Re: The set of necessary FISONs

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).

>
The set of citizens changes
(a set that is mathematically describable). The set of known prime numbers changes
(a mathematical set).

Unchanging functions can represent changes.
{citizen}: {time} → 𝒫{possible.citizen}
{known.prime}: {time} → 𝒫{primes}
For a single t₁, {citizen}(t₁) doesn't change.
For all times t₂,
Nikola.Tesla ∈ {citizen}(t₁)
has the same truth value, either T or F.
The function doesn't change.
Nikola Tesla's citizenship status changes.
There are times t₁ and t₂ such that
Nikola.Tesla ∉ {citizen}(t₁)
Nikola.Tesla ∈ {citizen}(t₂)
The unchanging function represents
a changing citizenship.
----

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.
However,
our sets do not change.
Things which change are not our sets.
Etc.
For a finite.sequences of claims in which
each claim is true.or.not.first.false,
each claim is true.
We rely upon each claim,
at each point at which it stands,
having the same truth value, either T or F.
If we can rely on that,
then we can _look_ at ⟨P P⇒Q Q⟩
and _see_ that Q is not.first.false
-- despite not.knowing what P or Q mean.
If
{citizen}(t₁) and {citizen}(t₂)
are NOT the same set
then
Nikola.Tesla ∉ {citizen}(t₁)
Nikola.Tesla ∈ {citizen}(t₂)
are NOT a claim and its negation
and
we CAN see some claims are not.first.false,
just by LOOKING at them.
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.

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.
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.