Re: William T. Parry gets rid of Disjunction introduction

On 2026-07-04 10:44, olcott wrote:
> On 7/4/2026 10:08 AM, André G. Isaak wrote:
>> On 2026-07-04 07:21, olcott wrote:
>>> On 7/4/2026 1:47 AM, Mikko wrote:
>>>> On 03/07/2026 18:04, olcott wrote:
>>
>>>>> P ⇒ Q
>>>>> P → Q
>>>>> P ⊃ Q
>>>>>
>>>>> are all abolished and replaced with the binary
>>>>> form of logical necessity: P □ Q
>>
>> There is no 'binary form of logical necessity.
> 
> That is why I just created one.

But you didn't define it.

>> □ is a unary operator and an expression like P □ Q makes absolutely no 
>> sense.
>>
> 
> Q is a necessary consequence of P makes perfect sense
> and corrects a fundamental error in the definition of
> valid deductive inference.

That would normally be written as □(P → Q), not as the nonsensical P □ 
Q. But you claim to have gotten rid of →, so how this is to be 
interpreted remains a mystery (and getting rid of → makes no sense since 
→ represents a specific truth table which still exists regardless of 
whether you've assigned a symbol to it or not)

>> If you want to use this as a binary operator you'd actually need to 
>> *define* it. You don't seem to grasp this. You can't just introduce a 
>> new operator and expect people to know what it means.
>>
> 
> □ Already means necessity, it is not that hard unless
> one makes great effort to pretend to not understand
> what is already unequivocally clear. >
>> Also, moving into the domain of modal logic would be an incredibly 
>> strange thing for you to do given that in previous posts you claimed to 
> 
> The only thing that I am using is logical necessity.

So how would you interpret 'necessity' without models?

André

>> reject the idea of models. But modal logic is *replete* with models. 
>> Modal logic operates over a set of many models. □P means that P is 
>> true in all accessible models of the system.
>>
>> André
>>
> 
> 

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