The Definition of Points
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From: Lester Zick on 31 Mar 2007 20:18 On Fri, 30 Mar 2007 12:37:58 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >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 how do you know not(true) doesn't equal "whizbang". >> 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. Thanks per say. Are there any other rules we should be aware of? >> 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. Well gee that's just swell, Tony. Are there any zero place operators we should be aware of or is that pretty much it? >> 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 You might ask Brian. I'm quite confident he does. ~v~~
From: Lester Zick on 31 Mar 2007 20:22 On Fri, 30 Mar 2007 12:42:06 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >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 "To be a statement"? What makes it not 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. Oooooookay then. Moving right along to the next true or not true compounding of "not". >> 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... Mightly nice of you. Or let's not. Makes me no never mind. >> 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... No of course it doesn't, Tony. Fact is it leaves open no possibility whatsoever because every time I ask you what possibility it leaves open you say none whatsoever per say. ~v~~
From: stephen on 31 Mar 2007 20:20 In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: >> In sci.math Brian Chandler <imaginatorium(a)despammed.com> wrote: >>> stephen(a)nomail.com wrote: >>>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >>>>> If all other elements in the sequence are a finite number >>>>> of steps from the start, and w occurs directly after those, then it is >>>>> one step beyond some step which is finite, and so is at a finite step. >>>> So you think there are only a finite number of elements between 1 and >>>> w? What is that finite number? 100? 100000? 100000000000000000? >>>> 98042934810235712394872394712349123749123471923479? Which one? >> >>> None of the ones you've mentioned. Although it is, of course, a >>> perfectly ordinary natural number, in that one can add 1 to it, or >>> divide it by 2, its value is Elusive. Only Tony could actually write >>> it down. >> >> These Elusive numbers have amazing properties. According to >> Tony, there are only a finite number of finite naturals. >> There exists some finite natural Q such that the set >> { 1,2,3,4,.... Q} >> is the set of all finite natural numbers. But what of Q+1? >> Well we have a couple of options: >> a) Q+1 does not exist >> b) Q+1 is not a finite natural number >> c) { 1,2,3,4, ... Q} is not the set of all finite natural numbers >> >> Tony rejects all these options, and apparently has some fourth >> Elusive option. >> >> Stephen >> > Oy. The "elusive" option is that there is no acceptable "size" for N. None of the options mention "size" Tony. What does "size" have to do with a, b or c? > That was really hard to figure out after all this time... Have you finally figured it out then? I somehow doubt it. As you have been repeatedly told, for years now, "size" is not a term used in set theory. So Tony, yes or no, does there does exist a finite natural Q such that {1, 2, 3, ... Q } is the set of all finite naturals? Stephen
From: Tony Orlow on 31 Mar 2007 20:25 stephen(a)nomail.com wrote: > In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> stephen(a)nomail.com wrote: >>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >>>> stephen(a)nomail.com wrote: >>> So in other words >>>>>>>>> An actually infinite sequence is one where there exist two elements, one >>>>>>>>> of which is an infinite number of elements beyond the other. >>> is not your "correct" definition of an "actually infinite sequence", >>> which was my point. You are so sloppy in your word usage that you >>> constantly contradict yourself. >>> >>> If all you mean by "actually infinite" is "uncountable", then >>> just say "uncountable". Of course an "uncountable sequence" >>> is a contradiction, so you still have to define what you mean >>> by a "sequence". >>> >>> > >> Please do expliculate what the contradiction is in an uncountable >> sequence. What is true and false as a result of that concept? > > A infinite sequence containing elements from some set S is a function > f: N->S. There are only countably infinite many elements in N, > so there can be only countably infinite many elements in a sequence. > If you want to have an uncountable sequence, you need to provide > a definition of sequence that allows for such a thing, and until > you do, your use of the word "sequence" is meaningless, as nobody > will know what you are talking about. > Oh. What word shall I use? Supersequence? Is that related to a subsequence or consequence? >>>>>> If all other elements in the sequence are a finite number >>>>>> of steps from the start, and w occurs directly after those, then it is >>>>>> one step beyond some step which is finite, and so is at a finite step. >>>>> So you think there are only a finite number of elements between 1 and >>>>> w? What is that finite number? 100? 100000? 