Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...
I think it has been said several times : The existence of a number/arithmetical proposition is the fact that its existence/truth does not depend on the fact that you exist/that it exists conscious beings capable of thinking of it. So the truth value of a proposition is independant of me. Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a wall. This is true, isn't it? It is certainly true independent of our minds. Indeed, it is true in such a way that even when all humans have died, this universe will have a contained a life-form which produced an author who wrote a book in which Humpty Dumpty fell off a wall. But neither Humpty Dumpty nor the fact that he fell off a wall were ever true in this universe - only that this story was written, and that many people read about it and could converse about it. So if you believe that numbers have an independent existence, then you would definitely also have to believe that Humpty Dumpty exists. Both are products of the mind. Either both exist, or both don't (other than as brain patterns). As much as I would like Humpty Dumpty to exist, I'm afraid that it is not so. Regards, Günther --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...
1Z wrote: Not even remotely. I fact, what I have said can be written as two valid syllogisms. Existence is availability for causal interaction Numbers are not available for causal interaction Numbers do not exist Platonism is the claim that numbers exist Numbers do not exist Platonism is false Wonderful! --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...
Bruno Marchal wrote: Le 17-août-06, à 00:14, complexitystudies a écrit : I recall it is just the belief that the propositions of elementary arithmetic are independent of you. Do you sincerley belief that 37 could be a non prime number? Or that the square root of 2 can equal to a ratio of two integers? Or that if you run a program fortran it could neither stop nor not stop? (When all the default assumption are on, to evacuate contingent stopping of a machine implemented in some deep story)? As 1Z has so nicely put, existence implies causal interaction. Numbers cannot causally interact, therefore they do not exist, save as thoughts in our brains. Of course I do not believe that 37 could be a non prime number, simply because what it means to be prime has been exactly defined in arithmetic. I just say that these are thought constructs with no independent existence (independent of human brains, not of a concrete human brain). You might say, that 37 was prime even in the Jurassic, but I say: nobody had invented arithmetic yet, so it's about as true as the fact that James Bond was played by Sean Connery was in the Jurassic. I define a system: 1 + 1 = 2 2 + 1 = 1 1 + 2 = 1 That's all. Okay, it doesn't describe much and probably isn't very useful, but other than that it is not inferior to peano arithmetic. Does my system now exist mind-independtly for all eternity? I have not yet seen a book on human brain which does not presuppose the understanding of the natural numbers. Of course, because it is a useful way to describe reality. But in our brains, not numbers operate, but chemicals. Numbers are not symbol. Symbols can be used to talk about numbers, but they should not be confused with numbers. You are right there of course. Symbols are only referents. What counts is meaning. What I meant to say is that the meanings we assign to number symbols exist only in our minds. Indeed, meaning _is_ only created by interactions between an agent and an environment. With both of these, no meaning. Indeed, in an mind-and-matter independent (=non existing )universe, arithmetic would be about as meaningless as it gets. The notion of same number seems to have occur much before we discovered counting. Farmers have most probably learn to compare the size of the herds of sheep without counting, just by associating each sheep from one herd to the another. But this as nothing to do with the fact that sheeps were countable before humans learn to count it. Humans and brains learn to count countable things because they are countable. Not exactly. Animals and babies can distinguish up to 2-3 objects (innate arithmetic, subitizing). The experiments with which this has been ascertained are both fascinating and entertaining (google is your friend ;-) This ability has an evolutionary advantage: it is necessary for higher organisms to distinguish more or less abundant food sources or numbers of predators. But this meaning this countability, arises out of the physical world, and is not independent of it. I think you are confusing the subject or object of math, and the human mathematical theories, which are just lantern putting a tiny light on the subject. Indeed I am not. I am just saying that there is no independent subject of