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

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Sujet : Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.math
Date : 16. May 2024, 17:50:57
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <45ce4f46-da35-4db2-9696-f88256c54532@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
User-Agent : Mozilla Thunderbird
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:

[Cisfinite induction] is complete.
There is no completing.activity,
so I wouldn't say it completes.

Cisfinite induction is NOT a process.
Cisfinite induction is an argument,
completely correct or completely incorrect.

You mean "not.ultimately.untrue"?
>
I don't know.
What does "not.ultimately.untrue" mean?

It's just an introdunce of introduction,
not contradicted by deduction.
Thank you for answering my question.
'introdunce' looks like a typo or a neologism.
But I get "not contradicted by deduction".
----
_In its correct context_
complete cisfinite induction
is NOT contradicted by deduction.
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".
We can say more than that, though.
_In its correct context_
DENYING complete cisfinite induction
IS contradicted by deduction.
Those who deny its completeness there
are, as we say, "wrong".
_In its correct context_
That is the essential qualification.
Context provides _true claims_ about
the objects of cisfinite induction.
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.
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.
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"?
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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