invisible horses pulling a car. You can reify the epistemological truth in some ontology, but there is no need to do that, and it makes the MB problem more difficult. In science, you can never proof that a theory is wrong, by changing ad-hocly the way you interpret the data. The epistemological view are secondary because they are recovered by the way machine looks at the arithmetical reality. The simplest ontology are the numbers, and the internal view, including the physical, are given by the arithmetical modalities, like Bp and Bp Dp, or the less arithmetical one, like Bp p, Bp Dp p, etc. At least in the toy theology based on the Theaetetus definition of knowledge (justified opinion which happens to be God's opinion (I mean which happens to be true)). Bruno -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164556.html Sent from the Everything List mailing list archive at Nabble.com. -- 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 . 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: bruno list
On 7/31/2011 1:19 AM, Craig Weinberg wrote: On Jul 30, 10:30 pm, Jason Reschjasonre...@gmail.com wrote: So the only sturcture in the universe that can perceive are neurons or groups of neurons? No, not at all. Everything perceives like what it is, Even software? Software isn't a thing in the way I'm using the word. It's an idea that informs a thing. What determines what software feels? The thing it runs on. When you play a computer game, you are running software on your brain. It feels like a computer game to you. If it runs on a computer with nobody playing it, there is no computer game being played, just circuits switching rhythmically. It can build a something larger, it just doesn't necessarily cohere as a single entity, and if it did, it may not resemble ourselves. But it could? I don't see why not. There might be a reason, but we wouldn't likely know it. And if it were designed with the same organization as a smaller sized brain, why wouldn't it? Organization alone is meaningless. To change the size of the brain runs into problems with the chemistry. The conjoined twins show that brains can be combined. It's the material and the function. From this it follows that a China brain would have mental states: it has the same material and function. A person standing next to another person is not the same thing as a molecule next to another molecule. If the Earth as a whole has a mental state, it may very well be able to use some arrangement of human bodies as a kind of neuron or something. On the scale of a planet, all of that molten iron and nickel swirling around may have a kind of consciousness that dwarfs our own. It won't be an animal feeling, with adrenaline and oxytocin emotions, but it could be unfathomably beautiful to be the biosphere and atmosphere, crust, mantle, and core with centuries passing like minutes. how do you figure? A human body is the same thing as a molecule in a neuron? A human brain is made of neurons, the china brain is made of neurons. (The brains of many individuals each functioning as a neuron does in a more conventional brain) Oh hold on. I read it wrong. Sorry . I thought the whole group was collectively acting as a single neuron. The problem is that acting like we think a neuron acts and being a neuron are two different things. If they did a China match instead, where each person pretended to be a molecule of phosphorous or whatever, there would be no way to make them act like fire so that there would be heat, flame, etc. The fact that the brain scales up from neurons is a crazy miraculous fragile thing, not a mechanical consequence of any old thing times a billion acting in a certain way. The way it acts is important, but only if what it is that's acting that way is the appropriate match for the actions. Church-Turing is false. If you can demonstrate this you will become famous, and probably win a Turing award (comes with $250,000). It's false and it's not falsifiable because it's defining one process as a function of the other, when in fact they are the same process. Explain why fire cannot be simulated by water? Because fire is a reaction which produces heat and light, and water does not. That is not an argument against my assertion that a Turing machine made of water can simulate the heat light and reaction products of fire. Heat and light cannot be simulated. They are experiences. It doesn't matter what the Turing machine is made of if it is not combustible. Again, you're just bringing the assumptions of a flawed model to their absurd conclusions. Not trying to criticize you personally, I'm just saying it's plain that water cannot simulate fire. You are confusing the exterior and interior. On the interior there is fire, in the exterior there is a Turing machine made of water. I understand what you're saying, but you're not getting my points. The interior of a machine made of ice has the interior experience of a machine made of ice, regardless of what that machine is doing. The experience you have is an