math outside of human brains. Mathematics is the study of rules we make up (axioms) and what follows of them (theorems). If we pick our axioms wisely, we can even model some aspects of the real, physical world with it. If numbers and their math was really invented, why should mathematicians hide some results, like Pythagoras with the irrationality of the square root of two, ... As David Deutsch says: math kicks back. That is very easy: the Pythagoreans assumed axioms, and thought they knew what would follow from them. Then, to their dismay, they found out that also somewhat else followed from the axioms than they had ideally envisioned, something that displeased their aesthetic sense. Only human factors involved here, no independent existence of math. It just shows how limited our thought is, and that we do not even anticipate theorems that follow from our axioms when they are rather simple. Also, concepts like infinity are most definitely not universal concepts out there, but products of our mind. I doubt any mind could ever produce infinity. But indeed, _only_ minds produce them, because, as you say, infinity is a concept, and concepts exist only in minds. In reality, there is no such thing as infinity. Even if space would expand infinitely, this infinity would not exist as a thing (except in the trivial *lol* sense as the universe exists), but would be a concept for us humans to talk about it. Concepts need not be precisely understood as to be concepts. For example, consciousness is definitely not understood, but talked about a lot. How does the human mind create the concept of infinity: Lakoff and Nunez have a nice metaphor: Humans see
Platonism vs Realism WAS: ROADMAP (well, not yet really...
Hi Bruno, Again we are discussing the arithmetical realism (which I just assume). A bold assumption, if I may say so. To be clear on that hypothesis, I do indeed find plausible that the number six is perfect, even in the case the branes would not have collide, no big bang, no physical universe. Six is perfect just because its divisors are 1, 2, and 3; and that 1+2+3 = 6. Not because I know that. I blieve the contrary: it is the independent truth of 6 = sum of its proper divisors than eventually I, and you, can learn it. I understand your argumentation well, because maybe one or two years ago I said nearly the same sentences to colleagues. But my exploration into cognitive neuroscience has exposed to me how mathematical thinking comes about, and that it is indeed not separable from our human brains. If you want, numbers are what makes any counting possible. Numbers are symbols we create in our minds to communicate with fellow individuals about things of importance to us. To paraphrase Descartes very liberally: We group, therefore we can count. Our act of arbitrary grouping (made a bit less arbitrary by evolution, which makes us group things which are good to our survival, like gazelles and spears or berries) let's us count and communicate the number. For the universe one apple may not exist, because in effect there are only quarks interacting. And at this level indeterminacy strikes mercilessly, making it all but meaningless to count quarks. Also, concepts like infinity are most definitely not universal concepts out there, but products of our mind. It is not because some country put salt on pancakes that pancakes do not exist there. Roman where writing 8 -3 for us 8 - 2. It is like saying 3*7 = 25 on planet TETRA. They mean 3*7 = 21, they just put it differently. Of course, symbolisms are arbitrary, but physical instantiation makes all the difference. No problem. I see you assume a physical universe. I don't. We havejust different theories. So, which experiment decides which is true? I think platonism derives it's power from misconceptions of the human mind. The unthinking stone would never construe such a thing as platonism. It would just exist - in a very real world ;-) Note that if you understand the whole UDA, Unfortunately, not yet, but I'm reading! you should realize that the price of assuming a physical universe (and wanting it to be related with our experiences *and* our experiments) is to postulate that you (and us, if you are not solipsistic) are not turing emulable. No problem. Why is that so? Could you clarify this issue? (I like to separate issues concerning the choice of theory, and issues concerning propositions made *in* a theory, or accepting that theory). Absolutely. But I think we have to start with our assumptions and try to scrutinize them very carefully. After all, we want to devote our minds to problems arising out of them during our lives, and thus the initial choice should not be made rashly, but only after careful review of our current body of knowledge. Best Regards, Günther --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: ROADMAP (well, not yet really...
