Re: Possible Worlds, Logic, and MWI
Re: possible worlds in logic. Logic (and its possible worlds semantics) says nothing (precise) about external reality. Logic only says something about the relationship of symbols in a formal language. Remember that the reason non-sloppy mathematicians use non-meaningful variable-names (i.e. terms) is to avoid names that connote something in the world and would lead one astray in understanding the precise formal semantics of the mathematical formulae. e.g. of problematic meaningful variable names: one = 2. two = 2. four = 4. therefore, one + two = four. This strict anonymous symbols interpretation is how one must treat formal logic and propositions expressed in formal logic too. Every time I read someone bemoaning how logic has difficulty with expressing what is going to happen in future, I think, why would you expect a formal system of symbols to have anything to do with future time in reality? As far as I know, there is no good formulation of a formal connection between a formal system and reality -unbalanced quotes, the secret cause of asymmetry in the universe. How's that for a quining paragraph? Is there? For example, truth is defined in formal logic with respect to, again, formal models with an infinite number of formal symbols in them. It is not defined with respect to some vague correspondence with external reality. Someone was writing about correspondence theory with this goal in mind many years back, and that sounded interesting. I haven't read Tegemark et al. What do they say about the formalities of how mathematics extends to correspond to, or to be? external reality? To me, there is still a huge disconnect there. E.g. again, Godel's incompleteness theorem is a theorem about the properties and limitations of formal symbolic systems. The original theorem says nothing whatsoever about reality itself, whatever that may informally be, nor about the limitations of human minds, unless we take minds to be theorem provers working on formal symbolic systems.
Re: Possible Worlds, Logic, and MWI
Interleaving... POINT 1 For example, truth is defined in formal logic with respect to, again, formal models with an infinite number of formal symbols in them. It is not defined with respect to some vague correspondence with external reality. Actually, science is just about such correspondences with external reality. I haven't argued that logic alone is a substitute for science, measurement, experimentation, refutation, correction, adjustment, model-building All I was saying is that the semantics that define the meaning with respect to each other of symbols and symbol-relationships is formal and, within each given well-formed framework, inarguable. whereas the semantics of the mapping of formal models to their supposed subject is not, itself, formal (yet anyway), and hence is suspect as to whether we understand it or get it right all the time. With science, all we have is: this formal symbol system (theory) A seems to correspond better to our current observations than any competing formal symbol system (theory) B (that we've conceived of so far), so we'll consider A (as a whole) to be TRUE i.e. the best observation-corresponding theory (for now.) This scientific process works pretty well but is somehow loosy-goosy and unsatisfying. Do theories which replace other older, now discredited theories, keep getting better and better? Probably yes. But what is the limit of that? Is there one? Or a limit in each domain about which we theorize? But hold on, most of the scientific revolutions tell us that we had a nice theory, but were theorizing about a badly-scoped, badly conceptualized idea of what the domain was. A better theory is usually a better set of formal, interacting concepts which map to a slightly (or greatly) differently defined and scoped external domain than the last theory mapped to. None of this is very straightforward at all. For example, would you go out on a limb and say that Einstein's theories are the best (and only true) way of modelling the aspects of physics he was concerned with? If so, would you be equally confident that his theories cover essentially all the important issues in that domain? Or might someone else, someday, re-conceptualize a similar but not 100% overlapping domain, and create an even more explanatory theory of fundamental physics than he came up with? Can we ever say for sure, until that either happens or doesn't? You can interpret the history of science in two ways: either we were just really bad at it back then (in Newton's day) and wouldn't make those kind of mistakes in our theory formation today, or you can say, no we're about as good at it as always, maybe a little more refined in method but not much, and we'll continue to get fundamental scientific revolutions even in areas we see as sacrosanct theory today. And the new theory will not so much disprove the existing one (as Einstein didn't really disprove Newton) but rather will be just relegating the old theory to be an approximate description of a partially occluded view of reality. And then one day, will the same thing happen again to that new theory? Is there an endpoint? What would the definition of that endpoint be? (SILLY) POINT 2 As far as I know, there is no good formulation of a formal connection between a formal system and reality -unbalanced quotes, the secret cause of asymmetry in the universe. How's that for a quining paragraph? I don't understand your secret cause of asymmetry in the universe point. We understand some things about symmetry breaking in particle physics theories, via gauge theories and the like. If you want more than this, you'll have to expand on what you mean here. It is a Koan (kind of). A self-referential, absurd example of a notion that an imbalance in a formal symbol system (the words I'm using, and the quotes) could possibly be the cause of asymmetry in the physical universe. It is an attempt to highlight the problems we get into when we confuse the properties of a model with the properties of the thing we are TRYING to model with it. Quining is the use of self-reference in sentences, often to achieve paradox. It is a childish ploy. e.g. of a Quine: Is not a sentence is not a sentence.
