18/09/24 13:13:25.50 b5cCvILu.net
>>61
つづき
Indeed, in the present context, it is perhaps useful to recall the following well-known
generalities concerning logical reasoning:
(GLR1) Given any mathematical argument, it is always easy to derive a contradiction
by arbitrarily identifying mathematical objects that must be
regarded as distinct in the situation discussed in the argument. On the
other hand, this does not, by any means, imply the existence of any
logical flaws in the original mathematical argument!
(GLR2) Put another way, the correct interpretation of the contradiction
obtained in (GLR1) is ? not the conclusion that the original argument,
in which the arbitrary identifications of (GLR1) were not in force, has logical
flaws (!), but rather ? the conclusion that the contradiction obtained
in (GLR1) implies that the distinct mathematical objects that were arbitrarily
identified are indeed distinct, i.e., must be treated (in order, for
instance, to arrive at an accurate understanding of the original argument!)
as distinct mathematical objects!
It is most unfortunate indeed that the March discussions were insufficient from
the point of view of overcoming these misunderstandings. On the other hand, my
own experience over the past six years with regard to exposing IUTch to other
mathematicians is that this sort of short period (roughly a week) is never sufficient,
つづく