On Mar 30, 2:31 pm, Virgil <vir...@ligriv.com> wrote: > In article > <64234559-3810-43e3-b49e-70f668c09...@kw7g2000pbb.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > On Mar 27, 8:06 am, "Ross A. Finlayson" <ross.finlay...@gmail.com> > > wrote: > > Ross citing himself brought nothing of value to anything. > --
"Nothing" has value to some. Here that's a simple reference to the void and epistemological content of "Nothing".
Then, I ask again: what _value_ have transfinite cardinals, in terms of application? Beyond the abstract and that pure mathematics is justified for itself: where is the natural placement of modern mathematics: for natural physics.
The answer as of yet is "none".
So, I can well see where's your "proof" (vis-a-vis truth in theory): where's your "use"? What arises from cites of transfinite cardinals, except, more of same?
Then, I can also well see that Hancher ignores presentation he doesn't like and can't attack: so for the rest of us, if you would, in any manner you see fit: draw a line.
Draw a line, are the points in order? Draw a line, is each but the first and last exactly defined by some previous and some following, even penultimate and next? Draw a line, is each defined by beginning and end?
Draw a line: is that uncountably many actions, or just one? For the infinitely many points on that line justly drawn from a point: are there countably many of them, or more than there are?
Because, there are certainly only countably many of them in a row.