Russian Name Worshipper mystics and Cantor's set theory
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From: John Wilkins on 20 Sep 2009 06:09 In article <9bdd12fa-2b13-4860-a4e5-eebabc173da8(a)13g2000prl.googlegroups.com>, Bappa <adda1234(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. > > > 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.
From: p=np-any+p-entropy on 20 Sep 2009 04:40 > In article > <9bdd12fa-2b13-4860-a4e5-eebabc173da8(a)13g2000prl.googl > egroups.com>, > Bappa <adda1234(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. If I made an atomic nuclear warhead and it blew up the entire planet would there have been science involved in doing so? By your fallacious argument there would not be because it is not repeatable. Your argument is shot down as invalid. Utterly defeated. 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. > > > > > 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.
From: Marko Amnell on 20 Sep 2009 09:03 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: Science is an essentially anarchistic enterprise: theoretical anarchism is more humanitarian and more likely to encourage progress than its law-and-order alternatives. 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. 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. 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. There is no idea, however ancient and absurd, that is not capable of improving our 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/feyerabe.htm > > 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. There is an element of mathematics that is similar to the arts but I would not call mathematics an art. Aesthetic considerations play a role in mathematics, but they also play a role in theoretical physics. 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.
From: Marko Amnell on 20 Sep 2009 09:04 On Sep 20, 11:30 am, "gratis-_+_8_Sum_" <scribio_v...(a)mail.org> wrote: > Dear Mark Amnell, > > You are a rock star for finding this! My 31st birthday is 9/23 and I > gave this title to 1 of the 2 people I know who asked me what I wanted > for my birthday. Thank you so much for finding this. It sounds so > neat, such cool rational thought in the face of mysticism to discover > greater truth! > > Thank you, > > Martin Musatov Glad you liked the book. I ordered it myself from Amazon. Only 17 dollars, so the recession is good for something.
From: John Wilkins on 20 Sep 2009 09:08
In article <6bdccf42-3c8c-45cb-b3ab-9cf06736ccaa(a)p23g2000vbl.googlegroups.com>, Marko Amnell <marko.amnell(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 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: > > Science is an essentially anarchistic enterprise: theoretical > anarchism is more humanitarian and more likely to encourage progress > than its law-and-order alternatives. Feyerabend did not advocate, probably, anarchism. He said that if there is supposed to be a single method, it is anarchism. But he did not think that; he thought that there were a number of methods in play. .... I gave a talk on this at one point: <http://scienceblogs.com/evolvingthoughts/2007/10/how_not_to_feyerabend. php> |