experience you are having regardless of what you are doing or perceiving - it's a human experience. On the interior there is thought and sensation, in the exterior there is a brain. On the interior is thought and sensation, in the exterior there is a man-made computer. Yes, except the thought of a computer is not understanding, it's just circuit navigation. The computer isn't a gestalt entity except in our experience. Pieces can burn out and it will never know the difference as a whole, different components will just have shorter circuits to run. Your ice fire makes no heat, consumes no fuel. Not externally, but it would internally. I understand why that makes sense, but it's incorrect. Heat cannot be simulated and it cannot be generated by an abstraction. There is no numerical formula which can create heat in and of itself. Craig Hi Guys, Strangely enough, our best explanation of heat tells us that heat is
Re: Math Question
On 7/31/2011 8:15 AM, Craig Weinberg wrote: Reblogging myself here, but curious to see what you think of the idea that 1 cannot be proven greater than 0. Someone’s comment on the previous chart mentioned the difficulty (impossibility?) of proving that 1 0. It’s an interesting kernel there, and it reminds me of the whole “time does not physically exist” realization. On one level, I can think of zero as having no different relation to 1 than it has with any other number. Zero does the same thing to any number as it does to one and should be thought of more properly as the hub of the decimal spiral. I’m no mathematician, but I suppose that 0 is also formally defined as an integer between 1 and -1 or something. Still it exposes the question of whether the elemental underpinnings of our ability to count is really anchored in anything at all other than our own anthropological conventions of counting. Beyond numbers themselves, it appears that the whole quantitative notion - of greater than or less than, and of ‘equal’ is nothing but a figment of our feelings about order. There may not be any inherent moreness to something than the absence of something. If it’s the same thing, it actually seems more palatable to see the absence of something being a condition predicated upon the things’ a priori presence, no? Even if we want to get into quantum atopoietic craziness where things come out of nothing, rendering such a possibility discretely seems to threaten the whole notion of mathematical coherence. If any or all quantities, variables, and formulas can be generated arbitrarily from 0, then 0 would seem to be the same thing as ∞, and greater than 1 or any other arithmetic expression. Anthrodeximal Numberline Maybe it’s time to create a new numberline, without all of the repetitive decimal numerals. Instead there could be a Wiki of new quantitative symbols and names which anyone can add to and own as a permanent vector in the schema. It would be easy to translate them to and from Arabic numerals online and some interesting possibilities for informal encryption and unanticipated mathematic-linguistic synchronicity. By removing the aspect of repetition, we would unmask the semantic bias of the math logos and arrive at a pure generic linear calibration defined only in it’s own idiosyncratic a-signifying terms. Sort of like breaking the mantra of math, it’s trance-like rhythms that disguise it’s human neurological origin from us. By adding more unique qualitative sense to the thing, the quality-flattening power drains out and the system seems to disqualify itself. Hi Craig, Umm, what would be the point of coming up with yet another representation system for quantities? We already established that a description is not its referent even though for every referent there is at least one description and for every description there is at least one referent. Zero, 0, null, the empty set is an absence of sorts; a placeholder. So in that sense it is a referent and just as space is 'the place where referents could be but are not', so too is 0. Onward! Stephen -- 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: COMP refutation paper - finally out
Bruno Marchal wrote: The notion of a TOE usually is used in a reductionist sense, as a theory that can be used to predict everything. A TOE should do that, in principle at least. Of course it should be able to predict everything which is predictible, in the right condition. No one asks for a TOE which can predict things which are not predictible. No TOE can predict that you will feel to be, just after the duplication, in W or in M. OK. But what is predictable may be quite limited in the end. Is there a result showing that it is possible at all to derive precise physical laws from COMP and a bet on our substitution level? Bruno Marchal wrote: I am critical of the very notion of a TOE. It doesn't make much sense. Even current physics clearly shows that results of experiments can't be predicted precisely. So is the TOE supposed to give a perfect probability distribution? But what is this even supposed to mean? The