Re: The shocking truth about the naturals

aatu.koskensilta@xxxxxxxxx wrote:
Once again someone has invoked the Löwenheim-Skolem theorem in support
of the idea that there is something problematic in proving this or
that collection uncountable, in some thread or another, here in our
sci.logic. Bori

s Borcic is my name. The thread is "math is a physical process" (somebody's crosspost) and what I precisely said was :

"[the] Downward Loewenheim-Skolem [theorem] is a set theory result that makes it an interesting problem to incontrovertibly prove the existence of more
than [countably] many of anything :)"

I find it fun to claim here that this very thread you initiated in parallel (and relative privacy) satisfies the above sentence *exactly*

The only problems are (1) the irony marker and (2) the subjectivity of "interesting".

But, (1) is a matter of lifting an ambiguity (where does the irony marker apply ?) and (imo) good faith entails to filter out conflictual interpretations with an appropriate lifting of ambiguity when possible. What should in your case directly lead to make (2) the solution to (1) and conversely, should it not ?

ng as this old argument is, it is curious it has
escaped the determined skeptic that the upward Löwenheim-Skolem
theorem incontrovertibly shows we can't really prove any collection
countable.

Since the above technically alludes to me (as current last representative), I guess it is legitimate for me to remark on it... that (1) my /own/ use of "incontrovertibly" indeed alluded to the unavoidability of "determined skeptics" and further adepts of the church of univocity, and (2) that my alluding to the necessity of counting with them is not sufficient cause to count myself among these groups.

But I guess this may be a difficult nuance for someone who uses "we" as you tend to do.

Regards,

Boris Borcic

Realising this, we must give up all of mathematics and take
up roller-skating, rolling on our way as we collect asparaguses.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus


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