On 05/16/2024 09:50 AM, Jim Burns wrote:
On 5/16/2024 5:03 AM, Ross Finlayson wrote:
On 05/15/2024 01:57 PM, Jim Burns wrote:
On 5/15/2024 3:56 PM, Ross Finlayson wrote:
On 05/15/2024 07:10 AM, Jim Burns wrote:
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[Cisfinite induction] is complete.
There is no completing.activity,
so I wouldn't say it completes.
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Cisfinite induction is NOT a process.
Cisfinite induction is an argument,
completely correct or completely incorrect.
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You mean "not.ultimately.untrue"?
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I don't know.
What does "not.ultimately.untrue" mean?
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It's just an introdunce of introduction,
not contradicted by deduction.
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Thank you for answering my question.
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'introdunce' looks like a typo or a neologism.
But I get "not contradicted by deduction".
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_In its correct context_
complete cisfinite induction
is NOT contradicted by deduction.
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Outside of its correct context,
we do not assert complete cisfinite induction.
⎛ To be pedantic, some people assert it there.
⎝ The technical term for them is "wrong".
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We can say more than that, though.
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_In its correct context_
DENYING complete cisfinite induction
IS contradicted by deduction.
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Those who deny its completeness there
are, as we say, "wrong".
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_In its correct context_
That is the essential qualification.
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Context provides _true claims_ about
the objects of cisfinite induction.
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If the context is of the correct type,
those true claims can be followed by
only not.first.false claims, bread crumbs
leading us to the statement of induction.
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Because of the way in which we arrive at
the statement of induction,
we know it is a true statement.
But the way in which we arrive
must start with the correct context.
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Other things, maybe darkᵂᴹ numbers, who knows?
which canNOT be followed by
a finite sequence of
only not.first.false claims
leading us to the statement of induction
are NOT asserted by us to have
complete cisfinite induction available.
>
You mean "not.ultimately.untrue"?
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For complete.cisfinite.induction in correct.context,
I mean "not.first.false", which I take to be
stronger than "not.ultimately.untrue".
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Yes, the "introdunce" is not a word.
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, and it's not so, it's sort of
the point that deductive inference, and the ab-ductive,
is wider in context then that in terms of "correct",
that it's sort of a matter of locality in terms.
Inductive inference, which you've attached to the
existence of an inductive set that has its own
baggage in opinion. A given schema for induction
has no more correctness, in its own vacuum, than
any other, 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", ....
One can contrive simple inductive arguments
that _nothing_ is so.
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.
About these universal quantifiers then, where the ideas
in the trigonometry and definitions about area and other
usual classical notions from geometry are their own thing,
it sort of relates that the other universal quantifier A
is like this A? then that A+ A* A$ sort of reflect what goes
along in terms of existential quantifiers, of the results of
the comprehension, about when things all have to be first-order,
that it's a most very natural sort of way to indicate
expansion in order in terms, what can't go missing
without loss of information.
About being stuck on an inductive track to the
inductive impasse of juxtaposed conclusions,
that you pick one without resolving the other
is just ignorant, that's its definition, "ignorance".
If not just blindness, ....
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