Re: William T. Parry gets rid of Disjunction introduction

On 7/6/2026 1:57 PM, André G. Isaak wrote:
> On 2026-07-06 11:54, olcott wrote:
>> On 7/6/2026 5:17 AM, Mikko wrote:
>>> On 04/07/2026 16:15, olcott wrote:
>>>> On 7/4/2026 1:37 AM, Mikko wrote:
>>>>> On 03/07/2026 17:46, olcott wrote:
>>>>>> On 7/3/2026 3:17 AM, Mikko wrote:
>>>>>>> On 02/07/2026 17:37, olcott wrote:
>>>>>>>>
>>>>>>>> x = "The Moon is made from green cheese"
>>>>>>>> y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
>>>>>>>> POE concludes (x ∧ ¬x) ⊢ y
>>>>>>>>
>>>>>>>> "the principle of explosion is the theorem according to
>>>>>>>>   which any statement can be proven from a contradiction"
>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>>
>>>>>>>> When you pay attention to the meaning of the words
>>>>>>>> and correctly apply correct semantic entailment on
>>>>>>>> the basis of the meaning of those words then the
>>>>>>>> principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
>>>>>>>
>>>>>>> No, it is not. The premise x above is a break from reality. But that
>>>>>>> is not in logic, it was introduced by you. Even without the 
>>>>>>> principle
>>>>>>> of explosion it is possible to infer a false conclusion from a false
>>>>>>> premise. 
>>>>>>
>>>>>> Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
>>>>>> and as you said my premise is literally FALSE
>>>>>> (P ∧ ~P) ⊢ FALSE
>>>>>>
>>>>>>> The principle of explosion merely facilitates tinding a
>>>>>>> conclusion that is so obviously false that it convincingly proves
>>>>>>> that the remise is false. 
>>>>>>
>>>>>> There is nothing semantically relevant that can be
>>>>>> proven from a contradiction besides bare FALSE and
>>>>>> bare FALSE only entails bare FALSE.
>>>>>
>>>>> Yes, there is. From the contradiction "I have blue eyes and
>>>>> I don't have blue eyes" one can prove "I have blue eyes" and
>>>>> "I don't have blue eyes", both of which are semantically
>>>>> relevant, and one of which in addition is false.
>>>>>
>>>>
>>>> That is greatly restricted from the POE.
>>>>   (P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
>>>
>>> If you can prove that FALSE is true then what is not true?
>>>
>>
>> That is not proving that false is true.
>> It is stipulating that contradictions
>> only derive bare FALSE.
> 
> Apparently you don't understand what 'derives' means.
> 

(P ∧ ~P) ⊢ ⊥ is a stipulated axiom. FALSE was the dumbed down version.

> When we say that X derives Y we mean that x entails that Y is *true*
> 
> So (P ∧ ~P) ⊢ FALSE means that (P ∧ ~P) proves that FALSE is true. That 
> would be a good example of an explosion.
> 
> André
> 


-- 
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).