The Definition of Points
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From: Brian Chandler on 26 Apr 2007 02:11 stephen(a)nomail.com wrote: > In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > > Well, if the axiom systems we develop produce the results we expect > > mathematically, then we can be satisfied with them as starting > > assumptions upon which to build. My issue with transfinite set theory is > > that it produces a notion of infinite "size" which I find > > unsatisfactory. I accept that bijection alone can define equivalence > > classes of sets, but I do not accept that this is anything like an > > infinite "number". So, that's why I question the axioms of set theory. > > Why would you question the axioms? The axioms do not contain the > words "number", "size", or "infinite". As you have been told over > and over again, the results do not depend on the names we use. Only the other day, Tony _appeared_ to agree that there was nothing at all "wrong" with cardinality, just as long as it wasn't called "size". Perhaps he really means he questions the names of the axioms of set theory... Well, who knows. He is spending his energies conversing with Liza at present, so give him a break. Brian Chandler http://imaginatorium.org
From: Brian Chandler on 26 Apr 2007 03:26 stephen(a)nomail.com wrote: > In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > > Well, if the axiom systems we develop produce the results we expect > > mathematically, then we can be satisfied with them as starting > > assumptions upon which to build. My issue with transfinite set theory is > > that it produces a notion of infinite "size" which I find > > unsatisfactory. I accept that bijection alone can define equivalence > > classes of sets, but I do not accept that this is anything like an > > infinite "number". So, that's why I question the axioms of set theory. > > Why would you question the axioms? The axioms do not contain the > words "number", "size", or "infinite". As you have been told over > and over again, the results do not depend on the names we use. Only the other day, Tony _appeared_ to agree that there was nothing at all "wrong" with cardinality, just as long as it wasn't called "size". Perhaps he really means he questions the names of the axioms of set theory... Well, who knows. He is spending his energies conversing with Liza at present, so give him a break. Brian Chandler http://imaginatorium.org
From: Lester Zick on 26 Apr 2007 13:46 On Thu, 26 Apr 2007 02:21:09 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >On Wed, 25 Apr 2007 11:27:00 -0700, Lester Zick ><dontbother(a)nowhere.net> wrote: > >>The fact is two of the predicates are true and one false. Does that >>mean t=0.000 or t=0.667? The same would apply to combinations of >>propositions. Are we supposed to be taking an arithmetic average or >>exercising some kind of intuitional insight? Not even to mention the >>weighting of predicates. I just can't imagine that all predicates have >>the same significance in terms of probablistic truth. Are we supposed >>to just adopt someones weighting opinions on the subject of truth? > >Porridge dancing again, Lester Yeah I really wish I knew what that meant, Ben. I wish even more that you knew what that meant. Then instead of merely dancing in oatmeal we might trip the light fantastic for a change. ~v~~
From: Lester Zick on 26 Apr 2007 14:49 On 25 Apr 2007 23:11:47 -0700, Brian Chandler <imaginatorium(a)despammed.com> wrote: >> Why would you question the axioms? The axioms do not contain the >> words "number", "size", or "infinite". As you have been told over >> and over again, the results do not depend on the names we use. > >Only the other day, Tony _appeared_ to agree that there was nothing at >all "wrong" with cardinality, just as long as it wasn't called "size". Cardinality refers to the number of. >Perhaps he really means he questions the names of the axioms of set >theory... What theory? I see no theory. I see axiomatic assumptions of truth. I see SOAP operas. I don't see any theory. What is it this set "theory" is supposed to explain that can't be explained without set "theory". ~v~~
From: Lester Zick on 26 Apr 2007 15:11
On Thu, 26 Apr 2007 02:19:36 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >>>Absolute truth underlies the universe. Science only confirms a >>>theoretical truth to within some degree of accuracy, or disproves it. >> >>So this absolute truth thingie, Tony. Does it lie out there in space >>with the conjunctions you hypothecate and the dimensions Ben >>hypothecates? > >Er... is this me? What dimensions that I hypothecate? I presume that >you no more know the meaning of the word "hypothecate" than you do the >meaning of "meretricious", because I have not mortgaged any >dimensions. Oh, Ben, Ben. You're so meretriciously pretentious sometimes. You "pledged" empirical tests of spatial dimensionality "as security" presumably for your standing as an empiric "without delivering over". In other words you mortgaged your standing as an empiric to undelivered empirical tests of spatial dimensionality. There is also a secondary usage for "hypothecate" meaning "hypothecize". But I much prefer the usage which sprang the trap I was confident you'd fall into or I wouldn't have included the observation to begin with (dangling preposition, what?) . I'm just so witty I can hardly stand it. > Assuming that you mean "hypothesised about", I feel it >only right to point out that I have not hypothesised the existence of >any dimensions beyond the standard three, since that number seems to >be sufficient to describe physical space as we percieve it. It was empirical tests of spatial dimensionality I was referring to. ~v~~ |