fom
Posts:
1,968
Registered:
12/4/12


Re: some amateurish opinions on CH
Posted:
Apr 9, 2013 4:33 PM


On 4/9/2013 2:38 PM, apoorv wrote: > 'There is , at least such a thing as "relative unaccountability" . > You can't enumerate the contents of an infinite integer list : > 1 , 0 , 1 , 0 , 1 ...... > > 'There's always the "...." left out . > However , you can unambiguously describe the infinite list by finite > wording : > > "an integer on the list has : > Value 1 if it's on an 'even position on the list' . > Value 0 if it's on an 'odd position on the list' . > > This finite description unambiguously captures my 'infinite list' . ' > > This finite description uses the universal quantifier, which > Allows a finite string of symbols to convey an infinite amount > Of information.Is that a realistic assumption? > Apoorv > >
Infinite, or, arbitrary?
Frege originally interpreted the universal quantifier in terms of arbitrary choice in his deductive calculus. Aristotle discusses the defeat of universal quantification if one tries to validate its use by counting instances (although my simplification has oversimplified).
The problem of deciding what is encompassed by a universal quantifier arises in applications. Model theory seems to reverse the situation.

