An uncountable countable set
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From: Virgil on 28 Sep 2006 13:09 In article <2e658$451b78ef$82a1e228$7519(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Tony Orlow wrote: > > > MoeBlee wrote: > > > >> Tony Orlow wrote: > >> > >>> Constructivism and Axiomatism are two sides of a coin. They can be > >>> reconciled in larger framework, I think. > >> > >> I don't know what your definition of 'axiomatism' is, but there are > >> axiomatic systems for constructive mathematics. > > > > I dunno. I was responding to Han's comment. I think he means > > constructive concepts vs. axiomatic declarations. > > It's a priorities issue. Do axioms have to dictate what constructivism > should be like? Should constructivism be tailored to the objectives of > axiomatics? I think not. > > Han de Bruijn But if you cannot clearly state what you are assuming/accepting as true, all you have is a morass of ambiguity.
From: Virgil on 28 Sep 2006 13:12 In article <cddac$451b7c18$82a1e228$8598(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <c43c$451a2703$82a1e228$4034(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>Virgil wrote: > >> > >>>In article <6e5c2$4518da26$82a1e228$6365(a)news1.tudelft.nl>, > >>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>> > >>>>Tony Orlow wrote: > >>>> > >>>>>Math=Science? > >>>> > >>>>Definitely, yes! > >>> > >>>Only if science is a subset of mathematics. > >> > >>Science is not a subset of mathematics. Neither is mathematics a subset > >>of science nowadays. If 1 = yes and 0 = no : > >> > >>mathematics | science | result > >>------------------------------ > >> 0 0 having a chat > >> 0 1 soft sciences > >> 1 0 nonsense maths > >> 1 1 exact sciences > > > > Correction: > > mathematics | science | result > > ---------------------------------------------- > > 0 0 having a chat > > 0 1 nonsense sciences > > 1 0 not yet applied maths > > 1 1 exact sciences > > OK. We are getting somewhere. So you believe that science without maths > is nonsense ? I am merely countering your nonsense that math without science is nonsense. According to history, and what can be deduced of prehistory, there was a good deal of math, at least arithmetic, around long before there was any science at all.
From: Virgil on 28 Sep 2006 13:16 In article <9fd0$451b7e7b$82a1e228$8977(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <451a8f41(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > >>For purposes of measure on the finite scale, infinitesimals can be > >>considered nilpotent. That's all. Do you disagree? > > > > I disagree that scale changes can convert between zero and non-zero. > > > > There are approximation methods is which products of small quantities > > are regarded as negligible in comparison to the quantities themselves, > > but they are always just approximations. > > Crucial question: are those "approximation methods" part of mathematics? > I'll take Yes or No as a sufficient answer. They are a part of the applications of mathematics to things other than mathematics, so they are marginal.
From: Virgil on 28 Sep 2006 13:19 In article <af46f$451b7f3e$82a1e228$9075(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Tony Orlow wrote: > > > Psychology (and I've studied it a bit) is only a science to the extent > > that it employs analysis. Most cognitive science uses at least > > statistics in order to establish any kind of certainty in its findings. > > I don't consider Freudian Analysis to be science. Do you? > > Why not? Does Freudian Analysis lead to a technology in a medical sense: > does it help to cure people from a mental disease? If the answer is yes, > then IMHO Freudian Analysis may be considered as a science. > > Han de Bruijn I find myself argeeing with Han on the issue as a whole, though I am somewhat doubtful of the efficacy of Freudian analysis.
From: Virgil on 28 Sep 2006 13:25
In article <2338c$451b828d$82a1e228$10092(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <451ad7e9(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > >> > >>Psychology (and I've studied it a bit) is only a science to the extent > >>that it employs analysis. > > > > That depends on your definition of 'a science'. There is nothing in my > > definition of 'a science' that requires mathematics (or that bars it > > either). > > How is this consistent with the second row in the following table, > which is from one of your previous posts in the same thread: > > > mathematics | science | result > > ---------------------------------------------- > > 0 0 having a chat > > 0 1 nonsense sciences ( !! ) > > 1 0 not yet applied maths > > 1 1 exact sciences > > Han de Bruijn It was merely a parody of your own parody. I am quite wiling to accept that there are sciences to which the need for mathematics is largely, if not completely, incidental. |