Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
fom

Posts: 1,968
Registered: 12/4/12
Re: mathematical infinite as a matter of method
Posted: May 3, 2013 8:03 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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,
it is consistent that there will be finite
sequences that are represented and that form
what is called a generic set. These sets
have a convergence property that permits the
construction of forcing models. Cohen used
this notion to derive generic reals.

So, with the current axiomatization of ZFC,
it is usually possible to take advantage of
countable ground models in such a way that one
can form a forcing model that includes all of
the original sets of the ground model and at
least one set not in the ground model.

This is one reason I do not agree with the
received paradigm concerning the standard
account of identity,

http://plato.stanford.edu/entries/identity-relative/#1

But, it is also why David Ullrich is correct if
I am interpreting your paraphrase faithfully.

You might look at the link:

http://plato.stanford.edu/entries/actualism/

Although it is not directly relevant to a
mathematical context, it reflects your sentiment
concerning the existence of objects that cannot
be actually realized (by formulas in this case).

In the link:

http://plato.stanford.edu/entries/existence/#FreRusExiNotProInd

you will find that Frege and Russell did not view
existence as a first-order property. So, one finds
one's self in the awkward trade-off between a comfortable
first-order paradigm for logic and a second-order paradigm
to establish a fixed notion of identity.

Hence, formulas alone are not enough (in my non-standard
views of these things).













Date Subject Author
4/21/13
Read mathematical infinite as a matter of method
fom
4/21/13
Read Re: mathematical infinite as a matter of method
Virgil
5/2/13
Read Re: mathematical infinite as a matter of method
Hercules ofZeus
5/2/13
Read Re: mathematical infinite as a matter of method
fom
5/2/13
Read Re: mathematical infinite as a matter of method
Virgil
5/3/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/3/13
Read Re: mathematical infinite as a matter of method
fom
5/3/13
Read not testability; arises due identity relation(s)
Brian Q. Hutchings
5/3/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/3/13
Read Re: mathematical infinite as a matter of method
fom
5/3/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/3/13
Read Re: mathematical infinite as a matter of method
fom
5/3/13
Read Re: mathematical infinite as a matter of method
fom
5/4/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/3/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/3/13
Read Re: mathematical infinite as a matter of method
fom
5/3/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/4/13
Read Re: mathematical infinite as a matter of method
fom
5/4/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/4/13
Read Re: mathematical infinite as a matter of method
fom
5/4/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/4/13
Read Re: mathematical infinite as a matter of method
fom
5/4/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/4/13
Read Re: mathematical infinite as a matter of method
fom
5/4/13
Read Re: mathematical infinite as a matter of method
Graham Cooper
5/3/13
Read Re: mathematical infinite as a matter of method
Graham Cooper

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.