Science
On Saturday, January 11, 2003, at 12:28 PM, Eric Hawthorne wrote: ... This scientific process works pretty well but is somehow loosy-goosy and unsatisfying. Do theories which replace other older, now discredited theories, keep getting better and better? Probably yes. But what is the limit of that? Is there one? Or a limit in each domain about which we theorize? Sometimes there is a refinement process which looks a lot like refinement of a computer program, in the sense that more and more of the desired specifications are met. (This is like a series of subsets of a set, with each smaller set converging on the perfect program, a kind of fixed point for the process. This set-theoretic view has an equivalent formulation in terms of a sequence of branch points, a type of lattice. Cf. Lattices and Order, by Davey and Priestley, for example.) Other times science proceeds via substantial paradigm shifts, well-covered by Kuhn of course. In these knowledgequake steps, the model of gradual refinement is essentially shifted to one where a change of basis occurs, where the very building blocks are altered. The transition from Ptolemaic to Copernican, for example, or from humors to microorganisms in medicine. Both relativity (special and general) and QM basically satisfy the correspondence principle by reducing to the classical theories at low relative speeds, with ordinary falling objects in gravity fields, and with macroscopic objects. (QM does not in the sense that many phenomena--slit and photoelectric, stability of atoms, etc.--have no classical theory. And electronics are all around us and need QM to explain. But QM reduces to classical in various obvious ways.) Hey, I'm not going to write a free-form essay here on science and the nature of theories, so I'll move on to your next point. But hold on, most of the scientific revolutions tell us that we had a nice theory, but were theorizing about a badly-scoped, badly conceptualized idea of what the domain was. A better theory is usually a better set of formal, interacting concepts which map to a slightly (or greatly) differently defined and scoped external domain than the last theory mapped to. None of this is very straightforward at all. For example, would you go out on a limb and say that Einstein's theories are the best (and only true) way of modelling the aspects of physics he was concerned with? Yes, I would, with some caveats. His 1905 theory has not been significantly changed, and it has been tested at a wide range of energies (e.g., slowed decay of muons in cosmic showers and accelerators, as one example). And his 1915 theory has been tested in various ways, with gyroscopes in orbit, astrophysical objects, lensing, etc. However, a new result could always force changes. So far, these have not been needed. (Also, there are new solutions to field equations, new mathematical formalisms like differential forms over standard tensors, and so on. Einstein did not wrap up all problems, even with gravitation. This is why much work was done later, and is still being done.) And quantum gravity and other theories of everything which unite the known forces, are very much up in the air at this time. So, yes, relativity was the best theory and remains so. Is it the only true theory for the things it covers? Certainly not. But science is an evolutionary process, in the evolutionary learning and selection sense. Until something challenges a theory, the theory lives. Until something better comes along... If so, would you be equally confident that his theories cover essentially all the important issues in that domain? Or might someone else, someday, re-conceptualize a similar but not 100% overlapping domain, and create an even more explanatory theory of fundamental physics than he came up with? Can we ever say for sure, until that either happens or doesn't? No, and I know of no scientists who claim that a theory is complete and not subject to challenge or replacement by other theories. But theories which appear to be comprehensive in the way QM (and QED and QCD) and relativity are, in their domains, are not lightly challenged. Especially they are not challenge by metapoints about how maybe there are theories which will someday subsume them. You can interpret the history of science in two ways: either we were just really bad at it back then (in Newton's day) and wouldn't make those kind of mistakes in our theory formation today, No, I don't think this can be said at all. Classical mechanics _is_ what relativity reduces to at speeds found on earth and in laboratories prior to the past century. There's a parsimony issue at work as well. Newton, Laplace, Lagrange, and all of the other classical mechanics folks might have had some inkling that they could incorporate fudge factors into their theories, parameters left blank until they could be filled in, but NO EXPERIMENTS and NO OBSERVATIONS needed
