Re: William T. Parry gets rid of Disjunction introduction

On 06/07/2026 20:54, 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.

By proof theoretic semantics whatever is derived is true is that system.
If the postulates or hypotheses include P and ~P then (P ∧ ~P) cna be
derived and from that FALSE, which is therefore PTS-true.

-- 
Mikko