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Natural Science Forum / Physics / Particle Physics / November 2004How to tell if a theory is a good one
I'm writing this just to set a line in the sand for both alternate-theory posters and to those who respond to those posters. All too often, pyrotechnic rhetoric gets in the way of a very simple evaluation. 1. A good theory has to refer to well-defined terms and concepts. It does no good to exploit the softness of common language to fuzz the boundaries of words. If you say "waves" and you don't mean everything that is included in the definition of a wave as physicists define it, then provide a careful and complete definition of your own, being sure to explicitly exclude the conventional connotations that don't apply. It's not necessary to adopt the same language and concepts from historically accepted physics terminology. If it were so, we would have not come to understand "rest mass", "invariant interval", "branes", "black holes", or "quarks". But it IS important to define carefully what you mean. But this isn't enough. 2. A good theory has to be self-consistent. That is, it can't predict something that is counter to another prediction, or can't predict something that is counter to one of its assumptions. It is not necessary that it be consistent with assumptions and predictions of other theories. If it were so, we would not have accepted the relativity of simultaneity. But it IS important to check that the theory is coherent. But this isn't enough. All too often, theorists come up with a model that is pleasing to the eye and self-consistent and think that those virtues alone make it appealing. 3. A good theory has to *qualitatively* account for all existing observations and experimental results that pertain to its domain. A theory that is patently inconsistent with a known result MUST be summarily discarded, no matter how well 1 and 2 are satisfied. It is not necessary that the underlying explanation agree with pre-existing theoretical explanations. If it were so, we would would have dismissed special relativity. But special relativity did not violate any hitherto observed behavior at low velocity, and there were therefore no good reasons to dismiss it on those grounds. But this isn't enough. A plausible explanation does not substitute for a real calculation. And this, unfortunately, is where most of our amateur theorists with alternate theories come to a grinding halt. 4. A good theory has to *quantitatively* account for all existing observations and experimental results that pertain to its domain. This is where mathematical underpinnings start to become required. You can't make a quantitative calculation of a behavior that can be measured without the mathematical representation of the theory. It is not important that the model agree with the form of the equations and formulas of other theories. If it were so, then the Copernican model of the solar system would not have supplanted the earth-centric epicycle model. But if the Copernican model had not been able to CALCULATE the position of the planets in the sky as well as, or better than, the epicycle model, then it would not have mattered how well 1 and 2 and 3 were satisfied. But this isn't enough. There may be dozens of completely equivalent models that adequately describe the same known phenomena, both qualitatively and quantitatively. If this is all a theory does -- match evenly against an existing model -- then it is no good. Here again is where many "alternative interpretations" fall flat. 5. A good theory has to *quantitatively predict* an observable behavior that has not yet been measured, and preferably a behavior that is at odds with the predicted behavior of other proposed theories. If it fails to predict anything new, then it must be dismissed as a theory, no matter how well 1, 2, 3, and 4 are satisfied. If Einstein had written general relativity, but he had failed to make the verifiable prediction that the apparent location of a star would shift so many arc-seconds during an eclipse, then it would have been a worthless theory. In this sense, most of the string models and spin-network models of the universe are NOT good theories yet, because they fail to make a verifiable prediction. In this sense, even the Standard Model with the Higgs boson is not a very good theory yet, because one of its primary verifiable predictions (the Higgs boson) has not been confirmed yet. Alternative-theory-proposers: the onus is on you to make sure your model satisfies ALL FIVE of the above requirements. If it does not, then the world has a complete right to summarily dismiss your conjecture. Alternative-theory flamers: the onus is on you to point accurately to the failing of the theory. Inconsistency with existing, verified *theories* is not a valid critique. For example, it is improper to discount a theory because it disagrees with Dirac's equation or because it violates a postulate of GR. It IS proper to point to an experimental observation which an existing theory gets correct and the proposed model does not (steps 3, 4 and 5 above). It is improper to discount a theory because the proposer has not calculated your favorite observable. It IS proper to point out that the proposed theory either doesn't have the mathematical equipment to calculate your favorite observable, or that it does but the calculation results in something contrary to what's actually seen. PD > Alternative-theory flamers: the onus is on you to point accurately to the > failing of the theory. The burden of proof of a theory lies squarely on the one proposing it. Bob Kolker >> Alternative-theory flamers: the onus is on you to point accurately to the >> failing of the theory. > > The burden of proof of a theory lies squarely on the one proposing it. > > Bob Kolker I think not. Theories cannot be proved. They can be tested, but never proved. You don't actually expect every new theory to be tested exhaustively by its authors, do you? That's an impossible task. The onus is necessarily on the opposition to provide an empirical contradiction to the theory. Richard Perry > I think not. Theories cannot be proved. They can be tested, but never > proved. You don't actually expect every new theory to be tested > exhaustively by its authors, do you? That's an impossible task. The > onus is necessarily on the opposition to provide an empirical > contradiction to the theory. I am well aware that proof in the mathematical sense is not possible. The burden of showing some evidence in favor of a theory lies with the one proposing it. If the proposer cannot establish the possibility that his theory might be sound on empirical grounds he is just blowing wind. Bob Kolker >> I think not. Theories cannot be proved. They can be tested, but never >> proved. You don't actually expect every new theory to be tested [quoted text clipped - 8 lines] > > Bob Kolker IOW, he should provide a test of the theory, one that distinguishes it from existing theory. Suppose, however, that the differences in predictions are much smaller than the available experimental precision? The onus is once again on the opposition. Richard Perry > IOW, he should provide a test of the theory, one that distinguishes it > from existing theory. > Suppose, however, that the differences in predictions are much smaller > than the available experimental precision? > The onus is once again on the opposition. Not at all. If the theory cannot be tested, it should be put away in a drawer until it can. Of course if someone falsifies the theory in the mean time, the matter is settled. In general, theories that cannot be tested are worthless. By that I mean if a theory does not produce a testable quantitative asertion it is vapor. It has no standing. Bob Kolker > In general, theories that cannot be tested are worthless. By that I mean > if a theory does not produce a testable quantitative asertion it is > vapor. It has no standing. > > Bob Kolker This is a key point. I have had to sit at parties, gunned down by ghost believers, god squaders, everyone with a belief - they all believe scientists are closed minds who cannot see it. So I say to them "yes you can believe, you can have a theory but you must produce something predicatable, something everybody can say yes this theory does indeed reproduce, time and time again, events, results that were once thought bizarre, but now completely explained". Of course they never can. 'My brother once saw this', 'my Aunt is convinced', 'my Uncle has a perpetual motion machine that generates all his energy needs' - but will never show you this device or reconcile that with his monthly energy payments! I say to them, believe in what you want, but if you cannot predict anything with it, it is worthless. Absolutely worthless. They never can, it is all one-off anecdotes. Incidentally, they never explain why ghosts go through walls, but don't fall through the floor. I guess Ghosts don't feel the gravitational force. 'God moves in mysterious ways'. In other words, we haven't a bloody clue - but we do have this golden waiver card (get-out clause), if we can't explain it, we just wheel out this old tosh. To re-quote Dr/Prof/Mr/Kolker > if a theory does not produce a testable quantitative asertion it is > vapor. It has no standing. Richard Miller > > In general, theories that cannot be tested are worthless. By that I mean > > if a theory does not produce a testable quantitative asertion it is [quoted text clipped - 34 lines] > > Richard Miller Let's be careful here. It could be that folks are just citing *observations* that have no current basis for explanation. You don't have to resort to ghosts or miracles to find those. Why are there three generations of quarks? Why don't photons couple to the Higgs and gain mass? What is the source of CP violation? What is the source of the cosmological constant? There are zillions of things that we don't understand. "Ghosts" as such are not an explanation -- they are a recognition of phenomena outside our understanding. As such, they should be relished and pursued, just as much as the hundreds of millions of Euros invested in finding the Higgs. PD Paul Draper: >Let's be careful here. It could be that folks are just citing >*observations* that have no current basis for explanation. You don't >have to resort to ghosts or miracles to find those. Well, one does resort to ghosts for gauge fixing, but they never appear in physical result. >Why are there three generations of quarks? Why don't photons couple >to the Higgs and gain mass? The most plausible (non-superficial) reason is best explained by the chain of questions it takes to get there. The photon remains massless (but see below) because charge is conserved. While that simply begs the question, if you look in the electroweak sector, you'll discover a diagram which constitutes a potential anomally in the weak axial current. There are a couple of possible scenarios in which such an anomally might be cancelled by another diagram. One is the exist- ence of right-handed fermion doublets, which would make the weak inter- action left-right symmetric. However, this has no support at all from experiment. The second alternative is to add additional left-handed fermion doublets to the theory in such a way as to cancel the anomally. In this case, we have lots of experimental support. The doublets are the quarks. As it turns out, this works if the quarks come in three types (i.e., color charges) and the number of quark generations equals the number of lepton generations. Actually, there is a well known case in which the U(1)_em symmetry _is_ broken, the photon acquires a mass and a higgs is produced: a superconductor. The cooper pairs are the higgs bosons (nothing precludes the higgs from being a composite). The meissner effect is a consequence of the photon mass. >What is the source of CP violation? A better question is why is the strong interaction cp-conserving and why does the weak interaction pollute the quark sector to such an extent? >What is the source of the cosmological constant? There are zillions >of things that we don't understand. [quoted text clipped - 3 lines] >and pursued, just as much as the hundreds of millions of Euros >invested in finding the Higgs. I'm not so sure _finding_ the higgs is all that important. Given the fact that it hasn't been found yet, it's possible that the simplest higgs model is not the one nature had in mind, so _not_ finding it, would at least point in some direction to possible new physics. Supersymmetry always seems to be ``just out of reach'' (for about 15-20 years now) and I'm not real certain it won't stay that way. > > IOW, he should provide a test of the theory, one that distinguishes it > > from existing theory. [quoted text clipped - 11 lines] > > Bob Kolker In a sense, this is right. The trick is finding the point when it should be put away in a drawer. A number of theories (M-branes, spin network TOEs, supersymmetry come to mind) show enough *theoretical* promise that folks want to work on it a while until they can get to the point where an experimental prediction can be calculated. Usually the problem is that 1st-order effects may be out of range of experiment, but 2nd- or 3rd-order effects (which are only understood once the 1st-order effects are calculated) might be more accessible. Again, it is tricky to dismiss a theory out of hand, without risking prejudicial blindness. PD > > I think not. Theories cannot be proved. They can be tested, but never > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 6 lines] > one proposing it. If the proposer cannot establish the possibility that > his theory might be sound on empirical grounds he is just blowing wind. Rigorous mathematical proof is not the last word either. Euclid is rigorously self-consistent and contains no flaws. Euclid doesn't work for land surveying or navigation. Euclid is incomplete vs. hyperbolic and elliptic geometries. The three taken together are *still* incomplete vs. Thurston's eight simply-connected geometric 3-manifolds with compact quotients. If the parity Eotvos experiment empirically falsifies the Equivalence Principle, then General Relativity that postulates it is only a heuristic, demoted in the same way Euclid fell to his Fifth (Parallel) postulate being counterdemonstrated by Riemann OTOH and Bolyai and Lobechevsky OTOH. If the parity Eotvos experiment fails, Einstein is validated but not proven. Until gravitation and quantum mechanics are functionally united, we can be utterly certain that at least one of them is wrong. Religion and politics are based upon absolutes and faith. They will always fail - bloodily dragging their adherents down with them. Science adapts and improves. Science and its adherents are smart enough to learn. That is what humanity is all about.  SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf In sci.physics Uncle Al <UncleAl0@hate.spam.net> wrote: <snip> > Religion and politics are based upon absolutes and faith. They will > always fail - bloodily dragging their adherents down with them. Religious theries are not inherently less testable than physical ones, as long as there is some divergance of religeous theory and the predictions made by science. If you hold that in 2020, there will be an anomolous ratio of hydrogen/duterium/tritium evaporating from comet X as it hits periapsis, and I hold that in 2020, the world will be painted a subtle shade of purple by God, both are equally testable. Something that's been missed is that the person doing the testing has to be able to report back. Belief in the afterlife is hard to prove - unless it turns out that ghosts have just been awaiting the development of suitably sensitive etevos balances to communicate through. > In sci.physics Uncle Al <UncleAl0@hate.spam.net> wrote: > <snip> [quoted text clipped - 15 lines] > ghosts have just been awaiting the development of suitably sensitive > etevos balances to communicate through. We lock and load the fist hemiparity Eotvos experiment next week. If I were Einstein's shade I'd be sweating it - Uncle Al played the violin. SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf > > > I think not. Theories cannot be proved. They can be tested, but never > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 22 lines] > functionally united, we can be utterly certain that at least one of > them is wrong. We can be fairly certrain that both of them are wrong. Since QM predicts Newton is right. And Relativity predicts Newton is wrong. And the only way that can happen is that Reimann is so wrong, that Einstein is partially-right. Since Riemann Geomety is consistent if Set Theory is consistent. And Set Theory is consistent iff Von Neumann Ordinals are consistent. And Von Neumamm Ordinals are consistent iff Neorther's Theorem is inconsistent. And Neorther's Theorem is inconsistent iff condensed matter doesn't exist. So the only way either QM or Relativity will be proven correct, is if the Higg's Boson w.nks and The Diracians actually proven that reality is not merely hot-air, a helium balloon, a superimposed Methane fart, and a philosopher. > Religion and politics are based upon absolutes and faith. They will > always fail - bloodily dragging their adherents down with them. > Science adapts and improves. Science and its adherents are smart > enough to learn. That is what humanity is all about. > > > > I think not. Theories cannot be proved. They can be tested, but never > > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 26 lines] > Since QM predicts Newton is right. > And Relativity predicts Newton is wrong. [snip crap] Newton sets h=0 and c=infinity. Newton is incomplete. QM sets G=0 and c=infinity. QM is incomplete. GR sets h=0. GR is incomplete. Untutored idiot. Why don't you pull your head out of your a.s http://www.mazepath.com/uncleal/sunshine.jpg and cite us an empirical instance where any of the foregoing physical theories are "wrong" within their boundary conditions? SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf > > > > > I think not. Theories cannot be proved. They can be tested, but never > > > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 31 lines] > QM sets G=0 and c=infinity. QM is incomplete. > GR sets h=0. GR is incomplete. GR sets nothing to zero, except QM morons who actually think know they know anything about calculus, nevermind logic. h and G and C are ALL universal non-zero constants, QM MORONS. Goedel and his Compleness Theorems have nothing to do with the theory. You freaking ignorant, less-than-worthless, Einstone wannabees from dot-ville. h was set to non-zero to the trivial initial conditions that Astromeners and Chemists are all morons, to be replaced by robots. C was set to a non-zero finite value because mathematician's are the universes most stupid and ignorant people, since Euclid to set non-zero by the Jesuits. G was forcefully set to non-zero because physicists are the universes' most ignorant people with their dysfunctional Q-bits that proclaims the non-existent of Solar Sytems and g. And instead replaces them with psychologists on Geometry Guard Duty, who are in actually the world's lowest IQ specimens, since Skinnerism was introduced into the Grand Unified Theory Of Sheep Evolution. > Untutored idiot. Why don't you pull your head out of your a.s > > http://www.mazepath.com/uncleal/sunshine.jpg > > and cite us an empirical instance where any of the foregoing physical > theories are "wrong" within their boundary conditions? That's quite impossible, Since Empricism went out of style the very day after fag Chemists and Physicists invented it. > > > > I think not. Theories cannot be proved. They can be tested, but never > > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 43 lines] > merely hot-air, a helium balloon, > a superimposed Methane fart, and a philosopher. Have you ever posted anything to these newsgroups that actually made any sense? > > > > > I think not. Theories cannot be proved. They can be tested, but never > > > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 45 lines] > > Have you ever posted anything to these newsgroups that actually made any sense? I've never posted *anything* to sci.relativity that didn't refer to born-again Christians, and simultaneous-syncopated Moses acid flashbackers from Israel, Iraq, and New Steinbenner City, located on the beautiful outskirts of Key New Jersey, Florida. So it would be possible for my posts to make sense iff Fidel Castro is NOT a world famous Communist, who probably was more igornant of anything Marx ever wrote than the science Frog druids form Europe are. > > > I think not. Theories cannot be proved. They can be tested, but never > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 27 lines] > Science adapts and improves. Science and its adherents are smart > enough to learn. That is what humanity is all about. You think you can explain existance when you cannot even explain the distribution of prime numbers? Back to square 0 for you. > You think you can explain existance when you cannot even explain the > distribution of prime numbers? Back to square 0 for you. Explain? The density of the primes has been known for over a century. Bob Kolker > > > I think not. Theories cannot be proved. They can be tested, but never > > > proved. You don't actually expect every new theory to be tested [quoted text clipped - 27 lines] > Science adapts and improves. Science and its adherents are smart > enough to learn. That is what humanity is all about. Solve it. >> I think not. Theories cannot be proved. They can be tested, but never >> proved. You don't actually expect every new theory to be tested >> exhaustively by its authors, do you? That's an impossible task. The >> onus is necessarily on the opposition to provide an empirical >> contradiction to the theory. > I am well aware that proof in the mathematical sense is not possible. > The burden of showing some evidence in favor of a theory lies with the > one proposing it. If the proposer cannot establish the possibility that > his theory might be sound on empirical grounds he is just blowing wind. So ? Do you mean that seriously and honestly ? Please tell me what you mean with "sound on empirical grounds" ? How do you take a theory that meets all observations (up to now), and additionally lets see known particle numbers ? I know that physicists are enraged if an engineer dares to propose such theory (even worse: supply with evidence), but would like to hear _your_ opinion. Ulrich http://home.t-online.de/home/Ulrich.Bruchholz/ > > >> [quoted text clipped - 16 lines] > such theory (even worse: supply with evidence), but would like to > hear _your_ opinion. Yes, seriously and honestly. But physicists are also seriously wary about points 4 and 5 in my original post. It's important that the "meets all observations" is quantitatively complete, not just qualitatively complete. The theory needs a framework that would allow that quantitative verification to be conducted. PD .. > Yes, seriously and honestly. > But physicists are also seriously wary about points 4 and 5 in my > original post. It's important that the "meets all observations" is > quantitatively complete, not just qualitatively complete. The theory > needs a framework that would allow that quantitative verification to > be conducted. I have no difficulties with that. The particle numbers are quantitatively met with the geometric theory. Ulrich > >> Alternative-theory flamers: the onus is on you to point accurately to the > >> failing of the theory. [quoted text clipped - 10 lines] > > Richard Perry By "proof", he meant some sort of evidence for the theory. For instance, if observations are consistent with the theory, that's evidence for it. If the creator of theory X wants to promote theory X as good, then they have to show that it meets the five requirements for a good theory, and if a critic wants to dismiss it as bad, then they have to show that it does NOT meet the requirements. > By "proof", he meant some sort of evidence for the theory. For instance, if > observations are consistent with the theory, that's evidence for it. Evidence but not proof. A physical theory is true if and only if ALL of its predictions are true. Since there are an infinite number of predictions a physical theory cannot be shown to be true in a finite interval