exact contrary. Comp is not just a change in 'perspective' (Aristotle - Plato), but the discovery of a creative bomb (the UM). With comp we begin to know that we don't know what we are doing. We can (machines can) understand that by trying to control it, we make it less controllable. A bit like a mother with a baby. That is not something entirely new, but here it appears in the 3-theories. Right. That's why we could almost say COMP is an anti-TOE. Bruno Marchal wrote: So no theory can explain everything. But we can show the necessity of there being a gap. OK. You are right. I will abandon the label TOE, for TOAE. Theory of almost everything. Well, but the part that is unexplainable doesn't seem to be small at all. Frankly it explains almost nothing (which is the most we will ever explain, as there is infinitely much to explain!). If anything, it shows there is an infinite hierarchy of ever more efficient theories. Which is quite an astounding result, don't get me wrong, but let's not make the mistake of adjusting to the immodesty of the reductionist materialists. This way you may not be taken as seriously, but being modest and honest seems more important to me. Bruno Marchal wrote: But *that* fact, that there are mysteries, is no more a mystery. At the cost that the very foundation of our theory is mysterious! We use a mystery to explain that there are more mysteries. Which is the best we can ever do - how exciting! Bruno Marchal wrote: And in that sense, comp provides, I think, the first coherent picture of almost everything, from God (oops!) to qualia, quanta included, and this by assuming only seven arithmetical axioms. I tend to agree. But it's coherent picture of everything includes the possibility of infinitely many more powerful theories. Theoretically it may be possible to represent every such theory with arithmetic - but then we can represent every arithmetical statement with just one symbol and an encoding scheme, still we wouldn't call . a theory of everything. So it's not THE theory of everything, but *a* theory of everything. -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164822.html Sent from the Everything List mailing list archive at Nabble.com. -- 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: COMP refutation paper - finally out
Bruno Marchal wrote: On 31 Jul 2011, at 18:24, benjayk wrote: Bruno Marchal wrote: Arithmetic just happens to be powerful enough to point towards it. All other universal systems accomplish the same. So to say just number relations exist and all else is an epistemological view on that is a very narrow interpretation. Arithmetical truth contains fortranic truth, lispic truth, combinatoric truth, etc. It does not contains theological truth, nor physical truth, except in the 'epistemological' points of view of the creature they have all. How exactly do we know that these epistemological truths are secondary / not ontological? I don't really see how COMP does tell us that, as it could well be that the assumptions COMP makes (including consciousness exists, in order to say yes, doctor) are in some sense equivalent to the epistemological points of view whose existence we derive from the assumptions of COMP. I can't prove this (I don't think it can be proven), but for me it seems like this is the case. It is just that we don't need to assume them. It is like the invisible horses pulling a car. True, but consciousness is there without being assumed. The theory cannot just ignore that. -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32164844.html Sent from the Everything List mailing list archive at Nabble.com. -- 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: bruno list
On 31.07.2011 19:12 Stephen P. King said the following: On 7/31/2011 1:19 AM, Craig Weinberg wrote: ... Your ice fire makes no heat, consumes no fuel. Not externally, but it would internally. I understand why that makes sense, but it's incorrect. Heat cannot be simulated and it cannot be generated by an abstraction. There is no numerical formula which can create heat in and of itself. Craig Hi Guys, Strangely enough, our best explanation of heat tells us that heat is a statistical properties of the motions of molecules. How is that? You can formally define heat in classical thermodynamics as well, for example dQ = dU + dW Well, the First Law is used to define the internal energy, but there is a trick. You start with an adiabatic process then you have the internal energy through the pure work and then you can go for the heat. -- 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: bruno list
