Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/18/2024 12:09 PM, Ross Finlayson wrote:

On 05/16/2024 09:50 AM, Jim Burns wrote:

[...]

>
I think that "correct", in context, is the entire
context, which is exactly what deductive inference
contains, explaining when inductive inference either
must complete, or meets its juxtaposition, with
regards to any two forces that balance and align
in symmetry.
>
So, what you are claiming is that inductive inference
is invincibly ignorant,

I am claiming that inductive inference
is invincibly modest.
Post.inference, we only assert claims about
whatever.it.is we described pre.inference.
Perhaps that doesn't seem modest,
because whatever.it.is is infinitely.many,
but induction holds for infinitely.many cisfinite ordinals
in the same way that geometry holds for infinitely.many
right triangles. Completely.

A given schema for induction has no more correctness,
in its own vacuum, than any other,

Induction on the cisfinite ordinals
⎛ those countable.back.to.0 after only
⎜ those countable.back.to.0
⎝ and also 0
is a theorem.
Theorems are not optional.

and when they're put together and don't
agree, then either they don't, and don't, or
don't, and do.
>
"Not.ultimately.untrue", ....

Induction on the cisfinite ordinals
is not.first.false in a finite sequence of
only not.first.false claims
which begins "A cisfinite ordinal is ... ".

One can contrive simple inductive arguments
that _nothing_ is so.

An example of such an argument would be clarifying here.

So, I'd say your definition of "correct", isn't,
and is simply a declaration of "relative" and "blind".
>
No offense meant, of course, it's so that paradoxes
are to be resolved, not obviated.