On 1/5/2013 5:41 AM, WM wrote: > On 4 Jan., 18:57, fom <fomJ...@nyms.net> wrote: >> On 1/4/2013 5:41 AM, WM wrote: > >>>>>> So we are not speaking about the same distinguishability criterion. >> >>> There is no other criterion. >> >> In logic, discernibility is taken to be with >> respect to properties. > > Can't a number be considered to be a property?
Usually logicians try to keep grammatical properties separate from "material" properties. Analysis of the paradoxes led to the use of formalized languages, in part, to prevent some self-reference attributable to the ability of natural languages to intermingle such references. So, I did not consider the property of the names in my response. On the other hand, it is in the canonicity of a given system of names that reflects their use as unique identifiers. But, at least where Leibniz identity of indiscernibles may be in play, the non-grammatical properties should be justifying the grammatical distinctions.
>> >> Your position seems to be that since the names determine >> the model which, in turn, determines the truth, then the >> names are the only criterion. > > The model determines the truth if the rules which have to be obeyed by > the names are taken from observation of reality.
Reality is subjective.
One of the goals of science is a version of truth that may be considered objective. What if a completed infinity is a necessary consequence of the objectivity of science?