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Пишет flaass (![[info]](http://lj.rossia.org/img/userinfo.gif){kind=small} flaass)@ 2002-12-23 20:45:00 |
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Saharon Shelah
Дал ссылку на Шелаха, но неспециалисты могут испугаться... скину-ка несколько забавных цитаток оттуда.
Judah has asked me to speak on the future of set theory. It seems I am not particularly suitable for such a lecture, as I have repeatedly preferred to try to prove another theorem than to prepare the lecture (or article); so why did I agree at all to such a doubtful endeavor? Well, under the hypothesis that I had some moral obligation to help Haim in the conference (and the proceedings) and you should not let a friend down, had I been given the choice to help with organizing the dormitories, writing a lengthy well written expository paper or risking making fool of myself in such a lecture, I definitely prefer the latter.
My feeling, in an overstated form, is that beauty is for eternity, while philosophical value follows fashion.
A disgusted reader may shout: ``Beauty? You found in your mess some trace of beauty?'' I can only say that I hear the music of those spheres or that every one likes his own dirt (the difference is small).
My feeling is that ZFC exhausts our intuition except for things like consistency statements.
Maybe the following analogy will explain my attitude; we use the standard American ethnic prejudice and status system, as it is generally familiar. So a typical universe of set theory is the parallel of Mr. John Smith, the typical American; my typical universe is quite interesting (even pluralistic), it has long intervals where GCH holds, but others in which it is violated badly, ... and it may have lots of measurables, with a huge cardinal being a marginal case but certainly no supercompact. This seems not less justifiable than stating that Mr. John Smith grew up in
upstate New York, got his higher education in California, dropped out from college in his third year, lived in suburbia in the Midwest, is largely of anglo-saxon stock with some Irish or Italian grandfather and a shade of hispanic or black blood, with a wife living separately and 2.4 children.
... neither could Mr. Smith have 2.4 children, and still the mythical ``normal'' American citizen is in a suitable sense a very real one. In this light, L [конструктивный универсум Геделя] looks like the head of a gay chapter of the Klu Klux Klan - a case worthy of study, but probably not
representative.
``Does this mean you are a formalist in spite of earlier indications that you are Platonist?'' I am in my heart a card-carrying Platonist seeing before my eyes the universe of sets, but I cannot discard the independence phenomena.
Дал ссылку на Шелаха, но неспециалисты могут испугаться... скину-ка несколько забавных цитаток оттуда.
Judah has asked me to speak on the future of set theory. It seems I am not particularly suitable for such a lecture, as I have repeatedly preferred to try to prove another theorem than to prepare the lecture (or article); so why did I agree at all to such a doubtful endeavor? Well, under the hypothesis that I had some moral obligation to help Haim in the conference (and the proceedings) and you should not let a friend down, had I been given the choice to help with organizing the dormitories, writing a lengthy well written expository paper or risking making fool of myself in such a lecture, I definitely prefer the latter.
My feeling, in an overstated form, is that beauty is for eternity, while philosophical value follows fashion.
A disgusted reader may shout: ``Beauty? You found in your mess some trace of beauty?'' I can only say that I hear the music of those spheres or that every one likes his own dirt (the difference is small).
My feeling is that ZFC exhausts our intuition except for things like consistency statements.
Maybe the following analogy will explain my attitude; we use the standard American ethnic prejudice and status system, as it is generally familiar. So a typical universe of set theory is the parallel of Mr. John Smith, the typical American; my typical universe is quite interesting (even pluralistic), it has long intervals where GCH holds, but others in which it is violated badly, ... and it may have lots of measurables, with a huge cardinal being a marginal case but certainly no supercompact. This seems not less justifiable than stating that Mr. John Smith grew up in
upstate New York, got his higher education in California, dropped out from college in his third year, lived in suburbia in the Midwest, is largely of anglo-saxon stock with some Irish or Italian grandfather and a shade of hispanic or black blood, with a wife living separately and 2.4 children.
... neither could Mr. Smith have 2.4 children, and still the mythical ``normal'' American citizen is in a suitable sense a very real one. In this light, L [конструктивный универсум Геделя] looks like the head of a gay chapter of the Klu Klux Klan - a case worthy of study, but probably not
representative.
``Does this mean you are a formalist in spite of earlier indications that you are Platonist?'' I am in my heart a card-carrying Platonist seeing before my eyes the universe of sets, but I cannot discard the independence phenomena.