On Jul 31, 9:16 am, Bruno Marchal marc...@ulb.ac.be wrote: Hi Craig, Sorry for having take some time to comment your posts. I will be busy the two next weeks, so be patient for possible comments. I comment all your 3 posts addressed to me in one mail. Thanks, yeah no rush. It seems like we might be going in circles, I keep thinking that I should try to sum up the core issues where we agree and disagree: Mainly I think that your model features arithmetic as a primitive, whereas I see arithmetic as a subjective experience, and that the relation of subjectivity to objectivity is primitive to me. Consequently it follows from your model that we would be able to produce Turing consciousness mathematically in any physical or informational medium whereas my model posits that consciousness is not produced but rather is the elaborated 1p correlate to 3p neurology x zoology x biology x chemistry x physics. On 28 Jul 2011, at 17:41, Craig Weinberg wrote: To say that it is representational is to conflate the referent and the signifier. Not at all. It is a bet on the invariance of our subjective experience on a substitution level. Biology illustrates already the idea in the language of chemistry. Comp does not imply that everything is representational, nor that Turing machine can simulate everything. On the contrary, some machine's attributes are not Turing emulable. What machine attributes are not Turing emulable? I thought Church says that all real computations are Turing emulable. In order for the machine to STOP, there doesn't automatically need to exist a 1p experience of a red sign. It depends on the machine. In the case of human, there usually are 1p experience. I assume comp. But stopping can be accomplished without the existence of any specific 1p experience, right? In our 1p, we see a red stop sign as a qualitative image, we understand it as a symbolic text, we interpret it as a pragmatic condition that motivates us to respond with motor commands to our body to push the brake, the brake stops the car. Yes. But that is not an argument that some machine cannot do that. In the comp theory, there is no need to eliminate the 1p experience. Don't confuse the comp theory, and its misuse by materialists. I'm trying to establish that a machine does not automatically do this. I only know comp theory from what I've learned from you. Through our interpretation we re-present the signifier, which is a representation-neutral experience of presented color, shape, size, and context. As the machine is a reverse engineered logic, we have no reason to presume that our signifier - the red light or sign, is presented just because a command is sent to the processor queue to stop the car when the ccd in the camera encounters electromagnetic changes of a particular sampled configuration. You are right, but this only means that we fail on the correct substitution level. If we are machine, we cannot know which machine we are, nor really which computations go through, but we still face something partially explainable. Yes, substitution level is the thing. I don't see the level as a simple point on a one dimensional continuum though. It's punctuated by qualitative paradigmatic leaps of synergy. Thus the big deal between an organism being alive or not. The entropy cost is not uniform, just as the different hues in the visible spectrum seem to appear to us as qualitative regions of color despite the uniform arithmetic of frequency on the band. Let's say that human consciousness spans the spectrum from red (sensation) to violet (abstract thought) with phenomena such as emotion, ego, etc in the orange-yellow-green zone. I think that a computer chip is like taking something which is pre- sensation (silicon detection = infra-red) and reverse engineering around the back of the spectrum to ultra-violet: abstraction without thought. If we want to go further backward into our visible spectrum from the end, I think we would have to push forward more from the beginning. You need something more sensitive than stone semiconductors to get into the visible red wavelengths in order to have the 1p experience get into the violet level of actual thought. Or maybe that wouldn't work and you would have to build through each level from the bottom (red) up. It's going to stop the car whether there is an experience of a sign or not. I say that there is an experience, but it's likely not remotely like a human signifier and would compare as one piano note compared to an entire symphony, if not the sum of hundreds of symphonies filtered through different molecular, cellular, physiological, neurological, and psychological audiences. My point works even if you decided that your generalized brain (the part of reality I need to emulate to get your consciousness preserved) is given by the quantum rational Heisenberg matrix, of the whole cluster of galaxies, at the level of
Re: bruno list
On Jul 31, 1:12 pm, Stephen P. King stephe...@charter.net wrote: Hi Guys, Strangely enough, our best explanation of heat tells us that heat is a statistical properties of the motions of molecules. How is that? I say that's the 3p view of it. Heat definitely makes molecules move, but it is the interior 1p excitement of molecules which corresponds to the movement. Both the 1p and 3p phenomena are both causes and symptoms of heat. Craig -- 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: Math Question
