Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]

WM <wolfgang.mueckenheim@tha.de> wrote:

On 23.03.2025 23:19, Alan Mackenzie wrote:

WM seemed to be saying that the "reality"/"substance" of any two sets
could be ranked, with one greater than the other (unless they were,
somehow, the same).

We should say: Sets with different elements like even and odd integers
have different substance but same amount of substance (number of elements).

Should we?  "Substance", in this sense, remains undefined.  To say
things about the "substance" of sets is thus nonsense.

You've said two sets like the even and odd integers have the "same
amount of substance"; more nonsense.  Then again, there's the set of
integers divisible by 4, already mentioned.  That will also have the
same "amount of substance" again, presumably.

Why don't you just use the word cardinality, like everybody else does.
It is defined mathematically, and generally understood.

Or can you refute my assertions of nonsense by defining this
"substance"/"Realität" in a mathematical fashion?

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).