Cantor Confusion
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From: Virgil on 1 Oct 2006 15:27 In article <1159724522.879743.47440(a)e3g2000cwe.googlegroups.com>, Han.deBruijn(a)DTO.TUDelft.NL wrote: > William Hughes schreef: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > If logic and set theory clash, abandon set theory. > > > > Indeed, but logic and set theory do not clash. > > Set theory and intuition about infinite sets > > clash. > > Then abandon _both_ (formal / mathematical) logic _and_ set theory. > > Han de Bruijn Better yet , retrain your intuition about sets, or suppress it entirely and merely follow where the logic leads.
From: Han de Bruijn on 2 Oct 2006 05:43 mueckenh(a)rz.fh-augsburg.de wrote: > This is the typical one-eyed view of a set theorist. The same we have > with Han's vase: Of course there is no ball which has not jumped out at > noon. We cannot name any such number. But the other eye should see that > there are more balls in than out at any time, including noon. The > refore set theory is useless. One cannot calculate meaningfully with > infinites! Affirmative, of course. One little side note: it's not "Han's vase". The original poster is by Theo Jacobs, who initiated a thread called "infinity": http://groups.google.nl/group/sci.math/msg/d2573fcb63cbf1f0?hl=en& Han de Bruijn
From: Han de Bruijn on 2 Oct 2006 05:47 Virgil wrote: > My logic and my set theory get along famously. Please, Virgil, show us some of your famous work. Han de Bruijn
From: William Hughes on 2 Oct 2006 07:44 William Hughes wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > William Hughes wrote: > > > > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > > William Hughes schreef: > > > > > > > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > > If logic and set theory clash, abandon set theory. > > > > > > > > > > Indeed, but logic and set theory do not clash. > > > > > Set theory and intuition about infinite sets > > > > > clash. > > > > > > > > Then abandon _both_ (formal / mathematical) logic _and_ set theory. > > > > > > We are left with intuition. Fine. Oh by the way > > > we are going to use my intuition. If you don't like > > > it, too bad. Only I can tell what my intuition is. > > > > Better read better the add-on between parentheses. > > We are left with common speech logic and no set theory. > > O.K. Call it what you want. But if you and I do not > agree on what common sense is, I am right. For example: It's common sense that you can't put more than an infinite number of balls in a vase. So if you remove an infinite number of balls there are no balls left. -William Hughes > > -William Hughes
From: Han de Bruijn on 2 Oct 2006 08:03
William Hughes wrote: > William Hughes wrote: > >>Han.deBruijn(a)DTO.TUDelft.NL wrote: >> >>>William Hughes wrote: >>> >>>>Han.deBruijn(a)DTO.TUDelft.NL wrote: >>>> >>>>>William Hughes schreef: >>>>> >>>>>>mueckenh(a)rz.fh-augsburg.de wrote: >>>>>> >>>>>>>If logic and set theory clash, abandon set theory. >>>>>> >>>>>>Indeed, but logic and set theory do not clash. >>>>>>Set theory and intuition about infinite sets >>>>>>clash. >>>>> >>>>>Then abandon _both_ (formal / mathematical) logic _and_ set theory. >>>> >>>>We are left with intuition. Fine. Oh by the way >>>>we are going to use my intuition. If you don't like >>>>it, too bad. Only I can tell what my intuition is. >>> >>>Better read better the add-on between parentheses. >>>We are left with common speech logic and no set theory. >> >>O.K. Call it what you want. But if you and I do not >>agree on what common sense is, I am right. > > For example: It's common sense that you can't put more > than an infinite number of balls in a vase. So if you remove > an infinite number of balls there are no balls left. I don't think there is any common sense about the infinite. Han de Bruijn |