Russian Name Worshipper mystics and Cantor's set theory
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From: Bappa on 21 Sep 2009 09:24 On Sep 20, 8:09 pm, John Wilkins <j...(a)wilkins.id.au> wrote: > In article > <9bdd12fa-2b13-4860-a4e5-eebabc173...(a)13g2000prl.googlegroups.com>, > > > > > > Bappa <adda1...(a)bigpond.com> wrote: > > On Sep 18, 3:42 am, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > > There is an interesting new book out about the > > > history of Cantor's set theory. It seems to > > > me that the book lends support to Feyerabend's > > > philosophy of science in _Against Method_. > > > Science can progress through *any* method, > > > Sorry, Marko, this is dead wrong. The only valid *method* in science > > is the *experimental* method - meaning, repeatability of results under > > controlled and same conditions. The rest is analysis and discussion. > > > This is what I was taught in my engineering institute (First Year) by > > the profs. in the Humanities Dept. IIT Kharagur was the only IIT > > where there was a firmly established and motivated Humanities > > department. > > Never take as gospel what you are taught in first year anything. Actually, what I take as gospel is what I learnt before I was ten. I had to unlearn many of the bad stuff since, such as relativity and quantum bullshit. Thirty years of professional engineering experience validates what I learnt from the humanities profs. Yes, they did teach us a lot of nonsense, such as conservation laws, relativity etc. which over the years I have painfully unlearnt, thanks again to the sterling lesson that I received. obBook: "Science Speaks" - I do not remember the author. This was the text book, from which I learnt this most important lesson. There was a chapter on the difference between the *experience* and the *experiment*, in that book. Too often, fools and scoundrels pretending to be scientists confuse the two very different things. When they do that, we have pseudo-science, and Einstein worshippers. Ugh. > > > > > > > > including the paradoxical fact that the progress > > > of mathematics was aided by the mysticism > > > of Russian mathematicians who accepted > > > Cantor's set theory because it fit their > > > mystical beliefs. > > > Now what has maths to do with science? The Queen of Arts is > > Mathematics, and Science pays the most humble homage to Her. > > > Cheers, > > > Arindam Banerjee.- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -
From: Bappa on 21 Sep 2009 09:47 On Sep 20, 11:03 pm, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > On Sep 20, 12:50 pm, Bappa <adda1...(a)bigpond.com> wrote: > > > On Sep 18, 3:42 am, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > > > There is an interesting new book out about the > > > history of Cantor's set theory. It seems to > > > me that the book lends support to Feyerabend's > > > philosophy of science in _Against Method_. > > > Science can progress through *any* method, > > > Sorry, Marko, this is dead wrong. The only valid *method* in science > > is the *experimental* method - meaning, repeatability of results under > > controlled and same conditions. The rest is analysis and discussion. > > I was referring to Paul Feyerabend. He was engaged in an argument > with philosophers of science such as Karl Popper If one cannot be a scientist, one can be a philosopher of science, evidently! Heh-heh. > over the question > of whether there is one single correct Scientific Method. The argument > is not over the necessity of experiments in science, but other issues. > Here is one summary of Feyerabend's arguments: Thanks for posting this. I will go through it. > Science is an essentially anarchistic enterprise: theoretical > anarchism is more humanitarian and more likely to encourage progress > than its law-and-order alternatives. The scientist can be anarchic, if he is independent and not under some institution. Science is not anarchic. It follows extremely well-laid and well-defined patterns and principles. The anarchy of the scientist lies in his revolt against a corrupting establishment, that corrupts science. Like, a person like me, who has debunked Einstein's wrong theories, is anarchic. But I have the greatest regard for the scientific method - which is EXPERIMENT. Beyond the experiment, there is the analysis. Wrong analysis, repetition of bungles and blunders, lead to disaster even when the experiment is correctly done. Check out www.users.bigpond.com/adda1234/MMInt.htm as an example, that shows how a correctly done experiment led to very bad and wrong and in fact disastrous results as a result of wrong analysis. > This is shown both by an examination of historical episodes and by an > abstract analysis of the relation between idea and action. The only > principle that does not inhibit progress is: anything goes. No, that is wrong. Immoral and cowardly approaches do not help in the least. In the long run, at least. > For example, we may use hypotheses that contradict well-confirmed > theories and/or well-established experimental results. We may advance > science by proceeding counter-inductively. Again, wrong. Einstein's theories were and are wrong. They were wrong because they were based upon a blunder, in analysing the results of the MM interferometry experiment. They were "proved" by the atom bomb apparently, but my new formula relating mass and energy shows how wrong they all were. Now, my formula will be proved right only when I make a model of an Internal Force Engine. That will be some experiment! Till then, my work is theoretical, and of no practical value - yet. > The consistency condition which demands that new hypotheses agree with > accepted theories is unreasonable because it preserves the older > theory, and not the better theory. Hypotheses contradicting well- > confirmed theories give us evidence that cannot be obtained in any > other way. Proliferation of theories is beneficial for science, while > uniformity impairs its critical power. Uniformity also endangers the > free development of the individual. So far so good. Yes there can be many theories, but only proper experiment can decide