The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: Tony Orlow on 30 Mar 2007 13:00 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>>> Whatever. Is a point really nothing? Is a zero really nothing? Who >>>>> cares. If you want to fudge things why not just say 1 is zero? Then we >>>>> can all stop worrying about it one way or the other and go home. >>>>> >>>> That would cause inconsistencies. :) >>> And 00*0=1 wouldn't cause inconsistencies? >>> >> I*i=1 doesn't. Well, as long as you know it's not the imaginary i.... > > Well that's only one potential inconsistency. You still haven't shown > why 00*0=1 and not some other finite. It looks to me like you're just > trying to axiatomize zero and points without being able to show why > infinitesimal bisective subdivision could never reach and surpass such > atomic points without reaching zero. > > ~v~~ I would assert that a number, I, exists which is greater than any finite number, and justify that axiom by considering the interval [0,1), where 0<1, and for x, y and z in [0,1), x<z -> Ey x<y ^ y<z. If there is a measurable interval, and any measurable interval can be divided into two measurable intervals by defining an additional point between the endpoints, then this process of defining additional points in the interval never ends. The number of individual points in the interval can be said to be greater than any finite number, because any finite number n, producing 2^n-1 intermediate points, still leaves points between those unincluded. So, we say that some infinite number of points exists in [0,1), called I, and that each point therefore occupies 1/I=i space on that line, an infinitesimal. 01oo
From: Tony Orlow on 30 Mar 2007 13:04 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>>> Okay, Tony. You've made it clear you don't care what anyone thinks as >>>>> long as it suits your druthers and philosophical perspective on math. >>>>> >>>> Which is so completely different from you, of course... >>> Difference is that I demonstrate the truth of what I'm talking about >>> in mechanically reduced exhaustive terms whereas what you talk about >>> is just speculative. >> You speculate that it's agreed that not is the universal truth. It's not. > > No I don't, Tony. It really is irritating that despite having read > E201 and E401 you call what I've done in those root threads > "speculation". What makes you think it's speculation? I mean if you > didn't understand what I wrote or how it demonstrates what I say then > I'd be happy to revisit the issue. However not questioning the > demonstration and still insisting it's speculation and no different > from what you say is just not okay. I've questioned that assumption all along. We've spoken about it plenty. > > I don't speculate "it's agreed" or not. I don't really care whether > it's agreed or not and as a practical matter at this juncture I'd have > to say it's much more likely not agreed than agreed. What matters is > whether it's demonstrated and if not why not and not whether it's > agreed or not since agreements and demonstrations of truth are not the > same at all. Agreements require comprehension and comprehension > requires study and time whereas demonstrations of truth only require > logic whether or not there is comprehension. > > ~v~~ Demonstrate what the rules are for producing a valid one of your logical statements from one or more other valid ones of your logical statements, because "not not" and "not a not b" are not standard valid logic statements with known rules of manipulation. What are the mechanics? As far as I can tell, the first is not(not(true))=true and the second is or(not(a),not(b)), or, not(and(a,b)). 01oo
From: Tony Orlow on 30 Mar 2007 13:06 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> You might be surprised at how it relates to science. Where does mass >>>> come from, anyway? >>> Not from number rings and real number lines that's for sure. >>> >> Are you sure? > > Yes. > >> What thoughts have you given to cyclical processes? > > Plenty. Everything in physical nature represents cyclical processes. > So what? What difference does that make? We can describe cyclical > processes quite adequately without assuming there is a real number > line or number rings. In fact we can describe cyclical processes even > if there is no real number line and number ring. They're irrelevant. > > ~v~~ Oh. What causes them? 01oo
From: Tony Orlow on 30 Mar 2007 13:07 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> Those aren't geometrical expressions of addition, but iterative >>>> operations expressed linguistically. >>> Which means what exactly, that they aren't arithmetic axioms forming >>> the foundation of modern math? The whole problem is that they don't >>> produce straight lines or colinear straight line segments as claimed. > >> Uh, yeah, 'cause they're not expressed gemoetrically. > > Well yes. However until you can show geometric expression are point > discontinuous I don't see much chance geometric expression will help > your case any. > > ~v~~ What does point discontinuity in geometry have to do with anything I've said? 01oo
From: Tony Orlow on 30 Mar 2007 13:08
Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> So, start with the straight line: >>> How? By assumption? As far as I know the only way to produce straight >>> lines is through Newton's method of drawing tangents to curves. That >>> means we start with curves and derivatives not straight lines.And that >>> means we start with curved surfaces and intersections between them. >>> >> Take long string and tie to two sticks, tight. > > Which doesn't produce straight line segments. > > ~v~~ Yeah huh 01oo |