of time. A physical theory is in one of two states: Falsified and not yet Falsified. In the mean time, a theory for which a finite subset of its possible predictions have corroberations for those predictions and no falsification has yet been made is a plausible theory. Plausibility is not equivalent to true. It just means people believe the results and are inclined to use them. For a while Newton's theory of gravitation was experimentally corroberated and not falsified. Then the anomalous advance of the perihelion of Mercury threw the matter into doubt. Since no cause of the anomaly could be empirically demonstrated and another theory (GTR) explained the anomaly, Newton's theory of gravitation is now considered falsified. Bob Kolker How can Newton's theory of gravitation be false when engineers use it every day in their calculations? You need to be able to identify some theories as being 'leass false' than others, or 'more useful', or 'approximately true'. Of course even QED and GR are only approximately true (nothing is absolutely true, or if it is you could never know it). > > By "proof", he meant some sort of evidence for the theory. For instance, if > > observations are consistent with the theory, that's evidence for it. [quoted text clipped - 19 lines] > > Bob Kolker > How can Newton's theory of gravitation be false when engineers use it > every day in their calculations? You need to be able to identify some > theories as being 'leass false' than others, or 'more useful', or > 'approximately true'. > Of course even QED and GR are only approximately true (nothing is > absolutely true, or if it is you could never know it). Since Newtonian gravitation cannot fully account for the motion of planets we know that it cannot be a fundemental theory of gravitation. There are other theories which account for motions for which Newtonian gravity fails. Even so, Newtonian gravitation is not off by too much so it is a useful heuristic. This means Newtonian gravitation is a handy dandy rule of thumb and along with course corrections will get our spacecraft to where they need to go. A true theory will always predict correctly within the error bars of the instruments. A pretty good heuristic will come close most of the time. Bob Kolker > > How can Newton's theory of gravitation be false when engineers use it > > every day in their calculations? You need to be able to identify some [quoted text clipped - 7 lines] > There are other theories which account for motions for which Newtonian > gravity fails. Since GR cannot fully account for the rotation curves of galaxies and the accelerated expansion of the universe we know that it cannot be a fundamental theory of gravitation. :-) Ken Seto > Even so, Newtonian gravitation is not off by too much so it is a useful > heuristic. This means Newtonian gravitation is a handy dandy rule of [quoted text clipped - 5 lines] > > Bob Kolker > Since GR cannot fully account for the rotation curves of galaxies and > the accelerated expansion of the universe we know that it cannot be a > fundamental theory of gravitation. :-) That is yet to be settled. It may be a situation like the anomaly of Uranis which lead to the discovery of Neptune or it could be a failure of the theory. More investigation will happen before a consensis is reached. Neptune was the dark matter for Uranis. It is possible that GTR fails in which case a better theory will have to be found. It sure won't be yours. Bob Kolker > > Since GR cannot fully account for the rotation curves of galaxies and > > the accelerated expansion of the universe we know that it cannot be a [quoted text clipped - 8 lines] > It is possible that GTR fails in which case a better theory will have to > be found. It sure won't be yours. You don't have the knowledge to judge my theory. Ken Seto > You don't have the knowledge to judge my theory. You don't have the mathematics to write an effective theory. You are a lite-weight. Why don't you read the journal or arxiv to see what real physics papers look like. Bob Kolker > > You don't have the knowledge to judge my theory. > > You don't have the mathematics to write an effective theory. You are a > lite-weight. Why don't you read the journal or arxiv to see what real > physics papers look like. You are an idiot to think that a theory need to have lots of equations to be an effective theory. The editors of Galilean Electrodynamics published several of my papers disagree with your erroneous view. Ken Seto >>>You don't have the knowledge to judge my theory. >> [quoted text clipped - 4 lines] > You are an idiot to think that a theory need to have lots of equations > to be an effective theory. You are an idiot to think that a bunch of handwaving assertion is a theory, that a theory can work with almost no equations. > The editors of Galilean Electrodynamics > published several of my papers disagree with your erroneous view. Hint: that's a point against, not for you. Galilean Electrodynamics publishes *lots* of crank stuff. Without bothering if it is coherent or not - they apparently only look if it is against the mainstream. Bye, Bjoern > > You don't have the knowledge to judge my theory. > [quoted text clipped - 3 lines] > > Bob Kolker Prove that the theory doesn't work, not just your dumb-$hit criticism. Show the actually fallacy in the theory ITSELF. > > > You don't have the knowledge to judge my theory. > > [quoted text clipped - 6 lines] > Prove that the theory doesn't work, not just your dumb-$hit criticism. > Show the actually fallacy in the theory ITSELF. If you haven't written the equations, you haven't got a theory. No one has to do your work for you. But once you've got a (predictive mathematically described) theory, everyone will be happy to have at it to find problems. That's how it works. > > "robert j. kolker" <nowhere@nowhere.net> wrote in message > news:<2tpprvF23gjlfU1@uni-berlin.de>... [quoted text clipped - 15 lines] > everyone will be happy to have at it to find problems. > That's how it works. I always thought a theory had to be checked out by experiments.....if it had not been then it was a hypothesis.....if the math works out it is still a hypothesis, until it is verified by experiment.... Hypothesis = educated...??....guess..... have fun....thinking....sno > > > "robert j. kolker" <nowhere@nowhere.net> wrote in message > > news:<2tpprvF23gjlfU1@uni-berlin.de>... [quoted text clipped - 20 lines] > hypothesis.....if the math works out it is still a > hypothesis, until it is verified by experiment.... That's why you write equations, so that you can make quantitative predictions about the outcomes of experiements. > Hypothesis = educated...??....guess..... > > have fun....thinking....sno > Hypothesis = educated...??....guess..... > > have fun....thinking....sno Correct. A hypothesis is an eductated guess which gets some clout when the guess are borne out by experimentation. Bob Kolker > If you haven't written the equations, you haven't got a > theory. No one has to do your work for you. But once > you've got a (predictive mathematically described) theory, > everyone will be happy to have at it to find problems. > That's how it works. Correct. Without the math there is no theory. Only hot air. Bob Kolker > Prove that the theory doesn't work, not just your dumb-$hit criticism. > Show the actually fallacy in the theory ITSELF. Prove that it DOES work by producing predictions that main line theories do not make then test them out. Scientific theories are shown to be useful by experiment and shown to be false by experiment. Midieval type disputations have no place in physics. Bob Kolker >> How can Newton's theory of gravitation be false when engineers use it >> every day in their calculations? You need to be able to identify some [quoted text clipped - 12 lines] >thumb and along with course corrections will get our spacecraft to where >they need to go. Whatever course corrections you apply are not to correct for the discrepancies between Newtonian gravitation and GR but for the much larger errors caused by uncertainties in the mass of the craft, magnitude and direction of thrust applied etc. Non of these is known to 7-8 digit accuracy, not even close. >A true theory will always predict correctly within the error bars of the >instruments. Don't forget the error bars of the input data. