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

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Herman Jurjus

Posts: 103
Registered: 9/7/09
Re: Mathematics as a language
Posted: Nov 3, 2010 8:58 AM
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On 11/3/2010 1:19 PM, Marshall wrote:
> On Nov 3, 3:23 am, Herman Jurjus<hjm...@hetnet.nl> wrote:
>> On 11/3/2010 6:52 AM, herbzet wrote:
>>
>>
>>
>>
>>

>>> Aatu Koskensilta wrote:
>>>> herbzet writes:
>>>>> Bill Taylor wrote:
>>
>>>>>> Or whether the number 6 really exists. Does it?
>>
>>>>> It *could* exist -- therefore, mathematically, it *does* exist.
>>
>>>> This is a traditional and appealing idea. But just what is meant by
>>>> "could" here? What sort of possibility is involved?

>>
>>> For rhetorical punch, I purposely left out the modifier, which is "logical".
>>
>>> What logically could exist -- that is, what is not inherently self-
>>> contradictory -- has mathematical existence.

>>
>> Corollary: CH is false.
>> Proof: Since Cohen 1963 we know that it is logically consistent to
>> assume that there exists S, subset of P(N), equipollent neither to N nor
>> to P(N).

>
> Consistent with what? In what theory?


Co-consistent with ordinary mathematics, of course.
(I.e. with ZFC, and then also with any weaker theory.)

--
Cheers,
Herman Jurjus


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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