Date: Apr 6, 2013 5:25 PM
Subject: Re: Matheology § 224
On 4/6/2013 3:51 PM, Virgil wrote:
> In article
> WM <firstname.lastname@example.org> wrote:
>> On 5 Apr., 23:54, Virgil <vir...@ligriv.com> wrote:
>>>> If not, how do you prove its finiteness?
>>> By finding its largest member.
>> Find the largest line of the list
>> 1, 2
>> 1, 2, 3
>> that cannot be removed without changing the union of the remaining
>> Regards, WM
> What makes you think that there is such a line?
> As far as I can see removing any one line alone from the union of all
> lines has no effect on the union.
> So which lines does WM claim satisfy his criterion?
I did this analysis elsewhere.
The sense of his question is that all the
lines satisfy the criterion. When all the
lines are removed, he perceives a contradiction
because the union over the empty set is not
the initial union over all of the monotonic
inclusive constructive sets of marks.
The problem with this reasoning is that a
contradiction is defined in terms of truth
and falsity of statements. The "property"
one would use for this induction, however,
does not change its truth value because
the empty set cannot be diminished by
removing lines. The inductive property
becomes vacuously satisfied at the "completion"
of the induction to the extent that one
may extend mathematics to WMytheology
to make such a statement.