Re: William T. Parry gets rid of Disjunction introduction

On 7/6/2026 9:11 PM, André G. Isaak wrote:
> On 2026-07-06 19:57, olcott wrote:
>> On 7/6/2026 8:49 PM, André G. Isaak wrote:
>>> On 2026-07-06 19:24, olcott wrote:
>>>> 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) ⊢ ⊥
>>>
>>> Which is simply a way of stating that (x ∧ ¬x) proves that ⊥ is true. 
>>
>> Proving that falsum is true seems like proving
>> that small is large.
> 
> But that''s exactly what you wrote.
> 
>>> How is that not an explosion? I don't think you grasp what ⊢ or ⊥ mean.
>>>
>>
>> Explosion means that anything at all can be proved
>> from a contradiction. I stipulate the nothing at
>> all can be proved from a contradiction.
> 
> But that's not actually what you wrote. You really don't understand the 
> notation you are using.
> 

∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
        Γ ⊢ ⊥
--------------------
derivation terminated
	

> And you can't 'stipulate' what logic can or cannot do. What it can do 
> follows from the axioms of the system.
> 
> André
> 


-- 
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).