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

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Daryl McCullough

Posts: 2,871
Registered: 1/29/05
Re: Mathematics as a language
Posted: Nov 4, 2010 7:58 AM
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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
>> self-contradictory, but the existence of A contradicts the
>> 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.
>
>I once asked about this of Thomas Forster, an admirable logician,
>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
Read Re: Mathematics as a language
Aatu Koskensilta
11/3/10
Read Re: Mathematics as a language
herb z
11/3/10
Read Re: Mathematics as a language
Herman Jurjus
11/3/10
Read Re: Mathematics as a language
Marshall
11/3/10
Read Re: Mathematics as a language
Herman Jurjus
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
Marshall
11/5/10
Read Re: Mathematics as a language
herb z
11/5/10
Read Re: Mathematics as a language
Herman Jurjus
11/6/10
Read Re: Mathematics as a language
herb z
11/6/10
Read Re: Mathematics as a language
James Dolan
11/6/10
Read Re: Mathematics as a language
Tim Little
11/6/10
Read Re: Mathematics as a language
Daryl McCullough
11/6/10
Read Re: Mathematics as a language
Marshall
11/6/10
Read Re: Mathematics as a language
Brian Chandler
11/6/10
Read Re: Mathematics as a language
Tim Little
11/7/10
Read Re: Mathematics as a language
lwalke3@lausd.net
11/8/10
Read Re: Mathematics as a language
Brian Chandler
11/7/10
Read Re: Mathematics as a language
herb z
11/7/10
Read Re: Mathematics as a language
Daryl McCullough
11/8/10
Read Re: Mathematics as a language
herb z
11/3/10
Read Re: Mathematics as a language
lwalke3@lausd.net
11/3/10
Read Re: Mathematics as a language
Marshall
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
herb z
11/3/10
Read Re: Mathematics as a language
Daryl McCullough
11/4/10
Read Re: Mathematics as a language
Bill Taylor
11/4/10
Read Re: Mathematics as a language
Daryl McCullough
11/5/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
Daryl McCullough
11/5/10
Read Re: Mathematics as a language
herb z
11/5/10
Read Re: Mathematics as a language
Daryl McCullough
11/4/10
Read Re: Mathematics as a language
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