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" > Don't forget the error bars of the input data. Yup. But they are gotten by measurement so it goes back to instruments again, including the Mark One Eyeball, courtesy of Evolution. Bob Kolker In article <2tj272F2054t2U2@uni-berlin.de>, "robert j. kolker" <nowhere@nowhere.net> writes: >mmeron@cars3.uchicago.edu wrote: > >> Don't forget the error bars of the input data. > >Yup. But they are gotten by measurement so it goes back to instruments >again, including the Mark One Eyeball, courtesy of Evolution. Aha. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" > How can Newton's theory of gravitation be false when engineers use it > every day in their calculations? You need to be able to identify some > theories as being 'leass false' than others, or 'more useful', or > 'approximately true'. > Of course even QED and GR are only approximately true (nothing is > absolutely true, or if it is you could never know it). The same way I can use KE = (1/2)m*v*v for kinetic energy, as long as v isn't too big. But if v gets to be about 3E7 m/s, then I start making mistakes in the KE of a few percent or so, and worse as v gets bigger. The same way I can design a clock pendulum to have a period that is proportional to the square root of the length, as long as the angle of the swing isn't too high. But if the angle of the swing gets to be above 15 degrees or so, I'm going to start making a mistake of a percent or so. Approximations work well -- admirably, in fact -- as long as you don't try to use them outside their limits of applicability. PD > > Alternative-theory flamers: the onus is on you to point accurately to the > > failing of the theory. > > The burden of proof of a theory lies squarely on the one proposing it. > > Bob Kolker This is true, which I also attested to in my post. But it's not that simple. Science is, by nature, a community process. Every theory must be checked against independent experimental confirmation. Most experimental results must be repeated by an independent measurement before becoming completely accepted. Consequently, the critique of new physics needs to abide by some solid sociological rules, as well. It's just as important that criticism of a new theory point correctly and cleanly to the SCIENTIFIC flaw. Part of the reason for this is that the temptation to dismiss a new model because it conflicts with prevailing wisdom is exactly what will make the critic a poor scientist him/herself. For whatever barriers you impose on others you will impose on your own mind, and if those barriers are misplaced, you may miss something crucial. PD | > > Alternative-theory flamers: the onus is on you to point accurately to the | > > failing of the theory. [quoted text clipped - 19 lines] | | PD Kolker has the remarkable ability to say all the right things but does not follow his own advice. The only appropriate word to describe this phenomenon is "hypocrisy". Androcles > > Alternative-theory flamers: the onus is on you to point accurately to the > > failing of the theory. > > The burden of proof of a theory lies squarely on the one proposing it. > > Bob Kolker Actually, it lies on the person who asserts something about the theory. If I say "yeah it's right!" then I have to show that it's right (ie. it satisfies the 5 requirements). If I say, "no it's wrong!" then I have to show it's failing. If the proposer is cliaming it's true, then they have to show it satisfies the requirements. If a critic says it's false they have to point to a VALID reason it's false. Again, you're wrong. > Again, you're wrong. The correctness of a theory consists exactly of the correctness of ALL of its predictions. That is why a physical theory cannot be shown to be true or correct since there are an infinite number of predictions. You are correct to this extent. To show a theory is false, one needs to produce a falsifying experiment. Otherwise we do not know whether the theory is true or false. An unfalsifed theory cannot be said to be true, since all of its possible predictions cannot be tested and shown to be true. So there are two states for a physical theory: False and Maybe False. True is not a demonstrable state for a theory. Bob Kolker > > Again, you're wrong. > > The correctness of a theory consists exactly of the correctness of ALL > of its predictions. That is why a physical theory cannot be shown to be > true or correct since there are an infinite number of predictions. That's right -- no theory is "completely true". None! > You are correct to this extent. To show a theory is false, one needs to > produce a falsifying experiment. Otherwise we do not know whether the > theory is true or false. An unfalsifed theory cannot be said to be true, > since all of its possible predictions cannot be tested and shown to be > true. Yep. > So there are two states for a physical theory: False and Maybe False. > True is not a demonstrable state for a theory. Yep. > Bob Kolker Then what does this "burden of proof is solely on the one proposing it" mean? Does that mean that someone who wants to say the theory isn't good is immune to having to show that it isn't? > Then what does this "burden of proof is solely on the one proposing it" > mean? > Does that mean that someone who wants to say the theory isn't good is immune > to having to show that it isn't? It is up to the proposer of theory to 1. Make predictions. 2. Perform experiments or propose experments to test the predictions If the predictions corroberate (which does not mean prove) the theory, then the theory can be taken seriously as a useful theory. If a theory makes to predictions it is worse than false. It is useless. Let he who proposes the theory make predictions with it and be ready to accept the tests that he and other people make of the theory. When Einstein created GTR he -proposed- as a test, the bending of light around the sun, and he showed that his theory accounted for the motion of Mercury. In short he made the effort to corroberate his theory. So I will restate my position, this time more precisely, I hope. He who proposes the theory must first show it accounts for all known facts in its domain of applicabablity and must propose testable predictions of facts not yet known to further corroberate the theory. It is up to the proposer to take those steps required to convince others that his theory ought to be taken seriously. Simply saying that no one (yet) shown it false is not sufficient. Bob Kolker Bob Kolker robert j. kolker: >> Again, you're wrong. > >The correctness of a theory consists exactly of the correctness of ALL >of its predictions. That is why a physical theory cannot be shown to be >true or correct since there are an infinite number of predictions. That's obviously wrong for several reasons. (1) You've based that belief on a proof in first order logic. But quantum mechanical predictions are probabilistic and there exists no arithemetic procedure for constructing a random number. You can pretend that there is some underlying physical ``cause'' that only appears random, but you're basically just defining something that means the same thing unless it predicts something different. Chaotic systems can have statistical escriptions but are really deterministic. Probabilistic systems are not deterministic and the only reality associated with such a system is in the statistics of the measurements. (2) An infinite amount of energy is required to for an infinite number of possible predictions. That is unphysical, so requiring a theory to make an infinite number of correct ones as a figure of merit contradicts the requirement of a theory to make physical predictions. In short, your argument is circular. You invoke goedel's theorem by requiring the sort of unphysical logical statement from which the theorem follows. Nothing requires any mathematical statement which could be proven true to represent a physical phenomenon. Physical phenomena need only be described by the mathematics needed to describe a finite number of phenomena. (3) Apart from the problem above, physical theories only have to make correct predictions. They are not required to make any predictions which are incorrect or prove that some additional mental masturbation designed for philosophical satisfaction is incorrect. Any reality associated with philosphical satisfaction which adds nothing to any physical prediction made without the additional philosophical content, amounts to solipsism. (4) Basicaly, you are making the same argument made for the ether, but you've dressed it up in the guise of first order logic. You've neglected to include the fact that physical phenomena are limited to the phenomena that occur in nature and you've offered no proof that an infinite number of anything has any physical meaning. > (4) Basicaly, you are making the same argument made for the ether, No. I insist that a true theory have no falsifying empirical instances. First Order Logic plus set theory is good enough for mathematics.