which one is the most correct at any given time. Till then, we live in the world of speculation. > There is no idea, however ancient and absurd, that is not capable of > improving our knowledge. Increasing knowledge is not the same as improving knowledge. The whole history of thought is absorbed into > science and is used for improving every single theory. Nor is > political interference rejected. It may be needed to overcome the > chauvinism of science that resists alternatives to the status quo. > No theory ever agrees with all the facts in its domain, yet it is not > always the theory that is to blame. Facts are constituted by older > ideologies, and a clash between facts and theories may be proof of > progress. It is also a first step in our attempts to find the > principles implicit in familiar observational notions. > As an example of such an attempt I examine the tower argument which > the Aristotelians used to refute the motion of the earth. The argument > involves natural interpretations - ideas so closely connected with > observations that it needs a special effort to realise their existence > and to determine their content. Galileo identifies the natural > interpretations which are inconsistent with Copernicus and replaces > them by others. > The new natural interpretations constitute a new and highly abstract > observation language. They are introduced and concealed so that one > falls to notice the change that has taken place (method of anamnesis). > They contain the idea of the relativity of all motion and the law of > circular inertia. > Initial difficulties caused by the change are defused by ad hoc > hypotheses, which thus turn out occasionally to have a positive > function; they give new theories a breathing space, and they indicate > the direction of future research. > In addition to natural interpretations, Galileo also changes > sensations that seem to endanger Copernicus. He admits that there are > such sensations, he praises Copernicus for having disregarded them, he > claims to have removed them with the help of the telescope. However, > he offers no theoretical reasons why the telescope should be expected > to give a true picture of the sky. > Nor does the initial experience with the telescope provide such > reasons. The first telescopic observations of the sky are indistinct, > indeterminate, contradictory and in conflict with what everyone can > see with his unaided eyes. And, the only theory that could have helped > to separate telescopic illusions from veridical phenomena was refuted > by simple tests. > On the other hand, there are some telescopic phenomena which are > plainly Copernican. Galileo introduces these phenomena as independent > evidence for Copernicus while the situation is rather that one refuted > view - Copernicanism - has a certain similarity with phenomena > emerging from another refuted view - the idea that telescopic > phenomena are faithful images of the sky. Galileo prevails because of > his style and his clever techniques of persuasion, because he writes > in Italian rather than in Latin, and because he appeals to people who > are temperamentally opposed to the old ideas and the standards of > learning connected with them. > Such 'irrational' methods of support are needed because of the 'uneven > development' (Marx, Lenin) of different parts of science. > Copernicanism and other essential ingredients of modern science > survived only because reason was frequently overruled in their past. > Galileo's method works in other fields as well. For example, it can be > used to eliminate the existing arguments against materialism, and to > put an end to the philosophical mind/body problem (the corresponding > scientific problems remain untouched, however). > The results obtained so far suggest abolishing the distinction between > a context of discovery and a context of justification and disregarding > the related distinction between observational terms and theoretical > terms. Neither distinction plays a role in scientific practice. > Attempts to enforce them would have disastrous consequences. > Finally, the discussion in Chapters 6-13 shows that Popper's version > of Mill's pluralism is not in agreement with scientific practice and > would destroy science as we know it. Given science, reason cannot be > universal and unreason cannot be excluded. This feature of science > calls for an anarchistic epistemology. The realisation that science is > not sacrosanct, and that the debate between science and myth has > ceased without having been won by either side, further strengthens the > case for anarchism. > Even the ingenious attempt of Lakatos to construct a methodology that > (a) does not issue orders and yet (b) puts restrictions upon our > knowledge-increasing activities, does not escape this conclusion. For > Lakatos' philosophy appears liberal only because it is an anarchism in > disguise. And his standards which are abstracted from modern science > cannot be regarded as neutral arbiters in the issue between modern > science and Aristotelian science, myth, magic, religion, etc. > Moreover, these standards, which involve a comparison of content > classes, are not always applicable. The content classes of certain > theories are incomparable in the sense that none of the usual logical > relations (inclusion, exclusion, overlap) can be said to hold between > them. This occurs when we compare myths with science. It also occurs > in the most advanced, most general and therefore most mythological > parts of science itself. > Thus science is much closer to myth than a scientific philosophy is > prepared to admit. It is one of the many forms of thought that have > been developed by man, and not necessarily the best. It is > conspicuous, noisy, and impudent, but it is inherently superior only > for those who have already decided in favour of a certain ideology, or > who have accepted it without having ever examined its advantages and > its limits. And as the accepting and rejecting of ideologies should be > left to the individual it follows that the separation of state and > church must be supplemented by the separation