Re: William T. Parry gets rid of Disjunction introduction

On 7/1/2026 12:37 PM, dbush wrote:
> On 7/1/2026 11:25 AM, olcott wrote:
>> On 7/1/2026 2:32 AM, Mikko wrote:
>>> On 30/06/2026 16:55, olcott wrote:
>>>> On 6/30/2026 3:10 AM, Mikko wrote:
>>>>> On 29/06/2026 16:55, olcott wrote:
>>>>>> On 6/28/2026 4:32 AM, Mikko wrote:
>>>>>>> On 27/06/2026 21:29, olcott wrote:
>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote:
>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote:
>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote:
>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote:
>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote:
>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote:
>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote:
>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics
>>>>>>>>>>>>>>>> gets rid of Disjunction introduction
>>>>>>>>>>>>>>>> to prevent the principle of explosion
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> A simple logical matrix and sequent calculus for
>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The main and distinctive feature of PAI (and of the many
>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is
>>>>>>>>>>>>>>>> the rejection of the classically valid principle of 
>>>>>>>>>>>>>>>> Addition,
>>>>>>>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In
>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a
>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability
>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is
>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary
>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> https://philarchive.org/archive/SZMASL
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> He also gets rid of an efficient way to convince people 
>>>>>>>>>>>>>>> who don't
>>>>>>>>>>>>>>> understand much of logic.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> As I recently showed in another post. I figured
>>>>>>>>>>>>>> all this out on my own. I didn't even know that
>>>>>>>>>>>>>> anyone else ever did this. I just knew that when
>>>>>>>>>>>>>> trying to find out what is deduced from a set of
>>>>>>>>>>>>>> premises that you cannot pop in another sentence
>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> By popping in another sentence from out of nowhere
>>>>>>>>>>>>>> (as it shows above) the principle of explosion is
>>>>>>>>>>>>>> derived.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The usual meaning of proof is a sequence of statement where 
>>>>>>>>>>>>> eachstatement either is a premis or follows from one or 
>>>>>>>>>>>>> more earlier
>>>>>>>>>>>>> statements 
>>>>>>>>>>>>
>>>>>>>>>>>> Except with Disjunction introduction, that is its problem.
>>>>>>>>>>>
>>>>>>>>>>> So you're saying that in the following natural language 
>>>>>>>>>>> statement:
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It is a key issue in that it creates the
>>>>>>>>>> psychotic break from reality known as the
>>>>>>>>>> Principle of Explosion, otherwise it may
>>>>>>>>>> make no difference at all.
>>>>>>>>>>
>>>>>>>>>> Stay on topic or I will block you.
>>>>>>>>>
>>>>>>>>> Explain in detail how the below which you dishonestly trimmed 
>>>>>>>>> is off- topic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The topic is how Disjunction introduction enables the
>>>>>>>> Principle of Explosion.
>>>>>>>
>>>>>>> It does not. In any sensible logic every tautology is provable.
>>>>>>> Then the principle of explosion follows.
>>>>>>
>>>>>> POE is unprovable in both of these more sensible systems
>>>>>> of logic.
>>>>>
>>>>> THe expression "these system" above does not denote.
>>>>
>>>> Parry’s logic of Analytic Implication
>>>
>>> If the intent was to include that in the denotation you failed
>>> to say something important.
>>>
>>
>> Parry’s logic of Analytic Implication
>> and Relevance logic are two sensible systems
>> that get rid of the Principle of Explosion.
>>
>> It was dead-obviously correct to anyone paying
>> any attention at all that every contradiction
>> only semantically entails FALSE.
> 
> False, as you have admitted on the record:
> 

Liar

> On 6/28/2026 11:56 PM, dbush wrote:
>  > On 6/27/2026 11:34 PM, dbush wrote:
>  >> On 6/27/2026 11:23 PM, olcott wrote:
>  >>> On 6/27/2026 9:02 PM, dbush wrote:
>  >>>> On 6/27/2026 9:53 PM, dbush wrote:
>  >>>>> On 6/27/2026 9:49 PM, olcott wrote:
>  >>>>>> On 6/27/2026 8:42 PM, dbush wrote:
>  >>>>>>> On 6/27/2026 9:40 PM, olcott wrote:
>  >>>>>>>> On 6/27/2026 8:29 PM, dbush wrote:
>  >>>>>>>>> Given that the following natural language statement is true:
>  >>>>>>>>>
>  >>>>>>>>> --------------------------------------
>  >>>>>>>>> Earth is the third planet from the sun.
>  >>>>>>>>> --------------------------------------
>  >>>>>>>>>
>  >>>>>>>>> In the following natural language statement:
>  >>>>>>>>>
>  >>>>>>>>> --------------------------------------
>  >>>>>>>>> At least one of the following statements is true:
>  >>>>>>>>> - Earth is the third planet from the sun.
>  >>>>>>>>> - <X>
>  >>>>>>>>> --------------------------------------
>  >>>>
>  >>>> Given that <X> is any *truth bearing* natural language statement,
>  >>>> does there exist a statement X such that the condition "At least one
>  >>>> of the following statements is true" is false?
>  >>>>
>  >>>
>  >>> Head games will be ignored.
>  >>>
>  >>
>  >> Explain in detail how this is a head game.
>  >>
>  >> Failure to either answer the above question or explain how it is a
>  >> head game in your next reply or within one hour of you next post in
>  >> this newsgroup will be taken as your official, on-the-record admission
>  >> that Disjunction introduction is in fact truth preserving and valid,
>  >> and therefore so is the Principle of Explosion.
>  >>
>  >
>  > Let the record show that Peter Olcott made the following post in this
>  > newsgroup:
>  >
>  > On 6/28/2026 10:52 PM, olcott wrote:
>  >  > Q also can't bake a birthday cake, this does not make
>  >  > Q in any way "incomplete" relative to what it was
>  >  > defined to do.
>  >  > ...
>  >
>  > And more that one hour has passed with no attempt to answer the above
>  > question or explain why it is a head game.  Therefore, as per the above
>  > criteria:
>  >
>  > Let The Record Show
>  >
>  > That Peter Olcott
>  >
>  > Has *Officially* Admitted:
>  >
>  > That Disjunction introduction is in fact truth preserving and valid, and
>  > therefore so is the Principle of Explosion.
> 


-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).