Xref: utzoo comp.ai:3003 talk.philosophy.misc:1777 Path: utzoo!attcan!uunet!lll-winken!lll-lcc!ames!pasteur!ucbvax!TAURUS.BITNET!shani From: shani@TAURUS.BITNET Newsgroups: comp.ai,talk.philosophy.misc Subject: Re: Fun with the semantics of paradox Summary: Ha! that's great! Message-ID: <936@taurus.BITNET> Date: 4 Jan 89 07:34:24 GMT References: <551@soleil.UUCP> Sender: daemon@ucbvax.BERKELEY.EDU Reply-To: Organization: Tel-Aviv Univesity Math and CS school, Israel Lines: 24 In article <551@soleil.UUCP>, peru@soleil.BITNET writes: > > From one point of view, sitting on the number line. You start running from > the origin to the right, 1, 2, 3, ... You go on to infinity. However, from > another point of view, this is always considered ONE number line. A single > defined entity. Defined, yet undefined (unbounded), by definition. > Yes. A great example. You see, the whole point here is, in which logic phase do you state your deffinition. If you have some knoladge in sets theory then you probebly know that the set of all natural numbers is the first infinite ordinal, an thus, it *is* a unit of the next higher ordninal. Infact, every ordinal is the set of all smaller ordinals, and thus, the priveus ordinal is his unit. Now. what does this has to do with paradoxes? because a paradox is meerly an indication for you that you are looking at things from a too low logic phase. you can't look at the natural numbers as a unit, from the point of view of the natural numbers! you have to do what is called a change of a secon degree, and to pass into a higher logical phase. Ofcourse, the only way to do that is to know that you are already there, i.e. to look at the set of natural numbers as a subset of that higher logical phase. O.S.