Re: Replacement of Cardinality (defining numbers as half finite, half infinite)

On 8/6/2024 3:58 PM, Ross Finlayson wrote:

On 08/06/2024 04:57 AM, Jim Burns wrote:

On 8/5/2024 11:05 PM, Ross Finlayson wrote:

What I would ask,
is that you surpass,
the inductive impasse,
with the infinite super-task.

>
Induction is a finite task of
reasoning about infinitely.many.

>
Thus deductive inference, ..., or, is it?

Inductive inference is one kind of
deductive inference:
a deductive inference from properties we know
finite.ordinals have because they are finite.ordinals.
⎛ What Mathematics calls "induction" is deduction.
⎜ What Physics calls "induction", for example,
⎜ our conclusion that the sun will rise tomorrow
⎜ because we know of many yesterdays it rose,
⎝ is a different kettle of fish.

The super-task or Thomson's Lamp has helped
to establish the infinitary as within reason.

If
⎛ making finite.length claims which
⎜ we know are true of infinitely.many
⎜ by making a claim about an indefinite one
⎝ which we know has no exceptions
is something you (RF) consider a supertask,
then
we -- although finite -- perform super.tasksᴿꟳ,
because (making...) is something we do.
I prefer not to consider that a super.task,
primarily because we are finite, which
seems to contradict our performing super.tasks.
However, my point is that we
⎛ make claims we know are true of infinitely.many
⎜ by making a claim about an indefinite one
⎝ which we know has no exceptions,
and therefore,
however things stand with supertasks,
we can, by (making...), learn about infinitely.many.