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 courseofvalues. >> >>>> 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.