of state and science, > that most recent, most aggressive, and most dogmatic religious > institution. Such a separation may be our only chance to achieve a > humanity we are capable of, but have never fully realised. > > http://www.marxists.org/reference/subject/philosophy/works/ge/feyerab... > > > > > This is what I was taught in my engineering institute (First Year) by > > the profs. in the Humanities Dept. IIT Kharagur was the only IIT > > where there was a firmly established and motivated Humanities > > department. > > > > including the paradoxical fact that the progress > > > of mathematics was aided by the mysticism > > > of Russian mathematicians who accepted > > > Cantor's set theory because it fit their > > > mystical beliefs. > > > Now what has maths to do with science? The Queen of Arts is > > Mathematics, and Science pays the most humble homage to Her. > > Many people would include mathematics as part of science. They used to give B.A. in maths, in the great days of maths. Science serves maths, not the other way around, in any honest establishment. Especially when by maths they mean statistics. > There is an element of mathematics that is similar to the > arts but I would not call mathematics an art. I would. Mathematics is the Queen of Arts, and Philosophy is the King. Aesthetic > considerations play a role in mathematics, but they also > play a role in theoretical physics. Arts is not just about aesthetics. Arts is about art - about subtle trickery - the means with which we differentiate ourselves from the denizens of the wild. > There are no experiments > in mathematics but the use of logical deduction sets it > apart from the arts. The fundamental concepts of mathematics > have a basis in experience, but the concepts have been > abstracted. I think we are on different wavelengths. I depend upon maths for my living. And the set theory you are talking about, is a daily phenomenon for me these days, when I write SQL code. Maths is abstract for dilettantes and those in academia maybe, but for an engineer/computer scientist/mathematical modeller/etc. like myself, it is very very concrete indeed. It is late, so I have not replied in greater detail. May do that later. Thanks a lot for your wonderful post, as illuminating as ever. Cheers, and with regards, Arindam Banerjee
From: Bappa on 21 Sep 2009 09:55 On Sep 21, 4:42 pm, Patok <crazy.div.pa...(a)gmail.com> wrote: > Marko Amnell wrote: > > On Sep 20, 12:50 pm, Bappa <adda1...(a)bigpond.com> wrote: > >> On Sep 18, 3:42 am, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > >>> There is an interesting new book out about the > >>> history of Cantor's set theory. It seems to > >>> me that the book lends support to Feyerabend's > >>> philosophy of science in _Against Method_. > >>> Science can progress through *any* method, > >> Sorry, Marko, this is dead wrong. The only valid *method* in science > >> is the *experimental* method - meaning, repeatability of results under > >> controlled and same conditions. The rest is analysis and discussion.. > > > I was referring to Paul Feyerabend. He was engaged in an argument > > with philosophers of science such as Karl Popper over the question > > of whether there is one single correct Scientific Method. The argument > > is not over the necessity of experiments in science, but other issues. > > Here is one summary of Feyerabend's arguments: > > Marko, I admire your patience and level-headedness in dealing with > certified wooden philosophers. > (A "wooden phlosopher" is a term used in some Eastern European > languages to describe pretend-intelligents --educated cretins, in other > words-- like this Arindam Banerjee). This one sounds like an Einsteinian! A fit candidate for the Usenet Rogues' Gallery of Arindam haters - we can squeeze him in, there is still room! :) :) > > -- > You'd be crazy to e-mail me with the crazy. But leave the div alone.- Hide quoted text -
From: Bappa on 22 Sep 2009 06:58 On Sep 21, 11:47 pm, Bappa <adda1...(a)bigpond.com> wrote: > On Sep 20, 11:03 pm, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > > On Sep 20, 12:50 pm, Bappa <adda1...(a)bigpond.com> wrote: > > > > On Sep 18, 3:42 am, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > > > > There is an interesting new book out about the > > > > history of Cantor's set theory. It seems to > > > > me that the book lends support to Feyerabend's > > > > philosophy of science in _Against Method_. > > > > Science can progress through *any* method, > > > > Sorry, Marko, this is dead wrong. The only valid *method* in science > > > is the *experimental* method - meaning, repeatability of results under > > > controlled and same conditions. The rest is analysis and discussion. > > > I was referring to Paul Feyerabend. He was engaged in an argument > > with philosophers of science such as Karl Popper > > If one cannot be a scientist, one can be a philosopher of science, > evidently! Heh-heh. > > > over the question > > of whether there is one single correct Scientific Method. The argument > > is not over the necessity of experiments in science, but other issues. > > Here is one summary of Feyerabend's arguments: > > Thanks for posting this. I will go through it. > > > Science is an essentially anarchistic enterprise: theoretical > > anarchism is more humanitarian and more likely to encourage progress > > than its law-and-order alternatives. > > The scientist can be anarchic, if he is independent and not under some > institution. Science is not anarchic. It follows extremely well-laid > and well-defined patterns and principles. The anarchy of the > scientist lies in his revolt against a corrupting establishment, that > corrupts science. Like, a person like me, who has debunked Einstein's > wrong theories, is anarchic. But I have the greatest regard for the > scientific method - which is EXPERIMENT. Beyond the experiment, there > is the analysis. Wrong analysis, repetition of bungles and blunders, > lead to disaster even when the experiment is correctly done. Check > out > > www.users.bigpond.com/adda1234/MMInt.htm as an example, that shows > how a correctly done experiment led to very