The Definition of Points
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From: Tony Orlow on 30 Mar 2007 13:24 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> Add 1 n >>>> times to 0 and you get n. If n is infinite, then n is infinite. >>> This is reasoning per say instead of per se. >>> >> Pro se, even. If the first natural is 1, then the nth is n, and if there >> are n of them, there's an nth, and it's a member of the set. Just ask >> Mueckenheim. > > Pro se means for yourself and not for itself. In my own behalf, yes. I don't have much to do > with Mueckenheim because he seems more interested in special pleading > than universal truth. At least his assumptions of truth don't seem > especially better or worse than any other assumptions of truth. > > ~v~~ He has some valid points about the condition of the patient, but of course he and I have different remedies. 01oo
From: Tony Orlow on 30 Mar 2007 13:25 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> If n is >>>> infinite, so is 2^n. If you actually perform an infinite number of >>>> subdivisions, then you get actually infinitesimal subintervals. >>> And if the process is infinitesimal subdivision every interval you get >>> is infinitesimal per se because it's the result of a process of >>> infinitesimal subdivision and not because its magnitude is >>> infinitesimal as distinct from the process itself. >> It's because it's the result of an actually infinite sequence of finite >> subdivisions. > > And what pray tell is an "actually infinite sequence"? > >> One can also perform some infinite subdivision in some >> finite step or so, but that's a little too hocus-pocus to prove. In the >> meantime, we have at least potentially infinite sequences of >> subdivisions, increments, hyperdimensionalities, or whatever... > > Sounds like you're guessing again, Tony. > > ~v~~ An actually infinite sequence is one where there exist two elements, one of which is an infinite number of elements beyond the other. 01oo
From: Tony Orlow on 30 Mar 2007 13:27 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>> Just ask yourself, Tony, at what magic point do intervals become >>> infinitesimal instead of finite? Your answer should be magnitudes >>> become infintesimal when subdivision becomes infinite. >> Yes. > > Yes but that doesn't happen until intervals actually become zero. > >> But the term >>> "infinite" just means undefined and in point of fact doesn't become >>> infinite until intervals become zero in magnitude. But that never >>> happens. >> But, but, but. No, "infinite" means "greater than any finite number" and >> infinitesimal means "less than any finite number", where "less" means >> "closer to 0" and "more" means "farther from 0". > > Problem is you can't say when that is in terms of infinite bisection. > > ~v~~ Cantorians try with their lame "aleph_0". Better you get used to the fact that there is no more a smallest infinity than a smallest finite, largest finite, or smallest or largest infinitesimal. Those things simply don't exist, except as phantoms. 01oo
From: Tony Orlow on 30 Mar 2007 13:33 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>> If I don't seem particularly interested in demonstrations of universal >>> truth it's partly because you aren't doing any and I've already done >>> the only ones which can matter. It's rather like the problem of 1+1=2 >>> or the rac trisection of general angles. Once demonstrated in reduced >>> mechanically exhaustive terms the problem if not its explication and >>> implications loses interest. If you want to argue the problem itself >>> go ahead. Just don't expect me to be interested in whether 1+1=2 or >>> whether you can trisect general angles. >> You assume OR in defining AND, and then derive OR from AND, all the >> while claiming all you've done is NOT. > > Of course I do. That's specifically why I chose to specify (A B) so I > could get around the presence of conjunctions like "or" which I didn't > know were there but I'll take your word for it since you seem to know > and say what's there and what's not without having to demonstrate it > whereas I'm forced to demonstrate what I say even though you don't. So > I suppose we can just assume (A B) means there's a conjunction > involved on your per say without having to demonstrate its presence. > > ~v~~ Okay, fill in this table for me please, explaining whether (A B) is true or false in the following circumstances: A B (A B) true true true or false? true false true or false? false true true or false? false false true or false? Now, we can see what 2-place operator you're talking about. 01oo
From: Tony Orlow on 30 Mar 2007 13:37
Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> Do you not assume anything? You sure do. You assume "not" is universally >>>> true. >>> No I don't, Tony. I certainly do not assume "not" is universally true. >>> I demonstrate "not" is universally true only to the extent "not not" >>> is self contradictory and self contradiction is universally false. >>> >> So you assume "not not" is self contradictory, even though that sentence >> no verb, so it not statement. "not not" is generally taken like "--", as >> the negation of negation, and therefore taken as positive. So, that >> assumption doesn't ring true. That's the root issue with this. > > Okay, Tony. I assume that self contradiction is false and "not not" or > the "contradiction of contradiction" or the "negation of negation" is > self contradictory. I admit it. But if they are then my demonstration > stands as true and "not" "contradiction" and "negation" are true of > everything and universally so. not(true)=false. > > So now as to whether "not not" the "contradiction of contradiction" > and the "negation of negation" are self contradictory or not I can > only appeal to phrasing like the "contradiction of contradiction" to > determine whether that means self contradiction. For if contradiction > of contradiction does not mean self contradiction I'm quite at a loss > to decide what it does mean. The opposite of contradiction is consistency. > > Now I consider all three phrasings to have the same significance as > well as phrasings such as "alternative to alternatives" and "different > from differences". And if you're here trying to tell me that there are > "alternatives to tautological alternatives mechanized through not" I'd > sure as hell like to know what they are. The enumeration of the possible operators, ordered by number of parameters, from false() and true() through and(a,b) and or(a,b). not(a) is the only significant 1-place operator. > > It just doesn't matter what "not not" is "generally taken to mean" > particularly if universally true of everything since "not" would then > have a variety of uses and implications depending on how it is taken > under what circumstances. However if you're suggesting there are > alternatives to tautological alternatives mechanized through not then > don't be shy; step up to the plate and spell out for us what they are. > > ~v~~ um..... not(unicorn). Is this universally true? Is there anything for which it is false? not(not(unicorn)). I don't have anything around there that that describes.....hmmmmm 01oo |