[*] It is good enough for physics. All the math used in physics is stated in terms of set theory and first order logic. All the inference rules used in mathematics (i.e. real and complex variables, group theory, linear algebra etc) uses the inferences rules of first order logic. Modus ponens. Modeus tollens, universal generalization, existential instantiation. The Ueber Requirement is the principle of non-contradiction. A good theory must not only be empircally correct, it must be logically and mathematically consistent. What I say has nothing whatsoever to do with aether. A physical theory cannot be proven to be empirically correct because any theory general enough to be useful makes an infinite set of testable predictions. There is neither time nor energy to test them all. The only thing we can be sure of is a falsification. Bob Kolker * Quine once quipped that set theory is second order logic in sheep's clothing. robert j. kolker: >> (4) Basicaly, you are making the same argument made for the ether, > >No. I insist that a true theory have no falsifying empirical instances. You're free to find such instances. In fact, you might as well accept the current theories which no believes are fundamental, since there exist no falsifying empirical instances. If there are, it's been kept a darn good secret. >First Order Logic plus set theory is good enough for mathematics.[*] It >is good enough for physics. Please construct a random number using any mathematical procedure ammenable to first order logic. Please explain how to obtain the correct entropy for N particles in n_1,...,n_j states, given that the counting argument used to define the entropy gives the wrong answer. What mathematical argument can you apply to differentiate between keeping and throwing away the N! ? Don't you think it would take somewhat less than 50 years or so to justify, if the answer could be deduced from simple first order predicate logic? All your're doing is counting. >All the math used in physics is stated in terms of set theory and first >order logic. No, it isn't. Find an algorithm that generates a random number. >All the inference rules used in mathematics (i.e. real and complex >variables, group theory, linear algebra etc) uses the inferences >rules of first order logic. Modus ponens. Modeus tollens, universal >generalization, existential instantiation. The Ueber Requirement is >the principle of non-contradiction. Use any or all of those rules to generate a random number. >A good theory must not only be empircally correct, it >must be logically and mathematically consistent. Then stop making illogical assumptions. It's absolutely stupid to require a theory to be unphysical in order for it to be an acceptable theory. I guess that since I haven't measured the mass of every hydrogen atom, there might be an anomolous one out there, that could potentially threaten a theory of hydrogen atoms, huh? Oh, but wait. If the mass were different, it wouldn't be a hydrogen atom. Gee, that presents a real dilemna regarding your assumption about universal quantification. You apparently think we assign properties to electrons and then check a lot of electrons to see if the electrons all have the same mass or something. Well, not really.That happened already, but instead of dumping the theory of the electron because a real heavy one was found, they just called it a muon. So, exactly how do I discover an electron that isn't really the electron defined in the theory? How about a hydrogen atom? Exactly how can I discover a hydrogen atom that isn't a hydrogen atom? >What I say has nothing whatsoever to do with aether. Sure it does. It's the same sort of kookyness. >A physical theory cannot be proven to be empirically correct because any >theory general enough to be useful makes an infinite set of testable >predictions. Then, I suggest not hopping on board a plane. >There is neither time nor energy to test them all. The only >thing we can be sure of is a falsification. Then, you're way ahead of the game. All theories are false, so you can justify any theory you like on the basis that someone might make it work well enough to eventually look scientific. > No, it isn't. Find an algorithm that generates a random number. There is no such algorithm. All algorithms are deterministic. Bob Kolker > >All the inference rules used in mathematics (i.e. real and complex > >variables, group theory, linear algebra etc) uses the inferences [quoted text clipped - 42 lines] > so you can justify any theory you like on the basis that someone > might make it work well enough to eventually look scientific. robert j. kolker: >> No, it isn't. Find an algorithm that generates a random number. > >There is no such algorithm. All algorithms are deterministic. Precisely. That was the point. > robert j. kolker: > > [quoted text clipped - 7 lines] > > Precisely. That was the point. I missed the point then. The nonexistence of a random number algorithm is the direct consequence of FOL and set theory. A full bore second order logic is not necessary to ground the mathematics used in physics. Bob Kolker > I guess that since I haven't measured the mass of every hydrogen atom, > there might be an anomolous one out there, that could potentially threaten > a theory of hydrogen atoms, huh? Oh, but wait. If the mass were different, > it wouldn't be a hydrogen atom. All it takes is one counterexample to negate the conjuction of all the premises underlying a theory. Modus Tollens. A valid principle of inference. The counter example does not tell which one of the underlying assumptions is wrong. It only tells you that one of the underlying assumptions is wrong. Either you accept the inference rules of FOL as operative or you don't. The majority of mathematicians do. And there is no such thing as a random number. There are sequences whose rules of generation are as long as the sequences themselves. These are Kolomogorf Random and the only random things I know of which exist mathematically. If you want to call a measurable function a random number, go right ahead. Bob Kolker robert j. kolker: >> I guess that since I haven't measured the mass of every hydrogen atom, >> there might be an anomolous one out there, that could potentially threaten [quoted text clipped - 3 lines] >All it takes is one counterexample to negate the conjuction of all the >premises underlying a theory. Modus Tollens. Define a counter example to a probabilistic prediction based upon a measurement consisting of one trial. >A valid principle of >inference. The counter example does not tell which one of the underlying [quoted text clipped - 3 lines] >Either you accept the inference rules of FOL as operative or you don't. >The majority of mathematicians do. Stop throwing out platitudes. >And there is no such thing as a random number. Then what do you call the probability for a nucleus to decay? >There are sequences whose rules of generation are as long as the >sequences themselves. These are Kolomogorf Random and the only >random things I know of which exist