bad and wrong and in fact > disastrous results as a result of wrong analysis. > > > This is shown both by an examination of historical episodes and by an > > abstract analysis of the relation between idea and action. The only > > principle that does not inhibit progress is: anything goes. > > No, that is wrong. Immoral and cowardly approaches do not help in the > least. In the long run, at least. > > > For example, we may use hypotheses that contradict well-confirmed > > theories and/or well-established experimental results. We may advance > > science by proceeding counter-inductively. > > Again, wrong. Einstein's theories were and are wrong. They were > wrong because they were based upon a blunder, in analysing the results > of the MM interferometry experiment. They were "proved" by the atom > bomb apparently, but my new formula relating mass and energy shows how > wrong they all were. Now, my formula will be proved right only when I > make a model of an Internal Force Engine. That will be some > experiment! Till then, my work is theoretical, and of no practical > value - yet. > > > The consistency condition which demands that new hypotheses agree with > > accepted theories is unreasonable because it preserves the older > > theory, and not the better theory. Hypotheses contradicting well- > > confirmed theories give us evidence that cannot be obtained in any > > other way. Proliferation of theories is beneficial for science, while > > uniformity impairs its critical power. Uniformity also endangers the > > free development of the individual. > > So far so good. Yes there can be many theories, but only proper > experiment can decide which one is the most correct at any given > time. Till then, we live in the world of speculation. > > > There is no idea, however ancient and absurd, that is not capable of > > improving our knowledge. > > Increasing knowledge is not the same as improving knowledge. > > The whole history of thought is absorbed into > > > science and is used for improving every single theory. Nor is > > political interference rejected. It may be needed to overcome the > > chauvinism of science that resists alternatives to the status quo. > > No theory ever agrees with all the facts in its domain, I don't see any facts going against the theories of gravitation, electromagnetics, atomic structure, etc. which form the core of hard science. I see lots of facts going against the theories of relativity and quantum and entropy. yet it is not > > always the theory that is to blame. Facts are constituted by older > > ideologies, and a clash between facts and theories may be proof of > > progress. No, it is a proof of regress. It is proof that bad theories are winning out over good theories. It is proof that the establishment is corrupt and forcing people to live in a world of lies. It is also a first step in our attempts to find the > > principles implicit in familiar observational notions. > > As an example of such an attempt I examine the tower argument which > > the Aristotelians used to refute the motion of the earth. Scratch any Einsteinian deep enough, and you will find an Aristotelian. Special relativity can be correct if and only if the Earth is standing still, so much I myself have proved beyond doubt. I suspect that the success of Einstein has some deep (and disgustingly wrong) theological basis. The argument > > involves natural interpretations - ideas so closely connected with > > observations that it needs a special effort to realise their existence > > and to determine their content. Galileo identifies the natural > > interpretations which are inconsistent with Copernicus and replaces > > them by others. Huh? Galileo found out with his telescope that Jupiter had moons. So if Jupiter's moons could go around Jupiter, the Earth could go around the Sun. It would then move, that is. Which was what Copernicus was saying, as opposed to the standard Aristotelian theory that the Sun and everything else was going around the Earth. The Church did not want to hear about the Earth's mobility, so they made Galileo shut up. Again, this was what I learnt in my First Year in Engineering from the Humanities Dept. We read the play "Galileo" by Brecht. > > The new natural interpretations constitute a new and highly abstract > > observation language. They are introduced and concealed so that one > > falls to notice the change that has taken place (method of anamnesis). > > They contain the idea of the relativity of all motion and the law of > > circular inertia. Here we go again, with wrong theories like relativity and circular inertia trying to out the right ones like gravity. Wrong observations and wrong deductions are crucial for the success of wrong theories. The MM interferometry experiment, with its wrong analysis, done many times by many people, is the biggest proof of this. > > Initial difficulties caused by the change are defused by ad hoc > > hypotheses, which thus turn out occasionally to have a positive > > function; they give new theories a breathing space, and they indicate > > the direction of future research. So long as folks still have wits and guts. What with idiot-box TV, novels and permissiveness, ease of every kind, junk food and establishmentarianism meaning safe and comfortable pensions after retirement for all the slimy sucking-up PhuDs, the very concept of anarchic research has long ceased to exist anywhere on the planet. Except, maybe, in Kazakhstan, where men are ruled by men and not by little girls. Because they have the best potassium, as we know, from Borat. > > In addition to natural interpretations, Galileo also changes > > sensations that seem to endanger Copernicus. He admits that there are > > such sensations, he praises Copernicus for having disregarded them, he > > claims to have removed them with the help of the telescope. However, > > he offers no theoretical reasons why the telescope should be expected > > to give a true picture of the sky. > > Nor does the initial experience with the telescope provide such > > reasons. The first telescopic observations of the sky are indistinct, > > indeterminate, contradictory and in conflict