Re: William T. Parry gets rid of Disjunction introduction

On 2026-07-04 19:18, olcott wrote:
> On 7/4/2026 7:43 PM, André G. Isaak wrote:
>> On 2026-07-04 18:33, olcott wrote:
>>> On 7/4/2026 7:23 PM, André G. Isaak wrote:
>>>> On 2026-07-04 18:08, olcott wrote:
>>>>> On 7/4/2026 6:57 PM, André G. Isaak wrote:
>>>>>> 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.
>>>>>>
>>>>>
>>>>> Tell me whether or not the numerical square root
>>>>> of a dead chicken can exist and why or why not.
>>>>> You must not start with any numerical value such
>>>>> as the weight of the dead chicken. You are only
>>>>> allowed to use its actual dead body.
>>>>
>>>> What does the above have to do with my claim that neither 
>>>> 'impossibly false' nor 'impossibly true' are English. 
>>>
>>> You did not seem to understand the meaning of the word impossible.
>>
>> You didn't use the word 'impossible'. You used the word 'impossibly' 
>> which is a different word. I understand the meaning of both perfectly 
>> well.
>>
>>>> In English, 'impossibly x' does not mean 'not possible to be x'. 
>>>> 'Impossibly' is an *itensifier* with a meaning of extremely. So 
>>>> 'impossibly true' would mean 'extremely true', which makes no sense 
>>>> since true is not a gradient concept.
>>>>
>>>>>>>> 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'.
>>>>
>>>> This question was the central point of my post and you have ignored 
>>>> it. I maintain that when you use the term 'necessary' your just 
>>>> tossing in a meaningless word for no reason. If you can answer the 
>>>> above question you will show me wrong.
>>>>
>>>
>>> The modal operators □ and ◊
>>>
>>> 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
>>
>> The modal operators don't *have* truth tables 
> I corrected this stipulative definition below.

Your definitions are not coherent.

> Validity and Soundness
> A deductive argument is said to be valid if and only
> if it takes a form that makes it impossible for the
> premises to be true and the conclusion nevertheless
> to be false. https://iep.utm.edu/val-snd/
> 
> Is corrected to mean
> A deductive argument is said to be valid if and only
> if it takes a form that anything besides true
> premises and true conclusion is invalid.
> 
> P □ Q means P(true) ∧ Q(true) is valid
> everything else is invalid.
> 
> P □ Q
> 0 0 0
> 0 0 1
> 1 0 0
> 1 1 1

That's simply the truth table for 'and'. It sheds no light on what it is 
your trying to convey by your use of 'necessity'. And the operator □ is 
already taken and is not a truth-functional operator so reusing it for 
something else is just plain stupid.

And snipping my question doesn't make it go away:

Can you give an example where (a) hold true but where (b) does not. An 
example from ordinary English is fine.

a) Q is a consequence of P
b) Q is a necessary consequence of P.

If you can't, your use of the term 'necessary' serves absolutely no purpose.

André

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