Re: The reality of sets, on a scale of 1 to 10 (theory of theories)

On 03/25/2025 09:40 AM, Jim Burns wrote:

On 3/24/2025 9:01 PM, Ross Finlayson wrote:

On 03/24/2025 05:39 PM, Jim Burns wrote:

On 3/24/2025 7:53 PM, Ross Finlayson wrote:

>

No, you still haven't confronted yourself
that the inconstancy of either platonism or formalism
is merely self-deceiving vacillation,

>
If a typical working mathematician,
on Sunday, affirms the Intermediate Value Theorem
as a formalist, and,
on weekdays, affirms the Intermdiate Value Theorem
as a Platonist,
what is that vacillates?
>

that it results then
for mathematics the theory both platonism and formalism,
and for physics a very thorough realism.

>
I don't seem to be able to parse that.

>
No?
>
Is it because you broke it in the middle then
don't have any sort of context and memory?

>
That doesn't seem to me to be a likely reason.
Not to brag, but
I can remember things which I've read
even more than three or four sentences earlier.
>
That you (RF) think that's a possible explanation
might offer insight into
why you (RF) quote 300 lines in order to
respond to the last three lines, and
treat the other 297 lines as though they don't exist.
>
There is no shame in having a memory problem.
However, it does present a pretty puzzle
for someone trying to communicate something
longer than a few lines.
>

I'd imagine it's difficult being a sort
of broken mirror/record and may well lead
to resentment those interrupting the continuity.

>
Hey! I've got an idea.
What if,
when someone asks you to explain what you're saying,
you explain what you're saying.
It's so crazy, it just might work.
>
----

the inconstancy of either platonism or formalism
is merely self-deceiving vacillation,

>
If a typical working mathematician,
on Sundays, affirms the Intermediate Value Theorem
as a formalist, and,
on weekdays, affirms the Intermdiate Value Theorem
as a Platonist,
what is it that vacillates?
>
>
>

For example, when a formalist platonist arrives at axiomless natural
deduction, and then a formalist non-platonist forgets or ignores that,
that's vacillation.
Otherwise one would indeed expect the truth of the thing for both.
Long ago I adopted the style to not cut the context because
it's too easy for it to be mutilated.
Then, as with regards to conversational digestion and
internalization, and memory, do you recall much from
the old sci.logic thread "Correct Presentation of the
Diagonal Argument"?
How about, "yin-yang ad infinitum"?
Perhaps, the "anti-digonal or only-diagonal, pick one" bit?
Platonists need not eschew formalism, nor for that matter
positivism and logicism, indeed the objects of the theory
are sort of the same. Mere logicist positivists have no
justification except a full-blown scientific theory that
then arrives at again a platonistic justification for it.
Or: there are _always_ ideals and truth doesn't care
whether or not its ontological status is currently
ontologically committed. By any given reasoner, ....
The vacillation and hypocrisy is considered generally
unsound, of course, where as well overgeneralizations
are generally unsound, yet, some ideals are of absolutes.