with what everyone can > > see with his unaided eyes. And, the only theory that could have helped > > to separate telescopic illusions from veridical phenomena was refuted > > by simple tests. > > On the other hand, there are some telescopic phenomena which are > > plainly Copernican. Galileo introduces these phenomena as independent > > evidence for Copernicus while the situation is rather that one refuted > > view - Copernicanism - has a certain similarity with phenomena > > emerging from another refuted view - the idea that telescopic > > phenomena are faithful images of the sky. Galileo prevails because of > > his style and his clever techniques of persuasion, because he writes > > in Italian rather than in Latin, and because he appeals to people who > > are temperamentally opposed to the old ideas and the standards of > > learning connected with them. Galileo prevailed far more over Aristotle (his orbiting moons shattered Aristotle's crystal spheres, remember) than Copernicus till Einstein came up with his relativistic bs; given the modern success of the Einsteinians (aka Aristotleians) it looks like his success has had a hopefully temporary break. I don't see how Galileo and Copernicus were at odds. Galileo's telescope showed the moons, and later on it was found that the movement of heavenly bodies made much more sense if the Copernican model was followed. > > Such 'irrational' methods of support are needed because of the 'uneven > > development' (Marx, Lenin) of different parts of science. > > Copernicanism and other essential ingredients of modern science > > survived only because reason was frequently overruled in their past. Reason was over-ruled only by by bigots, like those who burnt Bruno for daring to say that the universe was infinite. Science has never gained from bigotry. > > Galileo's method works in other fields as well. For example, it can be > > used to eliminate the existing arguments against materialism, and to > > put an end to the philosophical mind/body problem (the corresponding > > scientific problems remain untouched, however). > > The results obtained so far suggest abolishing the distinction between > > a context of discovery and a context of justification and disregarding > > the related distinction between observational terms and theoretical > > terms. Neither distinction plays a role in scientific practice. > > Attempts to enforce them would have disastrous consequences. > > Finally, the discussion in Chapters 6-13 shows that Popper's version > > of Mill's pluralism is not in agreement with scientific practice and > > would destroy science as we know it. Given science, reason cannot be > > universal and unreason cannot be excluded. This feature of science > > calls for an anarchistic epistemology. The realisation that science is > > not sacrosanct, and that the debate between science and myth has > > ceased without having been won by either side, further strengthens the > > case for anarchism. > > Even the ingenious attempt of Lakatos to construct a methodology that > > (a) does not issue orders and yet (b) puts restrictions upon our > > knowledge-increasing activities, does not escape this conclusion. For > > Lakatos' philosophy appears liberal only because it is an anarchism in > > disguise. And his standards which are abstracted from modern science > > cannot be regarded as neutral arbiters in the issue between modern > > science and Aristotelian science, myth, magic, religion, etc. > > Moreover, these standards, which involve a comparison of content > > classes, are not always applicable. The content classes of certain > > theories are incomparable in the sense that none of the usual logical > > relations (inclusion, exclusion, overlap) can be said to hold between > > them. This occurs when we compare myths with science. It also occurs > > in the most advanced, most general and therefore most mythological > > parts of science itself. There is real science, upon which engineering is based. Then there is wrong science, upon which academics thrive, under the patronage of the politicians. Wrong science is far more dishonest than voodoo. > > Thus science is much closer to myth than a scientific philosophy is > > prepared to admit. Myth is wonderful, for it deals with the deepest ideas of existence. The scientist can derive inspiration from myth, especially in a cynical atheistic world. However, science has nothing to do with myth. It is one of the many forms of thought that have > > been developed by man, and not necessarily the best. It is > > conspicuous, noisy, and impudent, but it is inherently superior only > > for those who have already decided in favour of a certain ideology, or > > who have accepted it without having ever examined its advantages and > > its limits. And as the accepting and rejecting of ideologies should be > > left to the individual it follows that the separation of state and > > church must be supplemented by the separation of state and science, > > that most recent, most aggressive, and most dogmatic religious > > institution. Such a separation may be our only chance to achieve a > > humanity we are capable of, but have never fully realised. It is too bad, that the atheists have made out science to be their religion. When it is just a straightforward, honest, meticulous set of methods (experiment) and fair and balanced observation, analysis, discussion leading to the formation of correct theories for correct predictions. It is a branch on the great tree of Art... > > >http://www.marxists.org/reference/subject/philosophy/works/ge/feyerab... > > > > This is what I was taught in my engineering institute (First Year) by > > > the profs. in the Humanities Dept. IIT Kharagur was the only IIT > > > where there was a firmly established and motivated Humanities > > > department. > > > > > including the paradoxical fact that the progress > > > > of mathematics was aided by the mysticism > > > > of Russian mathematicians who accepted > > > > Cantor's set theory because it fit their > > > > mystical beliefs. > > > > Now what has maths to do with science? The Queen of Arts is > > > Mathematics, and Science