The Definition of Points
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From: Lester Zick on 31 Mar 2007 20:13 On Fri, 30 Mar 2007 12:33:00 -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: >> >>>> 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: What table, Tony? What true false? >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. What two place operator, Tony? Would you care to define any of these terms before talking about them or should we try to talk about them before defining them? I don't mind talking about tables, true, false, two place operators, etc. before defining them but then I insist on my definitions intead of yours. Of course I can't tell exactly what my definitions might be until I define them in preference to yours. But that doesn't really matter since they're my definitions to begin with. ~v~~
From: Tony Orlow on 31 Mar 2007 20:14 Virgil wrote: > In article <460ee48e(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > >> Why? What have I defined, if not a sequence? Is there a word for it? It >> must "exist", if I assert so. > > Does TO now claim the right of God to make things exist by His command? > > I understand that God is a jealous God, and takes such usurpations in > very bad part. I claim equal right to use existential instantiation. Tony
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 |