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Topic: mathematical infinite as a matter of method
Replies: 25   Last Post: May 4, 2013 11:24 PM

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 fom Posts: 1,968 Registered: 12/4/12
Re: mathematical infinite as a matter of method
Posted: May 3, 2013 10:13 PM

On 5/3/2013 7:54 PM, Graham Cooper wrote:
> On May 4, 10:03 am, fom <fomJ...@nyms.net> wrote:
>> On 5/3/2013 5:03 PM, Graham Cooper wrote:
>>
>>
>>
>>
>>
>>
>>
>>
>>

>>> On May 3, 8:15 pm, fom <fomJ...@nyms.net> wrote:
>>>> On 5/3/2013 2:43 AM, Graham Cooper wrote:
>>
>>>>> Its not possible to test Equality by Extension in the inf. case.
>>
>>>> That is correct Herc.
>>
>>>> On the other hand, it is not possible to interpret
>>>> the universal quantifier as a universal statement if
>>>> it is interpreted as a course-of-values.

>>
>>>> Aristotle wrote this. It is ignored by a certain
>>>> contingent of the mathematical community who merely
>>>> argues on the basis of beliefs concerning infinity.

>>
>>>> You know well that any computer system balances
>>>> choices that affect performance. Relational databases
>>>> run faster on logic chips optimized for integral
>>>> arithmetic as opposed to floating point. The analogy
>>>> applies here.

>>
>>>> Brouwer had been clear concerning how the effectiveness
>>>> of working with finite sets differed from working
>>>> with infinite sets. But, the reason infinity enters
>>>> mathematics is because it is how the identity relation
>>>> is extended to convey the geometric completeness of a
>>>> line when used to represent the real number system.

>>
>>>> Infinity does not arise because of testability. It
>>>> arises because of the nature of the identity relation.

>>
>>> If there are more SETS in ZFC than FORMULA in ZFC
>>> (David C Ullrich)

>>
>>> ZFC FORMULA | ZFC SETS
>>
>>> 1 ___________ a i
>>> 2 ___________ b p q r
>>> 3 ___________ c j n
>>> 4 ___________ d s t k u v
>>> 5 ___________ e z w
>>> ...

>>
>>> THEN WHAT DO YOU MEAN BY ...
>>
>>> A SET OF ZFC ?
>>
>> I actually agree with you somewhat here.
>>
>> Nevertheless, if one restricts to countable
>> models, then it is clear that there must be
>> real numbers not represented. In particular,

>
>
> No, you're entitled to that view but hundreds of people say it is NOT
> clear.
>

I will look at the rest in a moment, but forcing
is not a diagonalization argument.

Date Subject Author
4/21/13 fom
4/21/13 Virgil
5/2/13 Hercules ofZeus
5/2/13 fom
5/2/13 Virgil
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Brian Q. Hutchings
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper