On 3/30/2013 6:12 PM, Ross A. Finlayson wrote: > 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. >
When the mathematicians drew lines, the critics did not like the lines that could be drawn.
When the mathematicians invoked infinitesimals, the critics did not like the infinitesimals that they could not see.
When the mathematicians invoked approximations, the critics did not like the incompleteness where numbers might be missed.
When the mathematicians invoked completeness, the critics did not like the infinity of unmissed numbers.
When the critics complain about infinity, they say "LOOK AT THE LINES THAT I DRAW!!!"