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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 11 May 2024 16:11:18 -0700
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On 05/11/2024 02:44 PM, Ross Finlayson wrote:
> On 05/11/2024 02:05 PM, Ross Finlayson wrote:
>> On 05/11/2024 12:24 PM, Jim Burns wrote:
>>> On 5/11/2024 11:47 AM, Ross Finlayson wrote:
>>>> On 05/11/2024 07:40 AM, Jim Burns wrote:
>>>
>>>>> [...]
>>>>
>>>> In the logical, the purely logical,
>>>> the syntax "is" the semantics.
>>>
>>> If what makes logic impure is
>>> to be about something,
>>> then it would make some sense to say that
>>> pure logic has no semantics
>>>
>>> ...which leads, by default?
>>> to syntax being the missing semantics, I guess?
>>>
>>> Sorry, I will not sign your petition.
>>> Syntax and semantics are more different than
>>> cabbages and kings.
>>>
>>> It seems to me that
>>> the purest of ultra.pure logic is actually
>>> _about_ claims,
>>> analogous to geometry being _about_ points,
>>> lines, plane.figures, and so on.
>>>
>>> It is an unbreakable law that
>>> the sum of the squares of the two shorter sides
>>> of a right.triangle is equal to
>>> the square of the third and longest side.
>>>
>>> It is an unbreakable law that
>>> a finite sequence of only not.first.false claims
>>> holds only true claims.
>>>
>>> It is an unbreakable law that
>>> Q preceded by P and P⇒Q is not.first.false.
>>>
>>>
>>
>> It's exactly about "not.ultimately.untrue" that
>> describes how there are "inductive impasses"
>> that belie their finite inputs.
>>
>> These are found in all the greatest seminal arguments
>> of objects of reason their dissonance yet harmony,
>> complementary duals, anything that's otherwise a
>> "paradox" of mathematical logic, which yet, is not.
>>
>> The "pure theory" is, "all the things, theoretically".
>>
>> Then in set theory there are ubiquitous ordinals,
>> for example, sharing the background, sharing the substrate,
>> of a continuum of objects, making the _bridges_,
>> the analytical _bridges_, the ponts.
>>
>> Where it's so that induction is unbreakable,
>> whether what _holds_ it, _is_ it, is the most
>> usual sort of example of comprehension and
>> quantification together.
>>
>> It's the most usual sort of example that
>> it _is not_, point to any argument about
>> Russell's "set" and any inductive set
>> which according to itself is the entire
>> world, or universe, of sets that don't
>> contain themselves, which you forget
>> is prohibited.
>>
>> So, the "conscientious" bit, is, even having
>> to always take into account any exceptions to
>> the rulial what are so rulial themselves,
>> regular, regularity, because "truth is regular".
>> Not: "regular is truth".
>>
>> It's not an unbreakable law that the Law of
>> Excluded Middle holds for all propositions,
>> because LEM or Tertium Non Datur TND, only
>> effect a reflection on a class of propositions,
>> not including those most pivotal and crucial,
>> of what would otherwise be logical antinomies,
>> which are not, because they are purely logical.
>>
>>
>> Of course any sort of gathering of propositions
>> is its own little pure logic itself, yet, we're
>> interested here in the foundations and altogether,
>> besides.
>>
>>
>> You speak of the meta-theory, and that there is one,
>> and we might call it pure logic, and it exists,
>> and we attain to it, because we're conscientious,
>> and, altogether thorough, as diligently as we can be,
>> mathematicians qua logicians qua theoreticians.
>>
>> Lock is lit, ..., and around it goes.
>>
>>
>
> Here's an example.
>
> You encounter a river, it's either Styx or Lethe, I forget.
> It's upon you to cross the river, or gorge, quite similar
> to the recent episode recounted of the requirements
> and consequences of crossing, or, not.
>
> So, you see a guy across the river, no surprise, it's Zeno.
> You imagine to consult him.
>
> "HOW DO I GET TO THE OTHER SIDE OF THE RIVER?"
>
> He hears your question.
>
> "COME AGAIN?
>
> "HOW DO I GET TO THE OTHER SIDE OF THE RIVER?"
>
> He considers you for a moment.
>
> "YOU ARE ON THE OTHER SIDE OF THE RIVER."
>
> Then I imagine you might clarify,
>
> "NO I MEAN TO YOUR SIDE OF THE RIVER."
>
> Then you notice he's standing next to you and
> says "go all the way across".
>
>
> It's like two inductive analysts were contradicting
> each other. One says "base case, subsequent
> case, case closed", and the other says "base case,
> subsequent case, case not closed".
>
> You just pick one?
>
>
>
>


The case is that induction goes through,
an inviolable law you call it:
does it go all the way through?
Does it complete?

See, the contrary inductive analyst just says
"in case you don't have a deductive argument why
something is so, induction is so much shifting-sands
and slippery-slope." He just has "the base case is
you haven't completed induction, and so is the
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