The Definition of Points
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From: Tony Orlow on 30 Mar 2007 13:42 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>>> It's universally meaningless in isolation. not(x) simply means >>>> "complement of x" or "1-x". You assume something else to begin with, >>>> which is not demonstrably true. >>> No I don't, Tony.I demonstrate the universal truth of "not" per se in >>> mechanically exhaustive terms through finite tautological reduction to >>> self contradictory alternatives which I take to be false to the extent >>> they're self contradictory. If you want to argue the demonstration per >>> se that's one thing but if you simply want to revisit and rehash the >>> problem per say without arguing the demonstration per se that's >>> another because it's a problem per say I have no further interest in >>> unless you can successfully argue against the demonstration per se. >>> >> not(not("not not")) >> >> "not not" is not self-contradictory-and-therefore-false. > > Well, Tony, let me ask you. If "not not" were self contradictory would > you agree with me that "not" would be true of everything inasmuch as > it would represent the tautological alternative to and the exhaustion > of all possibilities for truth between "not" and "not not"? If "not not" were demonstrated to be a statement that implied its own negation then "not not not" would have to be true, but it's only equivalent to "not" in the normal usage of "not", which doesn't make "not not" constitute a statement. > > Because I mean there are probably people out there who wouldn't agree > self contradiction is false hence tautological alternatives must be > true so I wouldn't know how to approach the demonstration of truth > with such people and if you're one such person I would see no point to > elaborating and arguing the problem further. Self-contradictory statements are false in a consistent universe. Let's assume the universe is consistent... > > However if you do agree what is not universally self contradictory is > perforce universally true then all we really have to decide is whether > "not not" the "contradiction of contradiction" the "alternative to > alternatives" "different from differences" and so on are universally > false and if so what the tautological alternatives to such phrases may > be and the exhaustive structure and mechanization of truth as well as > the demonstration of truth in universal terms would become apparent. > > ~v~~ Not being universally self-contradictory does not make a statement true. It just leaves open the possibility... 01oo
From: Tony Orlow on 30 Mar 2007 13:49 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >>> This is why science is so useful because you stop arguing isolated >>> problems to argue demonstrations instead which subsume those isolated >>> problems. There's simply no point to arguing such problems >>> individually as to whether "not" is universally true of everything or >>> whether there are such things as conjunctions not reducible to "not" >>> in mechanically exhaustive terms unless the demonstration itself is >>> defective and not true. And just claiming so per say won't cut it. >>> >> Your "not a not b" has an assumed OR in it. > > The problem is not whether it has or doesn't, Tony, but how do you > know and how can you demonstrate the truth of that claim. I mean there > is no visible indication what the relation between A and B is. You > might consider the relation between them is "or" but we have no > evidence that this conjecture is right and not just rank speculation. > I mean there are plenty of people out there who insist that relations > between any two items like A and B are theistic, deistic, or even the > product of aliens and UFO's. Please choose true or false, if you didn't do it last time: a b not a not b true true true or false? true false true or false? false true true or false? false false true or false? > > Consequently it's not my assumption of any relation between A and B > but my demonstrations of relations between them that matters. Sure I > can assume anything I want. And on previous occasions I certainly have > assumed the relation between them was a functional if not explicit or > because it seems to me the most plausible mechanical relation likely. > But that doesn't mean it's necessarily true. You need to define what relation your grammar denotes, or there is no understanding when you write things like "not a not b". > > However the fact is that given two different things A and B we can > combine them with compoundings of "not" and when we do certain > conjunctive relations between them fall out the first of which is > "and" and the next of which is "or". That's how we can tell