Obections to Cantor's Theory (Wikipedia article)
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From: MoeBlee on 28 Jul 2005 17:47 >From a post by malbrain(a)yahoo.com: > MoeBlee wrote: > > >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, > > This is a negation of the history of mathematics. Mathematics has a > "current state-of-affairs" in relation to REALITY also. Ask any > high-school or junior-college teacher of mathematics. I think you're speaking tongue in cheek and about some other pedgogical matters? Just in case you're not, I didn't claim that it is impossible for mathematics to give a theory for a particular state of affairs in the physical world or a non-physical one, but rather that mathematics in general can't be tied to a particular state of affairs in the physical world. Even granting, for sake of argument, a platonist view, I don't think this entails that mathematics cannot rationally study theories that don't conform to a particular platonist universe. I'm happy to hear arguments to the contrary, though. But, again, if you we're just joking around, then nevermind this reply. MoeBlee
From: malbrain on 28 Jul 2005 17:55 MoeBlee wrote: > >From a post by malbrain(a)yahoo.com: > > > MoeBlee wrote: > > > >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, > > > > This is a negation of the history of mathematics. Mathematics has a > > "current state-of-affairs" in relation to REALITY also. Ask any > > high-school or junior-college teacher of mathematics. > > I think you're speaking tongue in cheek and about some other pedgogical > matters? No. > Just in case you're not, I didn't claim that it is impossible > for mathematics to give a theory for a particular state of affairs in > the physical world or a non-physical one, but rather that mathematics > in general can't be tied to a particular state of affairs in the > physical world. And that negates history. It is by man's nature tied to the CURRENT state of affairs in the physical world. > Even granting, for sake of argument, a platonist view, > I don't think this entails that mathematics cannot rationally study > theories that don't conform to a particular platonist universe. I'm > happy to hear arguments to the contrary, though Sorry, but what's the platonist view? karl m
From: malbrain on 28 Jul 2005 18:15 Virgil wrote: > In article <MPG.1d52e828a17493c1989fdb(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > Daryl McCullough said: > > > Tony Orlow (aeo6) wrote: > > > > > > >Daryl McCullough said: > > > > > > >> So, you agree that for *finite* sets, two sets have the same > > > > > > >> bigulosity if and only if there is a bijection between the two? > > > >> But that no longer holds for infinite sets? > > > >> > > > >> Then how is bigulosity an improvement over cardinality? > > > >Because Bigulosity takes into account the nature of the bijection > > > >in order to determine a precise relative size of infinity. > > > > > > In other words, bigulosity is whatever you want it to be, and so > > > you have a lot more flexibility. Just make it up as you go along. > > > > > > A = the set of natural numbers { 0, 1, 2, ... } B = the set of > > > base ten numerals { "0", "1", "2", ... } C = the set of base > > > two numerals { "0", "1", "10", "11", "100", ... } > > > > > > A and B have the same bigulosity. A and C have the same bigulosity. > > > But B and C do *not* have the same bigulosity (clearly C has a > > > smaller bigulosity than B). That's bigulosity for you... > > > > > > -- Daryl McCullough Ithaca, NY > > > > > > > > If you consider your numerals to have N digits, then base ten has > > 10^N elements and base 2 has 2^N elements > > So that TO is declaiming that the number of naturals is dependent on the > base in which they are to be represented? > > Those mushrooms TO is nibbling must be really potent! Mushrooms are part of both, food and medicine. You need an expert. karl m
