Sets/Classes, and the state of modern philosophy (was Re: Rob Zook Wed, 14 Jan 1998 14:52:46 -0600 At 01:18 PM 1/13/98 -0600, Saul Epstein wrote: >>>Oh! That I didn't know. I mean, how often does anyone bother to >>>define a set of things that have nothing in common? >> >>Not, "nothing in common", but not necessarily similar. For example, the >>set of all things in the trash can. Most of the things in my trash can >>have no similarity to each other, but they do have one thing in common - >>location inside the same container. > >So am I understanding correctly that what matters is what "owns" the >similarity? Objects with similar locations may constitute a set on that >basis, but if the objects THEMSELVES aren't similar, they can't constitute a >class? Well, English does not define it's words explicitly and specifically enough for me to know how to answer that. I think of a set as a collection of objects, irregardless of what else they may have in common. If I want to emphasis, that they do have qualities associate with some classification in some classification scheme, I use the word class. A set can include a number of elements with similar qualities or not. A class refers specifically to a number of elements with similar qualitities. Using them interchangable would seem to loose that distinction and we have those two words to make this distinction. They operate at different levels of abstraction. >>>That's what I meant. ("different relationships _between sets_") So >>>"Some Vulcans are male" notes an intersection of the set "Vulcans" >>>and the set "Male things." >> >>But that's a slightly different distinction. I mean it's one >>assumption, behind the phrase, but interprating it as only meaning >>that looses the other connotation of class - elements possessing >>similar qualities. > >This potentially confuses me again. Location seems to me to be a >property, so that objects whose locations are similar could, according >to this, constitute a class of similarly located objects. Do objects in >a class have to be similar in all their properties? AACKK!! Location a property? Uhhh..,I'm going to forget you wrote that. Essentially, the contents of the set are irrelavent beside the fact that someone has arbitratily decided to put them in a set. I could just as easily say some set contained everyting existing in the past, now, in the future plus all those things in every single being in the universe's fantasies. Another example may help. I could say the set A consists of "1", "A", "*", an apple, my brother Ryan, the sweet scent of a rose, and the sound of one hand clapping. A set simple refers to _any_ arbitrary grouping of some elements. A class refers to a grouping of some elements based on some arbitrary distinction between having some quality and not having that qualitity, i,e. some classification scheme, or method of catagorization. One can call a class of things the set of all things belonging to the class. One could say the class of all similarily groupped things in a set. But "set" does NOT EQUAL "class". >>>> >Then there are no entities. >>>> >>>> I don't understand, how that follows. I was trying to make a >>>> distinction between words for things, and das ding an sich. >>>> An entity is a word, which describes something at the most >>>> abstract level possible. And so it represents an abstraction >>>> we have created of some thing. A purely mental abstraction. >>> >>>What I meant to suggest was this question. What is a thing with no >>>qualities? It isn't. >> >>That seems like a nice strange loop too. > >I'm just curious to know if it's your understanding that an undefined >thing can exist. Exist how? <*> can never be defined. So yes. But we can never interact with <*>, only bits we seperate out by arbitrarily comparing them to other bits. So, no. >>>The names of entities are words. Words are entities, and therefore >>>their own names. I'm not using entity to mean the idea or the name of >>>something. We have other words for that. >> >>What I meant was entity refers to a object devoid of any it's >>possible characteristics or qualities, i,e. at the most abstracted >>level. > >OK. I don't think objects exist at that level. Actually, I mispoke, I reread the definition of entity, and it does refere to something that has a quality - that of existing. But exist how? In once sense, nothing exists except for <*>. In another sense, the word "entity" exists as a piece of information that most speakers of English know. In yet another sense, that I can refer to something as an entity, making only a distinction that it either exists or does not, exists as an idea in my mind. In even another sense, my pain exist, and while you can observe that I make certain predictible reactions when someone kicks me in the shins, you can never experience my pain, but my pain exists never the less. As an idea in my mind, as a set of physiological reactions, and as a set consisting of the whole of all of that and more. As a class of experience, or sensation. Ad nausium. >OK. That's not my understanding of the word "entity," hence my >objections. At the most abstract level possible, <*> and all of its bits >are isomorphic, in that they are equally amorphous. Which makes talking >about the bits..,unlikely? Isomorphic to what? Above the level of <*> comes the abstracted, period. All besides <*> else we create, and yet that's not complete either because <*> includes us and all we create. It's a strange loop. You cannot pin it down precisely. <*> referts the set of all things including itself. I cannot explain it any better than that. Perhaps when I finnally make it all the way thru _Goedel, Escher, and Bach_, I'll be able to explain myself better. >But if we are to create any value through being in and interacting with >the world, we have to ignore it. No, one must never ignore it that's the whole point. One must be constantly aware that the play-doh castles one makes out of <*> are just one's creations, and one should not mistake them for <*> or take them too seriously. But, yet in another sense Yes, because we never really enjoy those sand castles unless we loose awareness that it's just a make beleive play-doh castle. >So it seems that the perfect mental state would be one of >simultaneous knowledge and ignorance of this one truth. Knowledge >because it is true, but ignorance because if it's true nothing else is. You just have to remember that one can play all the games one wishes as long as you don't forget they are just games - non-disinterest/non- attachment. >>>And hence my clarification that I meant acts a question mark, >>>not as a question. >> >>Well, I guess I did not find that very clear-ifying ;-) > >Then, or now? I could spend more time on that, which would certainly be >more constructive. Yes, please, let us return to linguistics, all this philosophy makes my head ache. Rob Z. -------------------------------------------------------- Outside of a dog, a book is a man's best friend. Inside of a dog, it's too dark to read. -- Groucho Marx