mathematically. Then you've made my point. >If you want to call a measurable function a random number, go right ahead. I'm not calling any function, measureable or otherwise, a random number. Are you incapable of reading what's written or what's the deal? > Gee, that presents a real dilemna regarding your assumption about > universal quantification. You apparently think we assign properties to [quoted text clipped - 5 lines] > in the theory? How about a hydrogen atom? Exactly how can I discover > a hydrogen atom that isn't a hydrogen atom? How do you propose to falsify any theory then? There is only one way. Prediction says X and experiment says not X. That is how a theory is falsified. True theories never make false predictions. All forms of inference are truth value preserving. The thing inferred as alwasy at least as true as the things assumed. Logic 101. Bob Kolker robert j. kolker: >> Gee, that presents a real dilemna regarding your assumption about >> universal quantification. You apparently think we assign properties to [quoted text clipped - 7 lines] > >How do you propose to falsify any theory then? That did not answer my questions. >There is only one way. Prediction says X and experiment says not X. >That is how a theory is falsified. While that is true in the sense of a tautology, you don't apply it the way you would like to make it appear. However, your original argument requires quantum mechanics to predict something which would falsify quantum mechanics if true, so you obviously don't care _what_ the theory actually predicts. What you care about is not having to deal with the possibility that the outcome of an experiment, such as timing the decay of one nucleus, is really probabilistic and has no underlying cause. In effect, you're trying to make quantum mechanics a classical hidden variable theory and pretend the hidden variables are unknowable. >True theories never make false predictions. Theories, true or otherwise never make predictions based upon your idea of the type of prediction the theory should make instead of the predctions the theory does make. >All forms of inference are truth value preserving. The thing inferred >as alwasy at least as true as the things assumed. Logic 101. Then repeat the course until you figure out that logic requires a probabilistic theory to make probabilistic prediction in order to be self-consistent and that probabilistic and statistical are not the same thing. You might investigate the difference in predicting hurricanes, for which the model is statistical and predicting the decay of one nucleus which is probabilistic, but obviously not statistical, unless you consider one nucleus to be statistical. The former is classical, deterministic and chaotic. The latter is probabilistic and ergodic. Of you want to discuss logic 101, you should first figure out why it's necessary to consider what the theory predicts when stating what measurements can falsify the theory. That doesn't seem to have registered with you. > Of you want to discuss logic 101, you should first figure out why > it's necessary to consider what the theory predicts when stating what > measurements can falsify the theory. That doesn't seem to have > registered with you. I ask you once again. How do you falsify a physical theory, given all that you have stated. If you can't falsify a theory empirically it is WORTHLESS. So tell us how to empirically falsify a statistical or probabalistic theory. Bob Kolker > I'm writing this just to set a line in the sand for both > alternate-theory [quoted text clipped - 3 lines] > 1. A good theory has to refer to well-defined terms and concepts. It > does no How about this #6. A good theory has to be falsifiable under some set of experimental facts. John Lowry Flight Physics > > I'm writing this just to set a line in the sand for both > > alternate-theory [quoted text clipped - 8 lines] > #6. A good theory has to be falsifiable under some set of experimental > facts. Does it have to consistent? Does it need to agree with experimental evidence? Do theories that gel with other theories better but are experimentally the same better? Are heroes that make more falsifiable predictions better again? Tons of questions remain. The point is no hard and fast rules exist - we must judge each on a case by case basis. Thanks Bill > John Lowry > Flight Physics > Does it have to consistent? Yes. Ex falsi quodlibet. From an inconsistent set of postulates any well formed statement can be inferred. Bob Kolker > > Does it have to consistent? > > Yes. Ex falsi quodlibet. From an inconsistent set of postulates any well > formed statement can be inferred. It is not that simple Bob. Theories with obvious inconstenticies would not be proposed by competent people in the first place. But what about more subtle ones? -such as my often quoted example of the Dirac delta function. Under Lebesque integration is it an inconsistent function yet was used for yonks by applied mathematicians no problemo. Exactly what was going on was eventually sorted out - but up until that point should we have dismissed the results thus obtained? No. What we should have done is exactly what did occur - we continue with the theory and see if the blemish can be fixed up - which it was. But what decides if an inconsistancy is merely a blemish that can be fixed up or something much more serious - all I can suggest is it need to be looked at on a case by case basis. But I suspect that most often it will be found to be of the blemish type and we can continue using until it is fixed up. Thanks Bill > Bob Kolker > > Does it have to consistent? > > Yes. Ex falsi quodlibet. From an inconsistent set of postulates any well > formed statement can be inferred. Since not everyone may be familiar with this, first a digression on logic to show why this is so. Let p and q be True/False propositions. What T/F proposition is equivalent p => q ? Well, when p => q is true, it can't be the case that p is true and q isn't. This motivates: (p => q) <=> ~(p and ~q) <=> (~p) or q Now suppose we have a formal axiom system that is inconsistent, i.e, there is a proposition b such that both b and ~b are true in the system. Consequenrly, (b and ~b) is also a true proposition. Let c by any proposition in the system, and consider [(b and ~b) => c] <=> ~(b and ~b) or c <=> (~b or b) or c But (~b or b) always true gives [(~b or b) or c] always true, which in turn gives [(b and ~b) => c] always true. Now (modus ponens) [(b and ~b) true gives c true. c was arbitrary, so any well-formed statement can be inferred in an inconsistent system! However, I have never seen any physical theory laid out as a formal axiom system. And if a physical theory were laid as out as a formal system it surely would be sufficiently complicated as to include Peano's axioms for the natural numbers. Thus, by Goedel's second incompleteness theorem, it would not be possible to demonstrate the logical consistency of the physical theory. Also, I think physicists use the term "consistent" to mean something different than do logicians. I'd like to see people in the group take stabs at defining (losely) what it means for a physical theory to be consistent. Take quantum electrodynamics (QED) as an example. Many physical results in QED are calculated using what are thought to be divergent (even after renormalization) asymptotic series. 1) Is QED a good theory? 