Re: Orlow cardinality question

On Mon, 20 Jun 2005 14:21:38 -0400, Tony Orlow (aeo6)
<aeo6@xxxxxxxxxxx> wrote:

>> >> >There is no such thing,
>> >> >and if ZFC claims there is, that's just another glob o' junk for the bucket.
>> >> >What axioms prove this? They need review.
>> >>
>> >> Then don't use ZFC. But, you should keep two things in mind.
>> >>
>> >> 1) Just because you don't like a result, it doesn't make it
>> >> inconsistant. You have claimed that ZFC is inconsistant, but so far,
>> >> you have only shown that it proves things you wish it wouldn't.
>> >
>> >I have shown that it makes assumptions that are inconsistent with other
>> >assumptions within set theory and outside of it.
>>
>> And anyone can show any theory to be inconsistent by making
>> assumptions outside of that theory. On the other hand, you have never
>> shown it to be inconsistent without making assumptions outside of set
>> theory.
>That's true, but the rules outside of set theory that I am using are ones which
>apply to the elements in any given exmaple. You can't use quantities or strings
>to prove your point, and then ignore the properties of quantities or strings.

Any property that isn't relevant can (and should be) ignored.

>> >> 2) You are going to have a hard time making what you want consistent
>> >> without introducing even bigger problems (from the point of view of
>> >> most mathematicians).
>> >
>> >I have heard that opinion numerous times, along with admonishments about how
>> >it's not that easy, etc. Yet, no one has pointed out, despite their claims to
>> >the contrary, any inconsistencies in my understanding, either internally or
>> >externally, with anything except cardinality, which doesn't agree with anything
>> >else anyway. There are no bigger problems this introduces. Only ones it
>> >addresses.
>>
>> Let's see. You don't think having the size of a set be dependent on
>> the characteristics of another set isn't a problem?
>You mean like comparing to a standard set?

I don't have a problem comparing things to a standard set. I do have
a problem with a claim about "size" where the relative sizes of sets
depends on the choice of a third set. I find that *extremely*
counter-intuitive.

>> You don't think
>> that having sets for which no size exists isn't a problem?
>I think there may be sets which are hard to compare to standard sets, but all
>sets have a size. What set did I say has no size? The set of finite naturals? I
>don't see that as any more of a problem than having no maximal element in your
>finite range. Live with it.

I don't have to. I have a perfectly servicable theory of set size
that doesn't have that problem.

>> You don't
>> think having sets with multiple sizes isn't a problem?
>I don't have sets with multiple sizes. I have set expressions which can be
>interpreted as different sets, depending on whther you are talking about
>quantity or symbolic representation. That's a step toward clarification, when
>you are using mixtures of these concepts and getting mixed results.

Yes, you do. You assigned a single set the sizes N/2 and N.

Martin

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