Hello to the List :-) The deductions made via UDA are impressing, but I would like to seriously question the Platonic Assumptions underlying all this reasoning. Arguments like the perfectness of 6 seem sensible at first sight, but only because we look at this with human eyes. 1) Mathematical thought only exists in human (or alien intelligent) brains. It thus has neural correlates. 2) These neural correlates are strongly coupled to our sensory experiences, how we experience the world in an embodied way. 3) No brains, no neural correlates, no mathematics. It doesn't make sense to argue about the perfectness of 6 when there is nobody around to argue, when nobody thinks about sixness. These concepts are ways of organizing the world around us, not platonic entities existing - indeed - where? 4) Why do we acknowledge some math as correct, other as not? It is only our grounding in reality, in our sensory experience, which let's us say: this mathematics describe reality sensibly. When we place one rock on another, then have two rocks, it is indeed not astounding that 1 + 1 = 2 in our symbol space. But, again, this is not a description of even an effect of math on reality, rather it is us getting back that what we have inferred beforehand. 5) Indeed, in advanced mathematics, one is often astounded that some math seems to perfectly fit reality, without us having thought of this application before. But in truth, this results from a selection effect of perception. The major body of mathematics is highly aesthetic but has no relevance to physical structures in the real world. Only the mathematics which fits (and getting this fit sometimes is not astounding, see point 4, because we laid it into the system by our experience of the sensory world) inspires some people to wonder why this works. Example: in many equations, we throw away negative solutions because they don't make sense. This illustrates that math doesn't fit by itself, we make it fit. 6) When we have accepted that mathematics does not exist in a platonic realm, but arises from our embodied experience of the world, we should humbly return to hypothesis, theory, validation, falsification, and a constant construction of a world around us which makes sense to _our specific human brains_, no more, no less. --- I think Quantum Weirdness, Gödels Incompleteness Theorem etc. are only consequences of our embodied mathematics, which has evolved on our macroscopical scale, and this granularity and method of reasoning is not adequate for dimensions which transend our immediate sensory experience. As such, I also find MWI and other extravagancies and erroneous way of approaching our current body of knowledge. This path leads astray. Science is successful because we stay connected with reality (our sensory, and enhanced - with machines - sensory experiences). We cannot hope for more, at least at our level of understanding. Interesting Literature: - Where Mathematics Comes from: How the Embodied Mind Brings Mathematics Into Being; George Lakoff and Rafael Nunez, 2001 - Metaphors We Live; George Lakoff, Mark Johnson 2003 - Chasing Reality. Strife Over Realism; Mario Bunge, 2006 (I can recommend nearly everything by Bunge, who excels at clear reasoning, and is committed to an unspeculative view on nature) Best Regards, Günther Bruno Marchal wrote: Le 14-août-06, à 19:21, Brent Meeker a écrit : But how must the perfect number exist or not exist? You say you only mean it must be true that there is a number equal to the sum of its divsors independent of you. Do you mean independent only in the sense that others will know 6 is perfect after you're gone, or do you mean 6 is perfect independent of all humans, all intelligent beings, the whole world? In the second sense. The perfectness of 6 is what would make any sufficiently clever entity from any possible (consistent) worlds, existing or not, to know that. In that sense it has to be a primitive truth. You can see this through a sequence of stronger and stronger modesty principles: 1) Bruno is not so important that 6 would loose its perfection after Bruno is gone; 2) The Belgian are not so important that 6 would loose its perfectness after the Belgian are gone; 3) The European are not so important that 6 would loose ... 4) The Humans are not so ... 5) The Mammals are not so ... 6) The creature of Earth are not so ... 7) the creature of the Solar system are not so ... 8) the creature of the Milky way are not so ... 9) the creature of the local universe are not so ... 10) the creature of the multiverse are not so ... 11) the creature of the multi multi verse are not so 11) the possible creatures are not so ... Yes, I think (and assume in the Arithmetical realist part of comp) that the fact that 6 is equal to its proper divisors sum, is a truth beyond time, space, whatever ... I have the
