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

On 3/24/2025 8:53 PM, Ross Finlayson wrote:

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

Considering [...]
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.

Would you like to pick an example other than
the linear and rotational in mechanics?
Generalized momenta,
like the linear and the rotational,
and generalized coordinates,
like displacement and rotation,
are a great success of classical mechanics.
Yes, they are conflated by generalizing,
and that highlights the analogies between them.
https://en.wikipedia.org/wiki/Generalized_coordinates

Your Zeno still isn't going anywhere,

Expect Zeno's intense program of not.going.anywhere
to continue.
We make claims in such a fashion that,
by looking at the claims, with or without understanding,
we know the claims are true.
Some claims we know are true
because
they are claims about what.we.mean,
and we know what.we.mean.
Trivially but fundamentally.
Other claims we know are true
because
we can _see_ with or without understanding
that they and each (finitely.many) prior claim
cannot be the first false claim.
A finite sequence of claims without a first.false claim
is a sequence without a false claim.
That's it.
No bridge to infinity.
-- We know what we mean.
-- We look at and recognize claims as not.first.false.
In our comfy chair, if we so choose.