Obections to Cantor's Theory (Wikipedia article)
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From: malbrain on 28 Jul 2005 15:21 Virgil wrote: > That TO still sees "path"s where none exist may be due to his excessive > self-medication. Medication is administered by doctors' order, where the final arbitration of "excessive" or "adequate" lay (with the doctor, not the patient). The only thing self induced is FOOD, as in FOOD-FOR-THOUGHT. karl m
From: Han.deBruijn on 28 Jul 2005 15:49 stephen(a)nomail.com wrote: > In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > > stephen(a)nomail.com wrote: > > >> In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >> > >>>Just as a matter of prevention, shouldn't we at least _try_ to find > >>>a way of living together, then? > >> > >> You are the one who seems to have a problem living together > >> with mathematicians. What is preventing you from simply > >> living and let live? > > > We don't care about telling lies ourselves, but we don't want that other > > people are lying to us. Isn't that so? :-( > > > Han de Bruijn > > I have no idea what you are trying to say. Do you think > mathematicians are lying to you? Look what some of those mathematicians have done: 0 = {} , 1 = {{}} , 2 = {{},{{}}} , 3 = {{},{{}},{{},{{}}}} , ... Let's get physical now. The empty set is nothing. Putting curly brackets around it still makes it nothing. Thus: 1 = {{}} = {} = 0 , 2 = {{},{{}}} = {{},{}} = {{}} = {} = 0 . Do I have to proceed? No. You can't create something from nothing. There is emptyness all over the place. So there's an obvious contradiction between mathematics and physicality. Common sense dictates then that one of the two must be ... lying. Han de Bruijn
From: stephen on 28 Jul 2005 16:03 In sci.math Han.deBruijn(a)dto.tudelft.nl wrote: > stephen(a)nomail.com wrote: >> In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> > stephen(a)nomail.com wrote: >> >> >> In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> >> >> >>>Just as a matter of prevention, shouldn't we at least _try_ to find >> >>>a way of living together, then? >> >> >> >> You are the one who seems to have a problem living together >> >> with mathematicians. What is preventing you from simply >> >> living and let live? >> >> > We don't care about telling lies ourselves, but we don't want that other >> > people are lying to us. Isn't that so? :-( >> >> > Han de Bruijn >> >> I have no idea what you are trying to say. Do you think >> mathematicians are lying to you? > Look what some of those mathematicians have done: > 0 = {} , 1 = {{}} , 2 = {{},{{}}} , 3 = {{},{{}},{{},{{}}}} , ... > Let's get physical now. Why? We are talking about mathematics? > The empty set is nothing. Putting curly > brackets > around it still makes it nothing. Thus: No. A set that contains nothing is different than nothing. An empty box is not nothing. <snip> > So there's an obvious contradiction between mathematics and > physicality. > Common sense dictates then that one of the two must be ... lying. No, there is a problem with how *you* are choosing to interpret sets. Again, you are insisting that mathematicians see things your way. It is rather disingenuous of you to then implore 'why can't we all get along?'. Stephen
From: Patrick on 28 Jul 2005 16:19 Han.deBruijn(a)DTO.TUDelft.NL wrote: > stephen(a)nomail.com wrote: > >>In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> >>>stephen(a)nomail.com wrote: >> >>>>In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>>> >>>> >>>>>Just as a matter of prevention, shouldn't we at least _try_ to find >>>>>a way of living together, then? >>>> >>>>You are the one who seems to have a problem living together >>>>with mathematicians. What is preventing you from simply >>>>living and let live? >> >>>We don't care about telling lies ourselves, but we don't want that other >>>people are lying to us. Isn't that so? :-( >> >>>Han de Bruijn >> >>I have no idea what you are trying to say. Do you think >>mathematicians are lying to you? > > > Look what some of those mathematicians have done: > > 0 = {} , 1 = {{}} , 2 = {{},{{}}} , 3 = {{},{{}},{{},{{}}}} , ... > > Let's get physical now. The empty set is nothing. Putting curly > brackets > around it still makes it nothing. Thus: > > 1 = {{}} = {} = 0 , 2 = {{},{{}}} = {{},{}} = {{}} = {} = 0 . The notion of subset, is distinct from the notion of member. {} is a subset of {}. {} is not a member of {}. The principal of extentionality says that two sets are equal iff they contain exactly the same members. You can't, under ordinary rules, claim that {{}} = {}, since the LHS has 1 member, and the RHS has none. As far as getting physical goes, there is a simple physical description of this situation: You have the following items: (1) a box that contains a box (2) an empty box (1) and (2) don't contain the same things physically, do they? You wouldn't say they are equal would you? This sort of reasoning, in addition to working well, has a nice physical interpretation. > Do I have to proceed? No. You can't create something from nothing. > There > is emptyness all over the place. > > So there's an obvious contradiction between mathematics and > physicality. > Common sense dictates then that one of the two must be ... lying. Well - what do you propose? That people shouldn't be allowed to do set theory?
From: MoeBlee on 28 Jul 2005 16:42
>From a post by Han.deBru...(a)DTO.TUDelft.NL: > > Let's get physical now. It seems that you miss that set theory and mathematics are not a narrative of the physical universe and set theory and mathematics do not denote with words that pick out objects and even concepts of the physical universe in the way that everyday language or physical sciences do. For that matter, mathematics can't be tied to a particular theory of the physical universe, since, such theories are about contingent states-of-affairs, whereas, even though mathematical theories are contingently true per structures, they are not contingent upon what may or may not turn out true in the physical universe. The applicability or interest of a mathematical theory may depend on what's true in the physical universe, but applicability and interest can't be tied to the kind of literalism that you demand. Mathematics needs to provide abstractions with which one can form theories that are subject to empirical testiing. The value of theories such as set theory is not in how they denote about the physical universe (they don't), but rather in the STRUCTURE ('structure' not necessarily used in the precise model theoretic sense) or the RELATIONS among the concepts in the theory. The primitives and axioms are given in order to provide a structure that does correspond to certain intuitive and practical mathematical thinking. For example, that the number one is the set that has as its member the empty set is not what's so important. What's important is that the number one, so defined, stands in all the RELATIONS with other numbers, so defined, that we require to reflect our intuitive and practical sense of how numbers work. MoeBlee |