The Definition of Points
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From: Lester Zick on 29 Mar 2007 18:21 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>> Bijections have their applications. I just don't think bijection alone >>> is all that significant for infinite sets. The actual mapping function >>> describes the relationship between infinite sets. >> >> Well if you mean "matching" don't say "bijection". I don't have any >> use for people whose only purpose in math is terminological regression >> and the creation of buzzwords instead of mechanical reduction. First >> they say they can't use generic language because it isn't sufficiently >> precise then they turn right around and corrupt the usage of perfectly >> acceptable generic words such as "cardinality" on the same basis. Such >> "mathematikers" are just speaking in tongues. They don't understand >> what truth is so they just proclaim whatever they say is mathematical >> truth because the domain of their discussion is supposed to be truth. >> > >It's the proper and commonly used term. "Matching" is more colloquial >and not well defined. A bijection between sets is a relation where each >element of each set corresponds to a unique element of the other set. >The mapping function is this relation, and a function from x to y can be >inverted to form a function from y to x. Where the function is expressed >as a formula, that formula characterizes the relative sizes of the sets. >The only restriction with this approach is that the bijection must be in >quantitative order for both sets. That's nice, Tony. Doesn't have much to do with my observation but I'm quite confident it'll get you a few rungs higher in mathematical hell. ~v~~
From: Lester Zick on 29 Mar 2007 18:28 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>> You don't really seem interested in demonstrations of truth, are you? >> >> What demonstrations of truth did you have in mind exactly, Tony? All >> I've seen so far are your ideas of truth per say and not per se.When I >> demonstrate truth the demonstration is per se by exhaustive mechanical >> reduction and not simply per say according to what seems plausible to >> me or anyone else just because I say so. What I don't seem interested >> in at the moment are more philosophical tracts when I've already shown >> the demonstration of universal truth by finite tautological reduction >> to self contradictory alternatives whereas all you've demonstrated is >> philosophical preferences for some variety of ideas apart form others. >> > >It would help if you could define a predicate, or mechanically >demonstrate how "not" is universally true, instead of just axiomatically >assuming it and subsequently deriving the fact through circular logic, Gee. You coulda fooled me. Thought I'd done exactly that. Perhaps you could show me where I just axiomatically assumed the universal truth of "not" in E201 and E401 without any kind of demonstration? >without even defining what "truth" means to begin with. If you want to >deal mathematically with logic, why don't you start by listing all the >possible states a statement can have with respect to "truth"? Can it be >true? Can it be false? Is there something in between? Well when you axiomatically assume assumptions of truth I guess there can be true, false, and everywhere in between, maybe truer and falser would be appropriate. But when you have to demonstrate truth without just assuming it the problem gets a little difficulter. ~v~~
From: Lester Zick on 29 Mar 2007 18:33 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~~
From: Lester Zick on 29 Mar 2007 18:35 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >> What you're trying to do is argue the problem and not its resolution >> or my demonstration of the universal truth of the problem. And I just >> don't care what you think about the problem of universal truth when >> you refuse to discuss any demonstration of the problem of universal >> truth or my demonstration of universal truth in mechanically reduced >> exhaustive terms. >> >> What difference can your opinions on the subject possibly make? I >> argue A and you come right back and say A can't possibly be true >> because you like B. You can't even say whether A and B are really >> different. All you say is that you like binary logic and conjunctions. >> Well I like them too. I just say that they're specialized instances of >> universal truth demonstrated through finite tautological regression to >> self contradictory alternatives and so far you have yet to adduce any >> arguments to the contrary much less any demonstration to the contrary. >> >> So I suppose the short answer is no I don't really seem to care about >> problems I've already solved. >Alright. Take your basic assumptions and build something useful, or >derive a new, or old, result from them. Gee that's swell, Tony. Thanks for nothing. ~v~~
From: Lester Zick on 29 Mar 2007 18:55
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. 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. 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. 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~~ |