Re: Platonism

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 12/03/04 

Date: Fri, 03 Dec 2004 18:57:18 GMT

tchow@lsa.umich.edu wrote:

> In article <41b134cb.73552732@netnews.att.net>,
> Lester Zick <lesterDELzick@worldnet.att.net> wrote:
>
>>The last time I looked, ordinals were defined as first, second, third,
>>etc. so I'm not sure I follow what you're saying here. I don't see
>>that first, second, third, etc. are identical with one, two, three,
>>etc. unless the differences between first, second, third, etc. are the
>>same as between one, two, three.
>>
>>(I'm not looking for you to explain contemporary mathematics to me. I
>>thought the question regarding ordinals and cardinals was pretty plain
>>to begin with.)
>
>
> I assume that "the question regarding ordinals and cardinals" was your
> question as to whether "the set of all natural numbers includes ordinal
> numbers or not." The answer in the context of contemporary mathematics
> is that it does, for the somewhat trivial reason that finite ordinals are
> identified with finite cardinals in contemporary mathematics. But now
> you say you don't want contemporary mathematics to be explained to you,
> so I'm at a loss as to what your question is.
>
> Are you asking how contemporary mathematicians can possibly equate
> finite ordinals and finite cardinals when ordinality and cardinality
> are such manifestly different concepts?
>
> Or are you asking whether the sentence "The set of natural numbers
> contains ordinals" is true in some context *other than* the context
> of contemporary mathematics? If so, could you explain more fully
> what this context is, since unfortunately it isn't so plain to those
> of us who are used to dealing with contemporary mathematics?

Point of information: regardless of whether we are talking within the
context of contemporary mathematics or within the context of natural
language, it seems to me that if we can distinguish between the
cardinals and the ordinals, well then sets of those things cannot be
identical. But certainly they can map one to one. What am i missing?

patty

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    ... >>The last time I looked, ordinals were defined as first, second, third, ... >>(I'm not looking for you to explain contemporary mathematics to me. ... for the somewhat trivial reason that finite ordinals are ... >identified with finite cardinals in contemporary mathematics. ...
    (sci.math)