Galileo's Paradox
in [Math]
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From: David Marcus on 9 Dec 2006 01:38 Tony Orlow wrote: > Virgil wrote: > > In article <4575b508(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Eckard Blumschein wrote:(deleted) > > > >> Now, just a minute, Eckard. You're contradicting yourself > > > > If even TO is taking EB to task, then EB must indeed be in a bad skin. > > Eckard and I are discussing things. We can disagree. It's not like > either of us agrees with a comfortable majority. so do we lose much > security in disagreeing with each other? Some of us are used to being > insecure, and yet, strong, and persisting, and surviving. I have a funny > feeling you did that, socially, during a period.... Life's like that. If there was really something wrong with mathematics, you would think that all the people who had discovered this error would agree on what it was. On the other hand, if all the people who think there is something wrong are just cranks, then there is no reason they should agree with each other. -- David Marcus
From: David Marcus on 9 Dec 2006 01:40 MoeBlee wrote: > Tony Orlow wrote: > > You might want to look into Internal Set Theory, a partial > > axiomatization of Nonstandard Analysis. > > Why do you say 'parital'? > > > Both infinitesimal and infinite > > values are "nonstandard", and no reference to "standard" values is > > allowed in the definition of any set. > > Not ANY set. IST includes standard sets too. You do realize that IST is > an EXTENSION of ZF, right? Why do you think Tony even knows what an "extension" is? -- David Marcus
From: Virgil on 9 Dec 2006 01:51 In article <MPG.1fe42308b91485ee989a0b(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Virgil wrote: > > In article <4579d1c7(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > I chose to work within computer science, after having planned to become > > > a mathematician, for the obvious reasons.... > > > > Couldn't cut it as a mathematician? > > Probably couldn't understand any of his math courses. I think TO once said that he disagreed with one of his math teachers so strongly that he decided to give up on math as a major. I suppose pat of it might have been that the teacher was a graduate assistant with a bad attitude, but I rather think that a large part of it was the student's bad attitude.
From: David Marcus on 9 Dec 2006 01:53 Tony Orlow wrote: > David Marcus wrote: > > Tony Orlow wrote: > >> Isn't the purpose of math be to quantify? > > > > No. > > What,in mathematics, has a solution which is neither a real measure, or > the measure of truth of a statement, 0, 1, or somewhere in between? > Measure=maths. You have a very limited view of what mathematics is. A better description is, Mathematics is the study of patterns. I believe Saunders MacLane presented this view in his book "Mathematics, Form and Function". You might like this book. MacLane believed set theory is not the best foundation for mathematics. -- David Marcus
From: Virgil on 9 Dec 2006 01:53
In article <MPG.1fe4233fd1946032989a0c(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Tony Orlow wrote: > > Okay, a "potential" infinite set is one where each element, like the > > naturals, has a specific string associated with it, which has a > > left-hand end. > > What do you mean "a specific string associated with it", and what is a > "left-hand end"? If TO means a string having a first character but not a last one, the set of all such is uncountable, so cannot represent a merely "potentially infinite" set. |