what the > originary implications between two distinct items is and has to be. Not if you assumed OR to begin with. In that case, you're as circular as anyone else, and more. Better to build up from true() and false() as 0-place predicates. > > But that doesn't mean there is any assumption of "or" between them > only that given two distinct things like A and B we can determine any > conjunctive relations between them without the implicit assumption of > or explicit use of conjuctions. And that means conjunctions and so on > are "in here" and not "out there" among distinct things themselves. Choose true or false above, and I guarantee you'll see it's the relation OR. > > You might argue that the fact that there are distinct things like A > and B necessarily implies conjunctive "or" relations between them to > the extent of and as a function of their "distinctness". But even here > I would argue that it is really more of an artifact of their material > nature than their distinctness much as the superimposition of certain > material field properties is assumed where fields such as gravitation > and electrical potential overlap in space. If both A and B matter, then you have a 2-place predicate. If both A and B have truth values of 0 or 1, then you have 2^2=4 possible input combinations. If the output can be either 0 or 1 for each of those, you have 2^4=16 possibly 2-place logical functions. You are using one of those 16 functions, and it's commonly called OR. > > However I would still contend there is no necessary conjunction > between A and B per se. All we do is negate them concurrently and > negate the result and repeat the process to ascertain when A and B > appear in their original instead of their negated form. And that > doesn't happen until the second iteration of the process when we can > first see A and B in their assumed hypothetical original forms instead > of not A together with not B. > > You see it really doesn't matter what you assume is there.If we assume > objects A and B we first encounter not A together with not B and not > "A or B". Then we negate that original negation and the result is an > "and" of the properties of A and B rather than an "or". But repeating > the process of negation of each and negation of the result results in > an "or" of their properties rather than the previous "and" from which > we can infer the actual presence and isolated existence of A and B. > > ~v~~ Eh. Choose true or false above and we'll see. 01oo
From: Tony Orlow on 30 Mar 2007 14:02 Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Your "not a not b" has an assumed OR in it. > > Tony, let me ask you something: without an AND or any other > conjunction how would you mechanize the OR conjunction you > claim I assume? And if it's just there as a basic circumstance of > nature how do you get from there to other conjunctions and logic > especially when you consider there's no necessity for conjoined > components to be present together at the same time? > > ~v~~ Logical Mechanics 101: 0-place predicates: false() 0 true() 1 1-place predicates: x 0 1 false(x) 0 0 x 0 1 not(x) 1 0 true(x) 1 1 2-place predicates: xy 00 01 10 11 false(x,y) 0 0 0 0 and(x,y) 0 0 0 1 not(x->y) 0 0 1 0 x 0 0 1 1 not(y->x) 0 1 0 0 y 0 1 0 1 xor(x,y) 0 1 1 0 or(x,y) 0 1 1 1 not(or(x,y)) 1 0 0 0 not(xor(x,y)) 1 0 0 1 not(y) 1 0 1 0 y->x 1 0 1 1 not(x) 1 1 0 0 x->y 1 1 0 1 not(and(x,y)) 1 1 1 0 true(x,y) 1 1 1 1 :) 01oo
From: Virgil on 30 Mar 2007 14:17 In article <1175275431.897052.225580(a)y80g2000hsf.googlegroups.com>, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > On Mar 30, 9:39 am, Tony Orlow <t...(a)lightlink.com> wrote: > > > They > > introduce the von Neumann ordinals defined solely by set inclusion, > > By membership, not inclusion. By both. Every vN natural is simultaneously a member of and subset of all succeeding naturals. > > and > > yet, surreptitiously introduce the notion of order by means of this set. > > "Surreptitiously". You don't know an effing thing you're talking > about. Look at a set theory textbook (such as Suppes's 'Axiomatic Set > Theory') to see the explicit definitions. On the other hand, Tony Orlow is considerably less of an ignoramus than Lester Zick.
From: Virgil on 30 Mar 2007 14:22
In article <460d4813(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > An actually infinite sequence is one where there exist two elements, one > of which is an infinite number of elements beyond the other. Not in any standard mathematics. In standard mathematics, an infinite sequence is o more than a function whose domain is the set of naturals, no two of which are more that finitely different. The codmain of such a function need not have any particular structure at all. |