pays the most humble homage to Her. > > > Many people would include mathematics as part of science. > > They used to give B.A. in maths, in the great days of maths. Science > serves maths, not the other way around, in any honest establishment. > Especially when by maths they mean statistics. > > > There is an element of mathematics that is similar to the > > arts but I would not call mathematics an art. > > I would. Mathematics is the Queen of Arts, and Philosophy is the > King. > > Aesthetic > > > considerations play a role in mathematics, but they also > > play a role in theoretical physics. > > Arts is not just about aesthetics. Arts is about art - about subtle > trickery - the means with which we differentiate ourselves from the > denizens of the wild. > > > There are no experiments > > in mathematics but the use of logical deduction sets it > > apart from the arts. The fundamental concepts of mathematics > > have a basis in experience, but the concepts have been > > abstracted. > > I think we are on different wavelengths. I depend upon maths for my > living. And the set theory you are talking about, is a daily > phenomenon for me these days, when I write SQL code. Maths is > abstract for dilettantes and those in academia maybe, but for an > engineer/computer scientist/mathematical modeller/etc. like myself, it > is very very concrete indeed. > > It is late, so I have not replied in greater detail. May do that > later. Thanks a lot for your wonderful post, as illuminating as ever. > > Cheers, and with regards, > > Arindam Banerjee
From: Michael on 22 Sep 2009 19:12
On Sep 22, 3:58 am, Bappa <adda1...(a)bigpond.com> wrote: > On Sep 21, 11:47 pm, Bappa <adda1...(a)bigpond.com> wrote: > > > > > > > On Sep 20, 11:03 pm, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > > > On Sep 20, 12:50 pm, Bappa <adda1...(a)bigpond.com> wrote: > > > > > On Sep 18, 3:42 am, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > > > > > > There is an interesting new book out about the > > > > > history of Cantor's set theory. It seems to > > > > > me that the book lends support to Feyerabend's > > > > > philosophy of science in _Against Method_. > > > > > Science can progress through *any* method, > > > > > Sorry, Marko, this is dead wrong. The only valid *method* in science > > > > is the *experimental* method - meaning, repeatability of results under > > > > controlled and same conditions. The rest is analysis and discussion. > > > > I was referring to Paul Feyerabend. He was engaged in an argument > > > with philosophers of science such as Karl Popper > > > If one cannot be a scientist, one can be a philosopher of science, > > evidently! Heh-heh. > > > > over the question > > > of whether there is one single correct Scientific Method. The argument > > > is not over the necessity of experiments in science, but other issues.. > > > Here is one summary of Feyerabend's arguments: > > > Thanks for posting this. I will go through it. > > > > Science is an essentially anarchistic enterprise: theoretical > > > anarchism is more humanitarian and more likely to encourage progress > > > than its law-and-order alternatives. > > > The scientist can be anarchic, if he is independent and not under some > > institution. Science is not anarchic. It follows extremely well-laid > > and well-defined patterns and principles. The anarchy of the > > scientist lies in his revolt against a corrupting establishment, that > > corrupts science. Like, a person like me, who has debunked Einstein's > > wrong theories, is anarchic. But I have the greatest regard for the > > scientific method - which is EXPERIMENT. Beyond the experiment, there > > is the analysis. Wrong analysis, repetition of bungles and blunders, > > lead to disaster even when the experiment is correctly done. Check > > out > > >www.users.bigpond.com/adda1234/MMInt.htm as an example, that shows > > how a correctly done experiment led to very bad and wrong and in fact > > disastrous results as a result of wrong analysis. > > > > This is shown both by an examination of historical episodes and by an > > > abstract analysis of the relation between idea and action. The only > > > principle that does not inhibit progress is: anything goes. > > > No, that is wrong. Immoral and cowardly approaches do not help in the > > least. In the long run, at least. > > > > For example, we may use hypotheses that contradict well-confirmed > > > theories and/or well-established experimental results. We may advance > > > science by proceeding counter-inductively. > > > Again, wrong. Einstein's theories were and are wrong. They were > > wrong because they were based upon a blunder, in analysing the results > > of the MM interferometry experiment. They were "proved" by the atom > > bomb apparently, but my new formula relating mass and energy shows how > > wrong they all were. Now, my formula will be proved right only when I > > make a model of an Internal Force Engine. That will be some > > experiment! Till then, my work is theoretical, and of no practical > > value - yet. > > > > The consistency condition which demands that new hypotheses agree with > > > accepted theories is unreasonable because it preserves the older > > > theory, and not the better theory. Hypotheses contradicting well- > > > confirmed theories give us evidence that cannot be obtained in any > > > other way. Proliferation of theories is beneficial for science, while > > > uniformity impairs its critical power. Uniformity also endangers the > > > free development of the individual. > > > So far so good. Yes there can be many theories, but only proper > > experiment can decide which one is the most correct at any given > > time. Till then, we live in the world of speculation. > > > > There is no idea, however ancient and absurd, that is not capable of > > > improving our knowledge. > > > Increasing knowledge is not the same as improving knowledge. > > > The whole history of thought is absorbed into > > > > science and is used for improving every single theory. Nor is > > > political interference rejected. It may be needed to overcome the > > > chauvinism of science that resists alternatives