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

On 03/24/2025 05:34 PM, Jim Burns wrote:

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

On 03/24/2025 11:20 AM, Jim Burns wrote:

>

A big criticism of using falsifiability
to determine what deserves the label 'science'
is that
a theory can pretty much always be saved
by tweaking in various ways.
(See also Ptolemaic epicycles.)
>
It seems that a theory can be saved
_and it will be saved_
until a better theory comes along.
Physics is not like mathematics.

>

Can't trust tweakers.
>
Any new scientific theory (of all the theories)
must not be falsified by _any_ of the data,
or it's just an application in a sub-field,
not "the theory".

>
https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Revolutions
⎛
⎜ Kuhn argued for an episodic model in which
⎜ periods of conceptual continuity and cumulative progress,
⎜ referred to as periods of "normal science",
⎜ were interrupted by periods of revolutionary science.
⎜ The discovery of "anomalies" accumulating and
⎜ precipitating revolutions in science leads to new paradigms.
⎜ New paradigms then ask new questions of old data,
⎜ move beyond the mere "puzzle-solving" of the previous paradigm,
⎜ alter the rules of the game and
⎝ change the "map" directing new research.
>

not "the theory".

>
You (RF) are concerned that some theory might not be
"the theory".
>
You can stop worrying about that.
_No_ theory in the physical sciences is "the theory".
>
Conceivably, someday,
if we avoid extincting ourselves (a big 'if'),
we will be glowy brains in glass tubes
betting our quatloos on thrall competitors,
and we will have "the theory".
>
Today is not that day.
>
>
>

Asimov in a preface to Boyer's history of mathematics
considers that mathematics is special and always, "grows".
Yet, sometimes it results in-grown, and pathological.
Still, he had a very high opinion of it, and himself.
Considering the Mertonian School a.k.a. the Calculators,
then Cavalieri and Galileo, then Newton and MacLaurin
yet so much so Leibniz, then about Lagrange after Maupertuis,
and very much so Hooke's law then down to Clausius,
about the "severe abstraction" of the "mechanical reduction",
has that when things get _conflated_ that aren't necessarily,
like the linear and rotational in mechanics or the
arithmetic and algebra, it's a _false_ conceit.
I.e. there's a whole buried treasure that is the prize.
And, adding on to it doesn't help since the false floor
is the only thing holding it up.
Your Zeno still isn't going anywhere,
and Aristotle's getting tired of you not checking yourself.
Yet, they get around and along just fine.
So, sometimes developments are backwards ingrowths.
Then there's a whole gamut of the "fictitious" and "virtual",
all quite real in the sense as they reflect the breakdown
of the metaphor the conceit, that then getting them together
in what's a sum-of-histories sum-of-potentials least-action
least-gradient that is-a the-physics, then at least here we
already have an axiomless natural deduction and axiomless natural
geometry with natural infinities and natural continuity.
Descriptive set theory is a usual sort of account of one relation,
then about all the objects of the mathematical universe that
the language of it is intended to convey, the, "heno-theory",
has that it's extra-ordinary and expansion of comprehension.
Russell's little paradise is as much a gaol.