On Jul 31, 11:58 am, Bruno Marchal marc...@ulb.ac.be wrote: How do we know that 0 has a successor though? If 0 x = x and x -0 = x then maybe s(0)=0 or Ezs(0)... Can we disprove the idea that a successor to zero does not exist? No. 0 is primitive term, and the language allows the term s(t) for all term t, so you have the terms 0, s(0), s(s(0)), etc. It sounds like you're saying that it's a given that 0 has a successor and therefore doesn't need to be proved. The rest follows from the axioms For all x 0 ≠ s(x), s(x) = s(y) - x = y (so that all numbers have only one successor. So you can, prove, even without induction, that 0 has a unique successor, different from itself. Sorry, I'm probably not at the minimum level of competence to understand this. I look on the net, but I see errors (Wolfram's definition is Dedekind Arithmetic!)? On wiki, the definition of Peano arithmetic seems correct. You need to study some elementary textbook in mathematical logic. Most presentation assumes you know what is first order predicate logic. You can google on those terms. There are good books, but it is a bit involved subject and ask for some works. Peano Arithmetic is the simplest example of Löbian theory or machines or belief system. It is very powerful. You light take time to find an arithmetical proposition that you can prove to be true and that she can't, especially without using the technics for doing that. Most interesting theorem in usual (non Logic) mathematics can be prove in or by PA. And PA, like all Löbian machine, can prove its own Gödel theorem (if I am consistent then I cannot prove that I am consistent). The I is a 3-I. Thanks, I'll see if I can nibble on it sometime. Craig -- 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: Math Question
On Jul 31, 1:19 pm, Stephen P. King stephe...@charter.net wrote: Hi Craig, Umm, what would be the point of coming up with yet another representation system for quantities? We already established that a description is not its referent even though for every referent there is at least one description and for every description there is at least one referent. Zero, 0, null, the empty set is an absence of sorts; a placeholder. So in that sense it is a referent and just as space is 'the place where referents could be but are not', so too is 0. Right. I like that. My point in the alt numeracy idea is to bring out the true a-signifying potential of quantity - to take generic mechanism to it's reductio ad absurdum and reveal the implicit sentimentality of arithmetic which is hidden in base-10 rhyming. If it looked like this instead: 1 2 3 4 5 6 7 8 9 A-Z Every name in every phonebook in India Every word in every language various random squiggles, etc then we could truly expunge all remnants of beauty or symmetry in arithmetic and reveal itself in pure abstraction and marvel at how utterly devoid of usefulness that makes it. That way we could recover our orientation to the genuine by admitting that what we get out of arithmetic is a happy feeling of satisfaction - dopamine, oxytocin, serotonin, and endorphins. Our 1p experience of a human brain in communion with the 1p sense of those categories of molecules are the primitives of arithmetic. Craig -- 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: Math Question
The following quote is from the book “What is Mathematics Really?” by Reuben Hersh “0 (zero) is particularly nice. It is the class of sets equivalent to the set of all objects unequal to themselves! No object is unequal to itself, so 0 is the class of all empty sets. But all empty sets have the same members….none! So they’re not merely equivalent to each other…they are all the same set. There’s only one empty set! (A set is characterized by its membership list. There’s no way to tell one empty membership list from another. Therefore all empty sets are the same thing!) Once I have the empty sets, I can use a trick of Von Neumann as an alternative way to construct the number 1. Consider the class of all empty sets. This class has exactly one member: the unique empty set. It’s a singleton. ‘Out of nothing’ I have made a singleton set…a “canonical representative” for the cardinal number 1. 1 is the class of all singletons…all sets but with a single element. To avoid circularity: 1 is the class of all sets equivalent to the set whose only element is the empty set. Continuing, you get pairs, triplets, and so on. Von Neumann recursively constructs the whole set of natural numbers out of sets of nothing. ….The idea of set…any collection of distinct objects…was so simple and fundamental; it looked like a brick out of which all mathematics could be constructed. Even arithmetic could be downgraded (or upgraded) from primary to secondary rank, for the natural numbers could be constructed, as we have just seen, from nothing…ie., the empty set…by operations of set theory.” Any comments or opinions on whether this theory is the basis for the natural numbers and their relations as is described in the quote above? Thanks -- 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.