The Definition of Points
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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
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 |