Am I a crank?
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From: MoeBlee on 30 Aug 2006 15:46 Virgil wrote: > Axioms are not at all definitions, nor are definitions axioms. One very common approach is that definitions in a theory are definitional axioms. They are axioms since they are not derivable from the other axioms of the theory. But if they satisfy the criteria of eliminability and non-creativity, then they are unlike non-definitional axioms in that sense. MoeBlee
From: Lester Zick on 30 Aug 2006 17:20 On 30 Aug 2006 01:02:23 -0700, schoenfeld.one(a)gmail.com wrote: > >Han de Bruijn wrote: >> schoenfeld.one(a)gmail.com wrote: >> >> > Han de Bruijn wrote: >> > >> >>Jesse F. Hughes wrote: >> >> >> >>>*Fortunately* mathematics is not an experimental science. >> >> >> >>Not true. Part of modern mathematics _is_ an experimental science. >> >>In very much the same way as physics is: theory as well as experiment. >> >>Or would you like to say that structural (numerical) analysis is not >> >>a form of mathematics? And how about computing a large prime number? >> >> >> >>Welcome to the 21th century! >> > >> > Wouldn't that be computer science? >> >> Is a simple calculation by hand (like 1 + 1 = 2) "computer science" ? > >No. > >> Or is it just mathematics? In the latter case, computing a large prime >> is also mathematics, because it could be done - in principle - by hand. >> (What else does computer science add except more speed and more space.) > >Then there is no experiementation. Mathematics is not an experimental >science, it is not even a science. The principle of falsifiability does >not apply. It does to axioms. ~v~~
From: Lester Zick on 30 Aug 2006 18:34 On Wed, 30 Aug 2006 13:38:10 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <c0kbf2d68q0iembtij08v9763k92e59fmt(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Wed, 30 Aug 2006 09:10:10 +0200, Han de Bruijn >> <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >> >> >Lester Zick wrote: >> > >> >> Actually an interesting prespective. Certainly mathematical axioms if >> >> not theorems are empirically established. >> > >> >Axioms are implicit definitions. > >Axioms are not at all definitions, nor are definitions axioms. Yeah, yeah, read what I wrote. >Axioms are declarative, definitions imperative. Which just means axiomites issue declarations and make fine emperors. >> Which are empirically established and not demonstrated. > >Lets see you *empirically establish* the axiom of infinity as given in Or let's see you not empirically establish it. > http://en.wikipedia.org/wiki/Axiom_of_Infinity > >Some of the other axioms/axiom_schemas of ZF are equally impossible to >establish empirically. Which at best just means they're problematic. ~v~~
From: Lester Zick on 30 Aug 2006 18:36 On 30 Aug 2006 12:46:06 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Virgil wrote: >> Axioms are not at all definitions, nor are definitions axioms. > >One very common approach is that definitions in a theory are >definitional axioms. They are axioms since they are not derivable from >the other axioms of the theory. But if they satisfy the criteria of >eliminability and non-creativity, then they are unlike non-definitional >axioms in that sense. Or as I believe I've already commented what mathematikers can prove true of axiomatic assumptions they call theorems and what they can't they call definitions. ~v~~
From: Lester Zick on 30 Aug 2006 18:37
On Wed, 30 Aug 2006 13:43:02 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <r7kbf2tlc70iqjm2rp4ktprl1o3uui79jf(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > > >> >Hello Crackpot. >> >> Crackpot=disagreer. Quite mathematical. > >Crackpots are those who disagree not only without supporting evidence >but despite contrary evidence. > >Like Zick. Like exactly what contrary evidence do you mean, sport? Your opinions and assumptions of what's true and false? Or in your case I guess I should say your opinion of what's not true and not false? ~v~~ |