Re: William T. Parry gets rid of Disjunction introduction

On 2026-07-04 22:05, olcott wrote:
> On 7/4/2026 10:52 PM, André G. Isaak wrote:
>> On 2026-07-04 21:17, olcott wrote:
>>> On 7/4/2026 8:28 PM, André G. Isaak wrote:
>>>> Q is a necessary consequence of P
>>>
>>> seems best handled by
>>> https://en.wikipedia.org/wiki/Relevance_logic
>>> or Parry's Entailment Logic
>>>
>>> P □ Q
>>> 0 0 0
>>> 0 0 0
>>> 1 0 0
>>> 1 1 1
>>>
>>> Changes the notion of valid inference too much.
>>
>> It doesn't change anything. It's simply invalid since its not a well- 
>> formed truth table.
>>
>>> I myself simply leap all the way to the end and
>>> say that the full natural language semantic meaning
>>> must be encoded for both P and Q such that P ⊢ Q
>>> by semantic entailment specified syntactically.
>>> This is accomplished in a language such as CycL.
>>> https://en.wikipedia.org/wiki/CycL
>>
>> The above sheds no light on anything. In particular it doesn't clarify 
>> what you think the difference between entailment and necessary 
>> entailment is which is the question I have been trying to get you to 
>> address.
>>
>>
> 
> *This says the whole thing better*
> P ⊢ Q means: syntactic derivation implements semantic entailment encoded 
> in the language. The inference rules are syntactic rules that realize 
> semantic entailment. These are the only allowed inference steps. The 
> entailment rules depend on the represented domain.
> 
> Dogs are cats ⊢ Monkeys have wings // rejected

The topic under discussion was Q, which contains neither dogs, cats, 
monkeys, or wings.

Why don't you illustrate your claim with an actual example from 
arithmetic. Say, for example 9 × 5 = 45. What exactly would be the 
"semantic entailments encoded in the language" involved here?

André

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