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Topic: Mathematics as a language
Replies: 35   Last Post: Nov 8, 2010 1:53 AM

 Messages: [ Previous | Next ]
 Daryl McCullough Posts: 2,871 Registered: 1/29/05
Re: Mathematics as a language
Posted: Nov 4, 2010 7:58 AM

Bill Taylor says...
>
>On Nov 4, 3:12 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
>

>> >What logically could exist -- that is, what is not inherently self-
>> >contradictory -- has mathematical existence.

>>
>> The problem with this is that there could be two different
>> mathematical objects, A and B, such that neither is inherently
>> existence of B. They can't, therefore, both exist.

>
>Exactly so!
>
>My favorite example being,
>(as someone just now pointed out half of),
>it is consistent with ZF that
>
>1) there exists a set of cardinality strictly between N & R;
>
>2) there exists a function on P(R) whose values
> are bijections between the argument and elements of N u {N,R}.

Thanks! That's a much better example than mine, because it's much
more concrete.

>1 & 2 are individually consistent with but jointly inconsistent
>with ZFC. (1) means CH is false, (2) means CH is true.
>
>who often claims informally that "consistency is existence".
>
>He refused to answer, saying only that "ontology is poisonous".
>
>I took that as meaning I'd won the argument! :)

No, it means that you're a snake. A poisonous one.

And I mean that in a good way.

--
Daryl McCullough
Ithaca, NY

Date Subject Author
11/2/10 Aatu Koskensilta
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