On 6/16/2013 3:49 AM, email@example.com wrote: > On Sunday, 16 June 2013 09:47:02 UTC+2, Virgil wrote: >> In article <firstname.lastname@example.org>, email@example.com wrote: > On Sunday, 16 June 2013 00:11:38 UTC+2, Virgil wrote: > >>> In my triangle every side is finite. Therefore it (the side) has two > endpoints. The above formula holds *for all n*. But every n is finite. > >> But then you have no last or limit triangle, merely an endless list of triangles, > > Yes. Endless is another name for infinite. >
What is common to completed infinities, as a logical species, is their inaccessibility from below.
If one focuses on limit ordinals, these objects are inaccessible relative to the successor construction.
If one focuses on the accepted construction axioms, these objects are inaccessible relative to the "inaccessible cardinals" which form the notion of universe discussed by Zermelo at the beginning of large cardinal theory.
When considering the nature of singular judgements in relation to universal judgements, Kant observed that a singular judgement is to universal judgement as an individual is to an infinity.
When completed infinities are referred to in logical language, all that occurs is that universals have to be interpreted in relation to "absolute infinity".
Endlessness need not be interpreted as you have stated. But, you respect neither mathematics based upon axioms nor logic based upon principles.