R: Possible Worlds, Logic, and MWI
Tim May: (Again, I currently have no pet theory of what Reality is. But I'm happy to be building a base of tools to be able to more intelligently comment later. Having a pet theory is not so important.) The best definition, imo, is: Reality is that which, when you stop believing in it, does not go away. - Phillip K Dick, in an essay (1978) titled How to Build a Universe that Doesn't Fall Apart Two Days Later. A Canadian coed asked him (1972) to define reality for a philosophy class she was taking. Leibniz also wrote: although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough if, using reason well, we were never deceived by it. * Borges. I mentioned him because of his seminal Garden of Forking Paths story. He was not the first to write about alternate histories...I'm not sure who wrote the first recognizable story in this genre. Probably as old a concept as any. Somebody thinks that J.L. Borges was an Everettista :-) http://www.lehman.cuny.edu/ciberletras/v1n1/crit_06.htm http://www-personal.umich.edu/~rojoa/ The Aquinas and Wyclif (and also Ockam!) wrote about the possibility of many universes, created by God. Sometimes I feel there is something good with MWI and there is something wrong with orthodox QM Consider a diaphragm, with two slits, slit 1 and slit 2. Each of these slits can be opened, or closed, by a shutter connected with a separate counter. A weak alpha-particle emitter is placed between the two counters. Imagine that, in the beginning of the gedanken experiment, both slits are closed. If an alpha-particle strikes one of the counters, the slit connected with this counter is opened, and the counters cease to operate, and a light-source is turned on, in front of the diaphragm, and this light-source illuminate a photographic plate placed behind the diaphragm. Following qm rules, we can write psi = 1/sqrt2 (psi_1 + psi_2) where psi_1 is the wavefunction describing the system when the slit 1 is open (psi_2 when the slit 2 is open). Thus, from the theory, we'll get the usual interference pattern, on the photographic plate behind the diaphragm. But if we keep our eyes opened, and we observe which slit is open (slit 1, or slit 2) then, in accordance with the complementarity principle and the projection postulate, a reduction takes place, and no interference pattern *should* appear on the plate. [L. Janossy, K. Nagy, Annalen der Physik, 17, 115-121, (1956)] s. - Gottfried Wilhelm Leibniz [The Monadology, 64-66] But the machines of nature, namely, living bodies, are still machines in their smallest parts ad infinitum. It is this that constitutes the difference between nature and art, that is to say, between the divine art and ours. And the Author of nature has been able to employ this divine and infinitely wonderful power of art, because each portion of matter is not only infinitely divisible, as the ancients observed, but is also actually subdivided without end, each part into further parts, of which each has some motion of its own; otherwise it would be impossible for each portion of matter to express the whole universe. Whence it appears that in the smallest particle of matter there is a world of creatures, living beings, animals, entelechies, souls. Each portion of matter may be conceived as like a garden full of plants and like a pond full of fishes. But each branch of every plant, each member of every animal, each drop of its liquid parts is also some such garden or pond. And though the earth and the air which are between the plants of the garden, or the water which is between the fish of the pond, be neither plant nor fish; yet they also contain plants and fishes, but mostly so minute as to be imperceptible to us.
