Re: Orlow cardinality question

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> stephen@xxxxxxxxxx said:
>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>> > Virgil said:
>> >>
>> >> Axioms are unfounded. That is the nature of axioms.
>> > Not good ones. Axioms should be well-considered, and not generated willy-nilly.
>>
>> So which of the axioms of set theory do you object to. Here is a list.
>>
>> http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
>>
>> >>
>> >> There may be reasons for choosing a particular set of axioms, but, once
>> >> chosen, they are all that one is allowed to consider in deciding what
>> >> follows from them.
>> > Allowed? Tie your own hands, not mine. In my world, any axiom which is assumed
>> > true may be used in any argument.
>>
>> So when someone is discussing Spherical Geometry, you think it
>> is perfectly valid to make arguments using Euclids Fifth Postulate?
>>
>> Stephen
>>
> Euclid's fifth is only true in the context of euclidean space.

Yes, so you cannot use it outside of that context. Just as
you cannot use "any axioms which is assumed true" outside
of the context in which it is assumed true.

> There are more
> general rules which can be applied. Certainly you are not sugesting that S^L as
> a measure of a set of generated strings is inappropriate for some reason in the
> context of sets? Does set membership allow one to make unique strings that have
> the same series of symbols? No. The rule still applies.

I have no idea what you are talking about. Once you pick
your axioms, you have to use those axioms. You cannot just
use "any axiom" in your proof.

And I noticed that you did not point out which of the axioms
of set theory you have trouble with. There are only 9 of them.

Stephen
.

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