Re: William T. Parry gets rid of Disjunction introduction

On 7/6/2026 6:49 AM, Tristan Wibberley wrote:
> On 26/06/2026 02:32, 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
> 
> 
> Is that available elsewhere without requiring that I agree to terms such
> as this expansive lot of stuff that has nothing to do with reading
> something that I should expect either is Parry or is no better:
> 
> https://www.cloudflare.com/privacypolicy/
> 
> 

I figured out the getting rid of disjunction introduction
is required by myself. William T. Parry is merely a guy
that agrees with me. He did carry this idea further.

Google Scholar crashed or I would have found you
a better article. https://scholar.google.com/
[William T. Parry, Entailment Logics

https://www.google.com/books/edition/Directions_in_Relevant_Logic/7lzuCAAAQBAJ?hl=en&gbpv=1&printsec=frontcover] 
  page 101

https://www.google.com/books/edition/Meaning_and_Proscription_in_Formal_Logic/NCpEDwAAQBAJ?hl=en&gbpv=1&dq=William+T.+Parry,+Entailment+Logics&pg=PP7&printsec=frontcover

-- 
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).