100000000000000000? >>>>> 98042934810235712394872394712349123749123471923479? Which one? >>>>> >>>> Aleph_0, which is provably a member of the set, if it's the size of the >>>> set. Of course, then, adding w to the set's a little redundant, eh? >>> Aleph_0 is not a finite number. Care to try again? >>> > >> It's also not the size of the set. Wake up. > > It is the cardinality of a set. Is that a number? There is no standard definition > of "size", as you have been told countless times for a couple > of years now. Size is an ambiguous word in any situation, and > there is no argument in set theory that depends on the word "size". > > Oh ambiguous... >>>>> It should be obvious that the number of elements between 1 and w is >>>>> larger than any finite natural number. Let X be a finite >>>>> natural number > 1. Then {2, 3, .. X, X+1, .. 2X } is a subset >>>>> of the elements between 1 and w that has more more than X elements. >>>>> >>>>> As I said, even you do not accept your own definition of "actually >>>>> infinite". >>>>> >>>>> Stephen >>>>> >>>> If you paid attention, the apparent contradiction would evaporate. The >>>> number of elements up to and including any finite element of N is >>>> finite, and equal to that element in magnitude. If the number is n, then >>>> there's an nth, and its value is n. As Ross like to say, NeN. We are not >>>> alone. :D >>>> Tony >>> But the question is not about the number of elements up and including >>> any finite element of N. I asked how many elements are between 1 and w >>> in the set {1, 2, 3, ..., w }. > >> w-2 are between w and 1. x-2 are between 1 and x. > > What is w-2? Remember, I am talking about the standard definition > of w. The set I am talking about does not contain a w-2. It > contains all the finite elements of N, and the element w. > How convenient. You can't move left from w. Well, that simplifies your dance, now, doesn't it? >> w is not an element of N, nor is it finite. > >> Oh, then why mention it? > > Is there some rule saying that we can only mention finite elements, > or elements of N? I can describe all sorts of sets such as > N U { 1/2 }, or N U { w } or N U { {1, 2}, {2, 3}, {3, 4} ... }. > Describe away - just don't expect it to prove anything if it's not pertinent. > The reason I mentioned it is because the set {1, 2, 3, ... w } > has the property that there exist two elements between which > there is an infinite number of elements, namely 1 and w. I know > that you do not consider {1, 2, 3, ... , w} an actually > infinite set, so I brought this up as an example of the fact > that even you do not agree with your own statement, which was: > >>> An actually infinite sequence is one where there exist two elements, one >>> of which is an infinite number of elements beyond the other. Prove to me, logically, that there exist more than any finite number of elements between 1 and w. > > And of course that was my whole point. Despite the fact that > you posted that as a definition of an actually infinite sequence, > even you do not think it is the definition of an actually infinite > sequence. > I do not think your example qualifies, logically. Sorry. >>> I know you are incapable of actually thinking about all the elements of N, >>> but that is your problem. In any case, N is not an element of N. >>> Citing Ross as support is practically an admission that you are wrong. >>> >>> Stephen >>> > >> Sure, of course, agreeing with someone who disagrees with you makes me >> wrong. I'll keep that in mind. Thanks.. > >> Tony > > No, agreeing with someone who makes absolutely no sense, such as > Ross, is tantamount to admitting you are wrong. Whether Ross makes any sense or not is a personal judgment, based on whether what he says jibes with anything one may or may not think. Some of what he says jibes for me. So Ross doesn't make no sense, from where I sit, even if he doesn't have a system that I completely grok. His is not incompatible with mine. Of course you > do seem to have caught on to the fact that Lester is full of nothing > but nonsense, so maybe there is hope for you yet. I see that Lester doesn't get the "establishment" position on logic, and I'd like to help. I don't think all his points are simply lines... ;) > > If you think Ross makes sense, explain his null axiom theory. > > Stephen > > > > I don't understand a theory without axioms, but I do understand the sentiment, and it's not dissimilar to Lester's. It's all about getting to the roots of the Tree of Knowledge, without undue assumptions. It's a worthy endeavor, even if fraught with entanglement and personal woe. The problem is, there's always two roots to every sprout...so let's all get used to it. Tony
From: Lester Zick on 31 Mar 2007 20:30
On Fri, 30 Mar 2007 12:49:54 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >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? Kinda hard to tell what these terms mean, Tony? Are there clues or do we just wing it? >> 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". Of course not. I didn't intend for my grammar to denote anything in particular much as Brian and mathematikers don't intend to do much more than speak in tongues while they're awaiting the second coming. >> 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. Of Christ. Don't you and the zero place predicates wait up for us. >> 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. Of course it is, Tony. I just tried to slip one over on you. OR Brian OR Virgil OR Stephen OR PD OR David Or Mikey Or someone else without saying so. ~v~~ |