The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: Lester Zick on 16 Mar 2007 19:53 On Thu, 15 Mar 2007 20:01:32 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Eric Gisse wrote: > >> On Mar 15, 2:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> [...] >> >> What is your background in mathematics, Lester? > >You have asked: "what is the empty set". And "Bob" is the answer. ~v~~
From: Lester Zick on 16 Mar 2007 19:54 On 15 Mar 2007 16:01:25 -0700, "Eric Gisse" <jowr.pi(a)gmail.com> wrote: >On Mar 15, 2:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > >[...] > >What is your background in mathematics, Lester? 1, 2, 3, that's all we happen to be . . . ~v~~
From: Lester Zick on 16 Mar 2007 21:02 On Fri, 16 Mar 2007 13:41:43 -0700, Bob Cain <arcane(a)arcanemethods.com> wrote: >Lester Zick wrote: > >> The technique of unambiguous definition and the definition of truth is >> simply to show that all possible alternative are false. Empirics and >> mathematikers generally prefer to base their definitions on >> undemonstrable axiomatic assumptions of truth whereas I prefer to base >> definitions of truth on finite mechanical tautological reduction to >> self contradictory alternatives. The former technique is a practice in >> mystical insight while the latter entails exhaustive analysis and >> reduction in purely mechanical terms. > >Can you provide a useful physical example of the latter? Hell, even a >useless one would be better than what you've provided so far. "Useful"? "Physical"? Don't know what you mean. Now if you'd just asked for a "true" example it would be a different matter. >What won't suffice is any example that defies consensus understanding. "You" being the consensus? Oh I can hardly wait. > If you provide a symbol string that only you can "understand" it >won't satisfy the challenge because it has no practical value. Are there any other rules you have in mind to determine the practicality of what you demand of me? C'mon now, stringellow, don't be shy. Last time I asked how to mechanize angular momentum as I recall you suggested a piece of string. Not very scientific but very practical.How about a piece of string for a useful, physical, example? ~v~~
From: Lester Zick on 16 Mar 2007 21:04 On 16 Mar 2007 10:48:47 -0700, "ken.quirici(a)excite.com" <ken.quirici(a)excite.com> wrote: >On Mar 13, 1:52 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> The Definition of Points >> ~v~~ >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> ~v~~ > >My impression is that Euclid defined a line, not in terms of points, >and never claimed a line was made up of points, but defined a line as >a geometrical object that has only the property of extensibility >(length, >where length can be infinite). > >He uses points in his proofs specifically as intersections of lines, >if I >remember correctly, and makes no attempt at describing or >explaining their density in a line. (You gotta lot of 'splainin to do, >Euclid!). Yeah, wherever did modern math get its quaint notions? No doubt somewhere along the way. Which way of course remains an issue of historical investigation. ~v~~
From: SucMucPaProlij on 17 Mar 2007 07:19
> > And I think you're making a little too much out of nominal circular > regressions. All you really have to do to define definition is prove > it satisfies it own definition. > 1) Definition for definition: "Definition is anything" 2) All you really have to do to define definition is to prove it satisfies its own definition. "Definition is anything" satisfies itself (it masturbates). Did I miss something? Second attempt 1) Definition is sentence that is always true. 2) Is sentence "Definition is sentence that is always true" always true? For mathematikers definition is sentence that is always true but there are other sentences that are always true ("two is more that one", "it is better to live 100 years as a rich man that one day as a poor woman") and you can hardly called them definitions. What will happened if I define definition as something that is not always true? It changes math altogether. If definition is not always true you can't use definition for point to tell if something is point. Mathematikers are strange liberals. They even give you right to destroy everything they believe in :)))) |