Re: William T. Parry gets rid of Disjunction introduction

On 2026-07-04 17:42, olcott wrote:
> On 7/4/2026 5:11 PM, André G. Isaak wrote:
>> On 2026-07-04 15:36, olcott wrote:
>>> On 7/4/2026 4:29 PM, André G. Isaak wrote:
>>>> On 2026-07-04 14:58, olcott wrote:
>>>>> On 7/4/2026 11:59 AM, André G. Isaak wrote:
>>>>>> 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), 
>>>>>
>>>>> That does not perfectly preserve the complete
>>>>> necessity between P and Q.
>>>>
>>>> What on earth does it mean for there to be a "complete necessity 
>>>> between P and Q". Necessity applies to propositions. It doesn't hold 
>>>> *between* things.
>>>>
>>>> □(P → Q) means that Q is necessarily implied by P. If you mean 
>>>> something other than that you're really going to have to clarify 
>>>> what you mean.
>>>>
>>>>> P □ Q   P → Q
>>>>> 0 ? 0   0 1 0
>>>>> 0 ? 1   0 1 1
>>>>> 1 0 0   1 0 0
>>>>> 1 1 1   1 1 1
>>>>> Q is a necessary consequence of P
>>>>> is the same as English If P then Q
>>>>> (a) false when P is true and Q is false
>>>>> (b) true  when P is true and Q is true
>>>>> (c) otherwise does not have a truth value.
>>>>
>>>> So again your veering into the territory of three-valued logic. If a 
>>>> truth table contains any symbol other than T or F, you're dealing 
>>>> with a three or more valued logic which means you have to completely 
>>>> redefine every single logical operator before you can proceed.
>>>>
>>>
>>> The English if P then Q only actually tells you
>>> P(true) then necessarily Q(true)
>>> Q(false) then necessarily P(false)
>>> IT DOES NOT TELL YOU MORE THAN THIS AND
>>> IT IS STUPID MISTAKE TO ASSUME OTHERWISE
>>> THE WAY THAT IMPLICATION STUPIDLY DOES.
>>
>> You're introducing the word 'necessarily' here without any attempt to 
>> explain what is meant by this (by you).
>>
> 
> I always use the ordinary English meaning.
> If P is true then Q is impossibly false.
> If Q is false the P is impossibly true.

'impossibly false' and 'impossibly true' aren't ordinary English.

>> What is the difference between
>>
>> a) Q is a necessary consequence of P.
>> b) Q is a consequence of P
>>
>> Give an example where b holds true but where a is false. If you can't 
>> do that, then your use of 'necessary' is completely meaningless verbiage.
>>
> 
> If someone smacks you in the face then
> you were hit in the face.
> 
> If you were NOT hit in the face then
> someone did not smack you in the face.

I asked for an example illustrating the different between 'necessary 
consequence' and mere 'consequence'. The two examples above don't even 
mention the word 'necessary'.

>>>> And there's nothing about the above table which in any way captures 
>>>> the meaning of 'necessity' so it's entirely unclear why you want to 
>>>> use the □ symbol here. Your '□' doesn't have any relation to 
>>>> necessity any more than '→' does above.
>>>>
>>>> Also note that formal logic is *not* c++. There's no such thing as 
>>>> operator overloading, so you can't take a unary operator and use it 
>>>> for some ill-defined binary operation as well. You need a new symbol 
>>>> since □ is already taken.
>>>>
>>>> P □ Q makes as much sense as P ¬ Q or P ∀ Q
>>>>
>>>>>> So how would you interpret 'necessity' without models?
>>>>
>>>> I note you didn't answer this. The notion of necessity in modal 
>>>> logic is intrinsically tied to model theory.
>>>>
>>>> How exactly are you defining 'necessity' if you're not making use of 
>>>> models?
>>>>
>>>> André
>>>>
>>>
>>> Do you know what propositional logic is?
>>> then that is one way to avoid models.
>>
>> Propositional calculus uses models. It's also extremely limited.
>>
>> André
>>
> 
> Are you referring to truth tables as models?

No.

André

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