Re: William T. Parry gets rid of Disjunction introduction

On 7/6/2026 7:47 PM, André G. Isaak wrote:
> On 2026-07-06 17:40, olcott wrote:
>> On 7/6/2026 6:37 PM, André G. Isaak wrote:
>>> On 2026-07-06 16:53, olcott wrote:
>>>> On 7/6/2026 5:50 PM, André G. Isaak wrote:
>>>>> On 2026-07-06 16:36, olcott wrote:
>>>>>> On 7/6/2026 5:15 PM, André G. Isaak wrote:
>>>>>>> On 2026-07-06 15:54, olcott wrote:
>>>>>>>> On 7/6/2026 3:20 PM, André G. Isaak wrote:
>>>>>>>>> On 2026-07-06 14:04, olcott wrote:
>>>>>>>>>
>>>>>>>>>> ⊥  ⊢ ⊥ no explosion.
>>>>>>>>>
>>>>>>>>> Of course that's an explosion. It says that ⊥ demonstrates that 
>>>>>>>>> ⊥ is true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> That you do not know what explosion is is not my mistake.
>>>>>>>> I thought that one of you two guys had a PhD in math
>>>>>>>> is that you or Alan?
>>>>>>>
>>>>>>> I do know what explosion is in the context of logic. Apparently 
>>>>>>> you do not. And I've never claimed to have a doctoracte in maths. 
>>>>>>> My background is in linguistics.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> You are flat our wrong about explosion.
>>>>>
>>>>> No. You claim that ⊥  ⊢ ⊥ which is to say that ⊥ can be derived 
>>>>> from ⊥. But in a consistent logic, ⊥ shouldn't be derivable from 
>>>>> *anything*. The 
>>>>
>>>>
>>>> It is not explosive, full stop you are wrong.
>>>
>>> You're really not qualified to make such a claim.
>>>
>>> André
>>>
>>
>> Define in your own words what you think that deductive
>> explosion means.
> 
> Odd that you should ask such a thing since you rarely if ever respond to 
> requests for you to explain things in your own words and instead post 
> links to wikipedia pages.
> 
> deductive explosion occurs when contradictory premises are introduced 
> into an argument therefore allowing anything, including false statements 
> to be derived.
> 
> You offered ⊥  ⊢ ⊥
> 
> ⊥ is the logical symbol representing a falsehood or contradiction. You 
> are therefore deriving a falsehood or contradiction which shouldn't 
> happen. The only reason you were able to do this is because your premise 
> was ⊥. That's explosion.
> 
> André
> 

OK good. I am stipulating that from contradiction only
falsum follows and from falsum only falsum follows
cutting off the legs of explosion.

∀x (x ∧ ¬x) ⊢ ⊥

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).