Re: Science
Dear Tim, this writing is not about YOU, only addressed to your post. It is about the topic of it. I have no argument with you, maybe you will have with me. I try not to repeat all that was priorly quoted nor your added texts, they all are available on the list. 'Science' is a battlecry, disputed on several lists (by several aspects of the particular lists) and I have not (yet) seen a universal agreement (what an overstatement!) about a fitting identification. This list - several years ago - took a free approach, alas lately more and more conventional opinions slip in, regrettable for me, because I hold that the conventional science establishment holds feverishly to old addages, acquired in times when the epistemic cognitive inventory was much less than available today (which is much less than that of tomorrow). Even the topics of the future build on ancient observations and their explanations (formalism), in order to conform with the scientists' earlier books, teachings, pupils, discussions. In MOST cases the methodology works in practical ways, builds technology, up to the point when understanding comes in. This is a many negated term, many so called scientists satisfy themselves with practical results (for tenure, awards, etc.) Few researchers take the stance to free their mind from learned prejudice and check the 'well composed' edifice of the scientific doctrines for sustainability under the newly evolved vistas. There were several on this list. Kuhn went to a considerable length, I would not guess if he 'wanted' to stay within the acceptability of the scientific audience, or his time did not ripen more segregation from the old 'paradigm' (as he said.) Bohm went a pretty uninhibited way, exceeding the level of the decade in which he developed the new ideas. Robert Rosen penetrated a field called 'complexity' (an inadequate word, we just don't know about a better one) from his ideas within mathematical biology - what he stepped out from freely (but was still impressed by the starting topics anyway, talking about 'live', cell, etc.). The new ideas were quickly absorbed into the existing formalistic mill - calculative obsolescence and semantic impropriety, which confused many. New science is like Tao: who says I developed a theory within it does not know what he talks about. Science is on the crossroad: (I wold not say bifurcation, because I have negative arguments against this concept) and we know only that something 'new' is in the dreams, we need more thinking before we can identify what. Speaking of science usually means old science. This list started out to serve the new science. It woulod be a shame to slip back into the conventionalities. Paradigm shift IMO is a mending of the old, not replacing it with new. In every branch of te sciences there are the holy cows which must not be questioned - or the chorus will cry unscientific. The scientific process works pretty well in developing new variants in the practical ways. It will preserve the ancient views. As Eric wrote: ...somehow loosy-goosy and unsatisfying. I am expecting a crucifixation. John Mikes - Original Message - From: Tim May [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, January 11, 2003 4:37 PM Subject: Science On Saturday, January 11, 2003, at 12:28 PM, Eric Hawthorne wrote: ...S N I P --Tim May
Re: Science
On Saturday, January 11, 2003, at 03:11 PM, John M wrote: This list - several years ago - took a free approach, alas lately more and more conventional opinions slip in, regrettable for me, because I hold that the conventional science establishment holds feverishly to old addages, acquired in times when the epistemic cognitive inventory was much less than available today (which is much less than that of tomorrow). Even the topics of the future build on ancient observations and their explanations (formalism), in order to conform with the scientists' earlier books, teachings, pupils, discussions. Given that there is no moderation, no censorship, it is clear that talk about this list...took is missing the point. This list is really the comments of those subscribed and contributing. As always, if you believe people are talking about the wrong things, your best approach to is to persuasively make your own points which you believe fit your conception of what subscribers to the list should be talking about. I have no understanding of what you mean by saying alas lately more and more conventional opinions slip in. If you think my views are too conventional, for example, or that I should not be posting to this list, I suppose you can ask Wei Dai to remove me. I believe nearly all of my posts are in the spirit of the list's charter, discussing as I do MWI, Tegmark/Egan, possible worlds, modal logic, etc. (I seldom if ever discuss the Schmidhuber thesis, and the COMP thesis, as these are not currently interesting to me. I notice plenty of other people discussing them, and I read their comments with _some_ interest, anticipating the eventual day when the COMP stuff is more germane to me.) In MOST cases the methodology works in practical ways, builds technology, up to the point when understanding comes in. This is a many negated term, many so called scientists satisfy themselves with practical results (for tenure, awards, etc.) Few researchers take the stance to free their mind from learned prejudice and check the 'well composed' edifice of the scientific doctrines for sustainability under the newly evolved vistas. There were several on this list. I cannot understand your point here. But if the several who were once here are no longer posting, I am not stopping them. The new ideas were quickly absorbed into the existing formalistic mill - calculative obsolescence and semantic impropriety, which confused many. New science is like Tao: who says I developed a theory within it does not know what he talks about. Science is on the crossroad: (I wold not say bifurcation, because I have negative arguments against this concept) and we know only that something 'new' is in the dreams, we need more thinking before we can identify what. Again, I have no idea what you are talking about here. Speaking of science usually means old science. This list started out to serve the new science. It woulod be a shame to slip back into the conventionalities. Talk to Wei Dai. I write what I think is true and important. --Tim May
