Re: William T. Parry gets rid of Disjunction introduction

On 07/07/2026 08:44 AM, Ross Finlayson wrote:
> On 07/06/2026 09:58 PM, Ross Finlayson wrote:
>> On 07/06/2026 08:28 PM, André G. Isaak wrote:
>>> On 2026-07-06 21:12, olcott wrote:
>>>> On 7/6/2026 10:03 PM, André G. Isaak wrote:
>>>>> On 2026-07-06 20:44, olcott wrote:
>>>>>> On 7/6/2026 9:41 PM, André G. Isaak wrote:
>>>>>>> On 2026-07-06 20:24, olcott wrote:
>>>>>>>
>>>>>>>> ∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
>>>>>>>> and
>>>>>>>>         Γ ⊢ ⊥
>>>>>>>> --------------------
>>>>>>>> derivation terminated
>>>>>>>
>>>>>>> That's simply gibberish.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> How do you think that:
>>>>>>  From a contradiction nothing follows
>>>>>> should be encoded?
>>>>>
>>>>> Since you don't understand the formalism you're trying to use, why
>>>>> bother trying to formalize it?
>>>>
>>>> Both LLMs agree that I am already correct.
>>>
>>> LLMs carry no weight in my opinion. And since you can't clearly express
>>> yourself, it wouldn't be clear exactly what they were agreeing with
>>> anyways.
>>>
>>>>> You can simply state it in English. but what you're stating is simply
>>>>> false.
>>>>
>>>> I am overriding and superseding the psychotic break
>>>> from reality of the principle of explosion.
>>>> Numerous famous logicians have done this same
>>>> thing in several different ways.
>>>
>>> They've done it by adopting paraconsistent logics which raise their own
>>> set of problems. Most importantly, though, none of them have claimed to
>>> have removed the principle of explosion from classical logic.
>>>
>>>>> The fact that *anything* follows from a contradiction
>>>>
>>>> Is totally fucked up nonsense that only a psychotic
>>>> would not reject in less than three seconds.
>>>
>>> Since the overwhelming majority of logicians accept this having spent
>>> far more than three seconds contemplating it, you might want to
>>> reconsider your position. You really should contemplate the possibility
>>> that you have misunderstood the topic.
>>>
>>>>> isn't some axiom that can be removed from standard logic and replaced
>>>>> with something else. It's a consequence of the basic definitions used.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> That breaks the coherence notion of truth.
>>>
>>> No, it does not.
>>>
>>> André
>>>
>>
>> I do, I say that classical logic since Chrysippus, with Aristotle,
>> is a modal, temporal, relevance logic: that "classical quasi-modal
>> logic" since Philo and Plotinus and usually in the classroom since the
>> 20'th century is _not_.
>>
>> Somebody like Richard McKeon reflects on this in his account of
>> Aristotle.
>>
>>
>> Then, "paraconsistent" or "non-classical logics" have that the
>> di-aletheic is just an account of a setting for resolving inductive
>> paradox, not accommodating it. I.e., when "non-classical" or
>> "synthetic" or "pluralistic" logics are mutually inconsistent,
>> they're mutually inconsistent.
>>
>>
>>
>> I've never accepted material implication since Philo and Plotinus,
>> and direct implication from the likes of Augustus de Morgan is
>> quite suitable for all logical purposes.
>>
>>
>> So, here there's a principle of inversion, sort of like what's
>> suggested by the recent talk about Prawitz and inversion principle,
>> and not tertium-non-datur and excluded-middle, since there are
>> non-binary propositions, and the account of weighing alternatives
>> itself is tertium-datur.
>>
>>
>> Then, there's a principle of thorough reason, beyond a principle
>> of "sufficient" reason, that like inverse subsumes and is sublime,
>> per Kant, for non-contradiction, then the thorough is: sufficient.
>>
>>
>> So, I remove the "quasi-modal" from classical logic,
>> and explosion goes with it.
>>
>>
>>
>>
>
> About "standard", the definition, there are a variety of usual meanings
> of "standard".
>
> The default, the common, and so on, then a usual idea is as to define
> the "non-standard", that the positive definition is to the negative
> term, as it were.
>
>
> So, having "infinity" or the "non-archimedean", or, the
> "super-archimedean", has that there are different accounts among the
> "non-" and the "super-", of the standard.
>
> So, "standard" usually enough means "regularity with a completion",
> like in set theory "an ordinary inductive set".
>
> Then, what "standard" means in "classical logic", it's sort of
> what follows from "standard vacuity", that the quasi-modal is
> as after making an account of using vacuity to make a regularity,
> instead of that vacuity or emptiness is ordinary, that like
> infinity, ordinary and extra-ordinary, is emptiness, ordinary
> and extra-ordinary.
>
>
> So, completion in mathematics and vacuity in logic, "ordinary"
> as "standard", then have that among accounts of _competing rulialities_,
> that's what's standard to one account is non-standard to
> the other account, here for example for "standard infinitesimals"
> and "standard type", where there are no _nulls_ the values in the
> language, and every type has its own empty set.
>
>
> So, then about what's given by _vacuity_ in logic, and called
> "material implication", is not _standard_ in a modal temporal
> relevance logic where references to empty values are typed.
>
>
> It's sort of like relational algebra where there are no nulls.
>
>
>
> So, it's simple and usually considered "trivial" what "basic quasi-modal
> logic" makes as a definition after "vacuity" to
> result what's its "regular" what's its "standard".
>
> Then, it's not trivial nor is it so in other accounts.
>
>
>

So, "super-classical", then, and, of the "extra-ordinary",
infinity and vacuity.

Then, according to ancient accounts, that's "classical",
and with "classical expositions of the super-classical".


Then, "extra-ordinary" is a term at least since Mirimanoff,
and many, many logicians explore super-classical and extra-ordinary
logics, not "non-classical" nor for that matter "classical quasi-modal",
what's their "super-standard".