to the status quo. > > > No theory ever agrees with all the facts in its domain, > > I don't see any facts going against the theories of gravitation, > electromagnetics, atomic structure, etc. which form the core of hard > science. I see lots of facts going against the theories of relativity > and quantum and entropy. > > yet it is not > > > > always the theory that is to blame. Facts are constituted by older > > > ideologies, and a clash between facts and theories may be proof of > > > progress. > > No, it is a proof of regress. It is proof that bad theories are > winning out over good theories. It is proof that the establishment is > corrupt and forcing people to live in a world of lies. > > It is also a first step in our attempts to find the > > > > principles implicit in familiar observational notions. > > > As an example of such an attempt I examine the tower argument which > > > the Aristotelians used to refute the motion of the earth. > > Scratch any Einsteinian deep enough, and you will find an > Aristotelian. Special relativity can be correct if and only if the > Earth is standing still, so much I myself have proved beyond doubt. I > suspect that the success of Einstein has some deep (and disgustingly > wrong) theological basis. > > The argument > > > > involves natural interpretations - ideas so closely connected with > > > observations that it needs a special effort to realise their existence > > > and to determine their content. Galileo identifies the natural > > > interpretations which are inconsistent with Copernicus and replaces > > > them by others. > > Huh? Galileo found out with his telescope that Jupiter had moons. So > if Jupiter's moons could go around Jupiter, the Earth could go around > the Sun. It would then move, that is. Which was what Copernicus was > saying, as opposed to the standard Aristotelian theory that the Sun > and everything else was going around the Earth. > > The Church did not want to hear about the Earth's mobility, so they > made Galileo shut up. > > Again, this was what I learnt in my First Year in Engineering from the > Humanities Dept. We read the play "Galileo" by Brecht. > > > > The new natural interpretations constitute a new and highly abstract > > > observation language. They are introduced and concealed so that one > > > falls to notice the change that has taken place (method of anamnesis).. > > > They contain the idea of the relativity of all motion and the law of > > > circular inertia. > > Here we go again, with wrong theories like relativity and circular > inertia trying to out the right ones like gravity. Wrong observations > and wrong deductions are crucial for the success of wrong theories. > The MM interferometry experiment, with its wrong analysis, done many > times by many people, is the biggest proof of this. > > > > Initial difficulties caused by the change are defused by ad hoc > > > hypotheses, which thus turn out occasionally to have a positive > > > function; they give new theories a breathing space, and they indicate > > > the direction of future research. > > So long as folks still have wits and guts. What with idiot-box TV, > novels and permissiveness, ease of every kind, junk food and > establishmentarianism meaning safe and comfortable pensions after > retirement for all the slimy sucking-up PhuDs, the very concept of > anarchic research has long ceased to exist anywhere on the planet. > Except, maybe, in Kazakhstan, where men are ruled by men and not by > little girls. Because they have the best potassium, as we know, from > Borat. > > > > > > > > In addition to natural interpretations, Galileo also changes > > > sensations that seem to endanger Copernicus. He admits that there are > > > such sensations, he praises Copernicus for having disregarded them, he > > > claims to have removed them with the help of the telescope. However, > > > he offers no theoretical reasons why the telescope should be expected > > > to give a true picture of the sky. > > > Nor does the initial experience with the telescope provide such > > > reasons. The first telescopic observations of the sky are indistinct, > > > indeterminate, contradictory and in conflict with what everyone can > > > see with his unaided eyes. And, the only theory that could have helped > > > to separate telescopic illusions from veridical phenomena was refuted > > > by simple tests. > > > On the other hand, there are some telescopic phenomena which are > > > plainly Copernican. Galileo introduces these phenomena as independent > > > evidence for Copernicus while the situation is rather that one refuted > > > view - Copernicanism - has a certain similarity with phenomena > > > emerging from another refuted view - the idea that telescopic > > > phenomena are faithful images of the sky. Galileo prevails because of > > > his style and his clever techniques of persuasion, because he writes > > > in Italian rather than in Latin, and because he appeals to people who > > > are temperamentally opposed to the old ideas and the standards of > > > learning connected with them. > > Galileo prevailed far more over Aristotle (his orbiting moons > shattered Aristotle's crystal spheres, remember) than Copernicus till > Einstein came up with his relativistic bs; given the modern success of > the Einsteinians (aka Aristotleians) it looks like his success has had > a hopefully temporary break. I don't see how Galileo and Copernicus > were at odds. Galileo's telescope showed the moons, and later on it > was found that the movement of heavenly bodies made much more sense if > the Copernican model was followed. > > > > Such 'irrational' methods of support are needed because of the 'uneven > > > development' (Marx, Lenin) of different parts of science. > > > Copernicanism and other essential ingredients of modern science > > > survived only because reason was frequently overruled in their past. > > Reason was over-ruled only by by bigots, like those who burnt Bruno > for daring to say that the universe was infinite. Science has never > gained from bigotry. > > > > > > > > Galileo's method works in other fields as well. For example, it can be > > > used to