From: MoeBlee on 28 Jul 2005 18:36 malbrain(a)yahoo.com wrote: > MoeBlee wrote: > > >From a post by malbrain(a)yahoo.com: > > > > > MoeBlee wrote: > > > > >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, > > > > > > This is a negation of the history of mathematics. Mathematics has a > > > "current state-of-affairs" in relation to REALITY also. Ask any > > > high-school or junior-college teacher of mathematics. > > > > I think you're speaking tongue in cheek and about some other pedgogical > > matters? > > No. > > > Just in case you're not, I didn't claim that it is impossible > > for mathematics to give a theory for a particular state of affairs in > > the physical world or a non-physical one, but rather that mathematics > > in general can't be tied to a particular state of affairs in the > > physical world. > > And that negates history. It is by man's nature tied to the CURRENT > state of affairs in the physical world. Perhaps we're using 'tied' in a different sense. Of course, any mathematics that has been accomplished is tied with the course of human events. Also, an important part of much mathematical motivation is to use mathematics for the sciences. I didn't write anything that disputes that. > > Even granting, for sake of argument, a platonist view, > > I don't think this entails that mathematics cannot rationally study > > theories that don't conform to a particular platonist universe. I'm > > happy to hear arguments to the contrary, though > > Sorry, but what's the platonist view? karl m I said 'a platonist view', not 'the platonist view'. I just mean the broad range of views that are proposed or discussed as some form of ontological, philosphical, or mathematical realism. As you must know, this is usually stated as the view that objects or states of affairs exist independently of consciousness of them. Perhaps the distinction is between what exists as an abstraction in consciousness and what exists non-physically independent of consciousness. Since 'platonist' does have common, though by no means exact or definitive, agreement as to its meaning, I don't know why you are asking me about it, unless I've used the term in some non-usual way, which it doesn't seem I have. I say this since I am not an expert and can't give you a better answer than can be given in many ordinary reference works and books and articles on the subject. MoeBlee
From: malbrain on 28 Jul 2005 18:51
MoeBlee wrote: > malbrain(a)yahoo.com wrote: > > > MoeBlee wrote: > > > >From a post by malbrain(a)yahoo.com: > > > > > > > MoeBlee wrote: > > > > > >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, > > > > > > > > This is a negation of the history of mathematics. Mathematics has a > > > > "current state-of-affairs" in relation to REALITY also. Ask any > > > > high-school or junior-college teacher of mathematics. > > > > > > I think you're speaking tongue in cheek and about some other pedgogical > > > matters? > > > > No. > > > > > Just in case you're not, I didn't claim that it is impossible > > > for mathematics to give a theory for a particular state of affairs in > > > the physical world or a non-physical one, but rather that mathematics > > > in general can't be tied to a particular state of affairs in the > > > physical world. > > > > And that negates history. It is by man's nature tied to the CURRENT > > state of affairs in the physical world. > > Perhaps we're using 'tied' in a different sense. Of course, any > mathematics that has been accomplished is tied with the course of human > events. Also, an important part of much mathematical motivation is to > use mathematics for the sciences. I didn't write anything that disputes > that. Tied: product of/conclusion from. Let's try Webster: 5. (Arch. & Engin.) A beam or rod for holding two parts together; in railways, one of the transverse timbers which support the track and keep it in place. > > > Even granting, for sake of argument, a platonist view, > > > I don't think this entails that mathematics cannot rationally study > > > theories that don't conform to a particular platonist universe. I'm > > > happy to hear arguments to the contrary, though > > > > Sorry, but what's the platonist view? karl m > > (...) I just mean the > broad range of views that are proposed or discussed as some form of > ontological, philosphical, or mathematical realism. I checked with wikipedia and found this: "One statement of this philosophy is the thesis that mathematics is not created but discovered in some undescribed realm." Since I am a materialist: mathematics is created. (...) > Since 'platonist' does have common, though by no means exact or > definitive, agreement as to its meaning, I don't know why you are > asking me about it, >From Webster, 1914: Pla"to*nist (?), n. One who adheres to the philosophy of Plato; a follower of Plato. Hammond. This doesn't illustrate much agreement, at least in 1913. You have one name in one realm. Is there better agreement today? > unless I've used the term in some non-usual way, > which it doesn't seem I have. I say this since I am not an expert and > can't give you a better answer than can be given in many ordinary > reference works and books and articles on the subject. You haven't used the term at all, yet. karl m |