2) Is QED a consistent physical theory? I think most mainstream people would answer "Yes." to 1), but the answers to 2) might include phrases like "domain of applicability." Regards, George > > > Does it have to consistent? > > [quoted text clipped - 46 lines] > I think most mainstream people would answer "Yes." to 1), but the answers to > 2) might include phrases like "domain of applicability." Modern views of renormalizabilty have changed somewhat - see http://math.ucr.edu/home/baez/renormalization.html. Thanks Bill > Regards, > George > However, I have never seen any physical theory laid out as a formal > axiom system. And if a physical theory were laid as out as a formal > system it surely would be sufficiently complicated as to include > Peano's axioms for the natural numbers. Thus, by Goedel's second > incompleteness theorem, it would not be possible to demonstrate the > logical consistency of the physical theory. Why is that? After all, it is a trivial mathematical exercise to demonstrate the consistency of Peano arithmetic. > > However, I have never seen any physical theory laid out as a formal > > axiom system. And if a physical theory were laid as out as a formal [quoted text clipped - 5 lines] > Why is that? After all, it is a trivial mathematical exercise to > demonstrate the consistency of Peano arithmetic. Then do so. According to Godel's second incompleteness theorem it can not be done. See http://www.faragher.freeserve.co.uk/godeldef2.htm. Thanks Bill > Then do so. According to Godel's second incompleteness theorem it can not > be done. What the incompleteness theorem implies (given the consistency of PA) is that no consistency proof for PA is formalizable in PA. This of course does not change the fact that it is a trivial mathematical exercise to demonstrate the consistency of Peano arithmetic. > What the incompleteness theorem implies (given the consistency of > PA) is that no consistency proof for PA is formalizable in PA. This > of course does not change the fact that it is a trivial mathematical > exercise to demonstrate the consistency of Peano arithmetic. How is that done. It is a relative consistency proof or an absolute consistency proof as would be gotten by producing a finite model? Bob Kolker > > What the incompleteness theorem implies (given the consistency of > > PA) is that no consistency proof for PA is formalizable in PA. This [quoted text clipped - 5 lines] > > Bob Kolker I would not even bother with that\. If it is that trivial then he/she should be able to reproduce it. The fact when I asked for that such a route was not chosen I think speaks volumes. Thanks Bill >> > What the incompleteness theorem implies (given the consistency of >> > PA) is that no consistency proof for PA is formalizable in PA. This [quoted text clipped - 5 lines] >> >> Bob Kolker >I would not even bother with that\. If it is that trivial then he/she >should be able to reproduce it. The fact when I asked for that such a route >was not chosen I think speaks volumes. Strictly speaking, Torkel's claim was too strong. It is not a trivial mathematical exercise to demonstrate the consistency of Peano arithmetic since such a demontration is not possible. On the other hand, assuming the consistency of ZF Set Theory, it becomes a trivial exercise to demonstrate the consistence of PA, i.e. if ZF is consistent, then PA is consistent. This is done by constructing a model of PA in ZF. One such model identifies N with the smallest limit ordinal, 0 with the empty set (i.e. the smallest ordinal), and the successor function is given by S(x) equals the union of x and {x} (i.e. the successor function maps each finite ordinal to its successor ordinal). Similarly, it is a little bit harder to demonstrate that the axioms for R are consistent if ZF is consistent. This is done by constructing a model for R in ZF. Torkel was presumably talking from the point of viewof taking the consistency of ZF a given. David ----- > On the other hand, assuming the consistency of ZF Set Theory, it becomes a > trivial exercise to demonstrate the consistence of PA, i.e. if ZF is > consistent, then PA is consistent. Invoking ZF is absurd overkill. Only a very modest amount of set theory is needed. Specifically, the theory ACA will suffice. > Torkel was presumably talking from the point of viewof taking the > consistency of ZF a given. No, I was talking from the point of view of ordinary mathematics. If you don't accept the trivial proof as proving the consistency of PA, then you have no reason to accept any other mathematical result proved at a similar level of mathematical abstraction. So just what are you (not you personally, but somebody who doesn't accept the consistency proof for PA as proving anything) prepared to accept in mathematics? > > On the other hand, assuming the consistency of ZF Set Theory, it becomes a > > trivial exercise to demonstrate the consistence of PA, i.e. if ZF is [quoted text clipped - 12 lines] > (not you personally, but somebody who doesn't accept the consistency > proof for PA as proving anything) prepared to accept in mathematics? That is the whole problem with Godels proof - it shows that certitude in mathematics is a chimera - any system at least as strong as arithmetic (and that included Peanos axioms, ZF and ZFC) can not be showmen to be consistent. As to what people are prepared to accept in mathematics - I suggest you might like to acquaint yourself with issues in the philosophy of mathematics - see http://www.rbjones.com/rbjpub/philos/maths/. As I have remarked many time philosophy does not seem to resole anything but does allow one to become acquainted with the issues involved so they can form their own opinion. Bill > That is the whole problem with Godels proof - it shows that certitude in > mathematics is a chimera - any system at least as strong as arithmetic (and > that included Peanos axioms, ZF and ZFC) can not be showmen to be > consistent. Nonsense. The incompleteness theorem shows nothing whatever about certainty in mathematics. Claiming that PA cannot be shown to be consistent is like claiming that we cannot prove the existenc of an infinity of primes - an arbitrary piece of skepticism. > > That is the whole problem with Godels proof - it shows that certitude in > > mathematics is a chimera - any system at least as strong as arithmetic (and [quoted text clipped - 5 lines] > consistent is like claiming that we cannot prove the existenc of > an infinity of primes - an arbitrary piece of skepticism. I suggest your use of the word 'certitude' would not agree with most peoples eg most people would say that not being able to prove something is consistent represents a lack of certainty on our part. But you are entitled to use words in any sense you like - just do not expect all to agree - or such semantic quibbling to be of any real consequence or value. It is obvious this exchange can go back and forth with no resolution so at this point I will say I have made my points and you have made yours - let others now judge. Bill > I suggest your use of the word 'certitude' would not agree with most peoples > eg most people would say that not being able to prove something is > consistent represents a lack of certainty on our part. Proving PA consistent is a trivial mathematical exercise. > > I suggest your use of the word 'certitude' would not agree with most peoples > > eg most people would say that not being able to prove something is > > consistent represents a lack of certainty on our part. > > Proving PA consistent is a trivial mathematical exercise. Did a quick internet search on Torkel Franzen - I think the following link says it all - http://c2.com/cgi/wiki?TorkelFranzen Hope he finds such amusing. Bill > Did a quick internet search on Torkel Franzen - I think the following link > says it all - http://c2.com/cgi/wiki?TorkelFranzen It's perfectly accurate. > > Did a quick internet search on Torkel Franzen - I think the following link > > says it all - http://c2.com/cgi/wiki?TorkelFranzen > > It's perfectly accurate. Naturally now I know his game I will no longer play. Come to think of it even doing this reply is playing - oh well none of us are totally logical are we? Bill > Naturally now I know his game I will no longer play. There is of course no particular reason why you should devote any energy to logic, Gödel's theorem, and so on. It's a very peripheral subject. But it is a striking and in my opinion noteworthy fact that so many people are led so far astray through having heard about the incompleteness theorem. >>Naturally now I know his game I will no longer play. > [quoted text clipped - 3 lines] > so many people are led so far astray through having heard about the > incompleteness theorem. I would not call it peripheral. It was enough to wreck Hilbert's |
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