Re: The set of necessary FISONs

On 2/26/2025 6:55 AM, WM wrote:

On 25.02.2025 19:39, Jim Burns wrote:

On 2/25/2025 3:58 AM, WM wrote:

On 24.02.2025 19:00, Jim Burns wrote:

On 2/24/2025 12:17 PM, WM wrote:

It is possible
but not useful to express this ponderously
by fixed sets.

>
Mathematical sets and
mathematical objects in general
do not change,
(although they can represent change in various ways).

>

Unchanging functions can represent changes.

>
Changing sets are functions of time or
of other properties.

Unchanging functions which represent changes
provide the opportunity to assemble
finite sequences of claims in which
we can _know_ just by _looking_ that
each claim is true.or.not.first.false, and thus
each claim is true.
Knowledge about what the claims are about
by _looking at the claims_

Addition and subtraction of sets are
a common techniques.
Thereby sets are changed.

>
Thereby a relationship between unchanging sets
is described.

>
That is the clumsy description.

>
It makes prose more readable to say "This set changes".
As long as that's understood to mean the other,
I don't see any great crime being committed.

>
So it is.

Saying
"This set changes"
and meaning
"This set is the value of an unchanging function,
fixed for each argument"
is one thing.
Sets literally changing is another thing:
another thing which thoroughly wrecks
how we learn about infinity.
Our sets do not change, not even
when we (informally? poetically? mistakenly?)
say they change.

Does doing things that way make clumsy prose?
Perhaps.
Many would consider clumsy prose to be a small cost
for the ability to reason reliably about
infinitely.many.

>
That is also possible with changing sets.

The method you (WM) propose in place of
using unchanging sets is performing supertasks.
...you vaguely propose.
Perhaps you will provide details one of these decades.
You occasionally pull out a quote from
one of our Revered Big Brains, intending to show
that they at least claimed to perform supertasks.
They did not perform supertasks.
Even if, under the influence of drugs or dementia,
they really did _claim_ that they performed supertasks,
they did not perform supertasks.
⎛ The exception is Chuck Norris.
⎝ Chuck Norris counted to infinity. Twice.

In order to be existing sets must be created
by men or by God.

>
No activity by men or gods is required
in order for a thing to satisfy a description.

>
If the description is the first,
then it constructs the set.

In this context,
'construct' means 'proves to exist'
Some descriptions describe
things which cannot exist,
four.cornered triangles, infinite FISONs, etc.
Things which cannot exist do not exist.

No agreement, no disagreement, no activity
by men or gods
permits or prevents,
in a finite.sequences of claims in which
each claim is true.or.not.first.false,
each claim being true.

>
The claims first must be made.

Not so, actually.
Made or not.made, if a claim _exists_
in a finite sequence all true.or.not.first.false,
then that claim is true.
This is not about the claim.maker.
It is about the finiteness of sequences and
the visibility of the not.first.false.ness of
some claims.
If you overdraw a checking account,
it is not the case that
someone must first compare deposits and withdrawals
before you have really overdrawn your checking.
It doesn't work like that.
These claims among
finitely.many all true.or.not.first.false
are true.
At some point, we learn that they're true.
Or maybe at no point do we learn they're true.
Our learning might be important to us,
but it has no effect on their truth.