eliminate the existing arguments against materialism, and to > > > put an end to the philosophical mind/body problem (the corresponding > > > scientific problems remain untouched, however). > > > The results obtained so far suggest abolishing the distinction between > > > a context of discovery and a context of justification and disregarding > > > the related distinction between observational terms and theoretical > > > terms. Neither distinction plays a role in scientific practice. > > > Attempts to enforce them would have disastrous consequences. > > > Finally, the discussion in Chapters 6-13 shows that Popper's version > > > of Mill's pluralism is not in agreement with scientific practice and > > > would destroy science as we know it. Given science, reason cannot be > > > universal and unreason cannot be excluded. This feature of science > > > calls for an anarchistic epistemology. The realisation that science is > > > not sacrosanct, and that the debate between science and myth has > > > ceased without having been won by either side, further strengthens the > > > case for anarchism. > > > Even the ingenious attempt of Lakatos to construct a methodology that > > > (a) does not issue orders and yet (b) puts restrictions upon our > > > knowledge-increasing activities, does not escape this conclusion. For > > > Lakatos' philosophy appears liberal only because it is an anarchism in > > > disguise. And his standards which are abstracted from modern science > > > cannot be regarded as neutral arbiters in the issue between modern > > > science and Aristotelian science, myth, magic, religion, etc. > > > Moreover, these standards, which involve a comparison of content > > > classes, are not always applicable. The content classes of certain > > > theories are incomparable in the sense that none of the usual logical > > > relations (inclusion, exclusion, overlap) can be said to hold between > > > them. This occurs when we compare myths with science. It also occurs > > > in the most advanced, most general and therefore most mythological > > > parts of science itself. > > There is real science, upon which engineering is based. Then there is > wrong science, upon which academics thrive, under the patronage of the > politicians. Wrong science is far more dishonest than voodoo. > > > > Thus science is much closer to myth than a scientific philosophy is > > > prepared to admit. > > Myth is wonderful, for it deals with the deepest ideas of existence. > The scientist can derive inspiration from myth, especially in a > cynical atheistic world. However, science has nothing to do with > myth. > > It is one of the many forms of thought that have > > > > been developed by man, and not necessarily the best. It is > > > conspicuous, noisy, and impudent, but it is inherently superior only > > > for those who have already decided in favour of a certain ideology, or > > > who have accepted it without having ever examined its advantages and > > > its limits. And as the accepting and rejecting of ideologies should be > > > left to the individual it follows that the separation of state and > > > church must be supplemented by the separation of state and science, > > > that most recent, most aggressive, and most dogmatic religious > > > institution. Such a separation may be our only chance to achieve a > > > humanity we are capable of, but have never fully realised. > > It is too bad, that the atheists have made out science to be their > religion. When it is just a straightforward, honest, meticulous set > of methods (experiment) and fair and balanced observation, analysis, > discussion leading to the formation of correct theories for correct > predictions. It is a branch on the great tree of Art... > > > > > > > >http://www.marxists.org/reference/subject/philosophy/works/ge/feyerab.... > > > > > This is what I was taught in my engineering institute (First Year) by > > > > the profs. in the Humanities Dept. IIT Kharagur was the only IIT > > > > where there was a firmly established and motivated Humanities > > > > department. > > > > > > including the paradoxical fact that the progress > > > > > of mathematics was aided by the mysticism > > > > > of Russian mathematicians who accepted > > > > > Cantor's set theory because it fit their > > > > > mystical beliefs. > > > > > Now what has maths to do with science? The Queen of Arts is > > > > Mathematics, and Science pays the most humble homage to Her. > > > > Many people would include mathematics as part of science. > > > They used to give B.A. in maths, in the great days of maths. Science > > serves maths, not the other way around, in any honest establishment. > > Especially when by maths they mean statistics. > > > > There is an element of mathematics that is similar to the > > > arts but I would not call mathematics an art. > > > I would. Mathematics is the Queen of Arts, and Philosophy is the > > King. > > > Aesthetic > > > > considerations play a role in mathematics, but they also > > > play a role in theoretical physics. > > > Arts is not just about aesthetics. Arts is about art - about subtle > > trickery - the means with which we differentiate ourselves from the > > denizens of the wild. > > > > There are no experiments > > > in mathematics but the use of logical deduction sets it > > > apart from the arts. The fundamental concepts of mathematics > > > have a basis in experience, but the concepts have been > > > abstracted. > > > I think we are on different wavelengths. I depend upon maths for my > > living. And the set theory you are talking about, is a daily > > phenomenon for me these days, when I write SQL code. Maths is > > abstract for dilettantes and those in academia maybe, but for an > > engineer/computer scientist/mathematical modeller/etc. like myself, it > > is very very concrete indeed. > > > It is late, so I have not replied in greater detail. May do that > > later. Thanks a lot for your wonderful post, as illuminating as ever.. > > > Cheers, and with regards, > > > Arindam Banerjee- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - Guts faith and goodness, but none of it matters without goodness. -- Martin Musatov |