Re: Extrapolating linear ratios

On Dec 18, 4:20 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
First, there are not only few people in general, but only few people
here in sci.logic. Everybody who is told that a function f(x) =< 1 for
_every_ finite x, knows that the average value for all finite x
cannot be 100.

THAT IS A *FINITE* average, DIP***!
That involves the SUM OF A FINITE number of terms!
You CAN HARDLY EVEN DEFINE a sum of AN INFINITE number of
terms IN A SIMILAR way to the one by which you define the finite
sum! Summing an INFINITE number of terms IS JUST DIFFERENT!
There are MANY DIFFERENT WAYS OF PASSING from finite to infinite.
You basically have to choose and bless one VIA AXIOMS.
Since you do not concede the validity of the axiomatic method to begin
with, you're just hopelessly lost all the time. You might actually be
able
to get some respect for your position IF YOU HAD SENSE ENOUGH TO
UNDERSTAND that axiomatizing it YOUR way might actually be consistent,
but that that doesn't stop axiomatizing it OUR way from being
consistent
AS WELL.

Why are only few people here understanding that?

There is nothing to understand.
You cannot define an "infinite average".
The closest thing to that would involve something like integration,
which is different because the interval ITSELF is continuum/
uncountable,
as OPPOSED to finite and discrete.

Because they have
been indoctrinated that the measure given by a bijection beats all and
every other rational arguing.

THAT IS A *DEFINITION*, yes. And more to the point,
SINCE THAT DEFINITION *HOLDS FOR ALL FINITE* sets,
YOU ARE THE ONE, if you are advocating that what holds for all finite
cases should hold for the infinite case, WHO IS OBLIGATED to agree
that infinite sets that can be mutually bijected MUST BE THE SAME
SIZE,
BECAUSE that's the way it is FOR ALL finite sets!!


In fact it is (under all _possible_ circumstances) but "... classical
logic was abstracted from the mathematics of finite sets and their
subsets .... Forgetful of this limited origin, one afterwards mistook
that logic for something above and prior to all mathematics, and
finally applied it, without justification, to the mathematics of
infinite sets. This is the fall and original sin of [Cantor's] set
theory ...." [Hermann Weyl]

Well, he's wrong. That's simple. It DOES NOT EVEN MATTER
what the origin was. What DOES matter is, CAN YOU DERIVE AN
INCONSISTENCY from it?? If not, then you simply have no grounds
for objecting.


.

Quantcast