CORRECT REASONING DERIVES TRUTH
When-so-ever truth preserving operations are applied to an initial set
of expressions of (formal or natural) language derive another expression
of language as a necessary consequence then reasoning is correct.

Furthermore when-so-ever the above process is applied to an initial set
of expressions of (formal or natural) language that are known to be true
(such as Haskell Curry elementary theorems) then we know that the
derived expression of language is true.
https://www.liarparadox.org/Haskell_Curry_45.pdf

Each of the two paragraphs above constitute proofs in correct reasoning,
they are comparable to valid argument and a sound argument in deductive
inference. Anything that diverges from the above model is not construed
as a proof in correct reasoning.

Correct reasoning differs from deductively valid inference in that the
conclusion must be a necessary consequence of its premises, thus the
principle of explosion is not allowed.

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. Otherwise, a deductive argument is said to be
invalid.

A deductive argument is sound if and only if it is both valid, and all
of its premises are actually true. Otherwise, a deductive argument is
unsound. https://iep.utm.edu/val-snd/

Principle of explosion
In classical logic, intuitionistic logic and similar logical systems,
the principle of explosion (Latin: ex falso [sequitur] quodlibet, 'from
falsehood, anything [follows]';
https://en.wikipedia.org/wiki/Principle_of_explosion

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

On 3/10/2022 8:29 AM, olcott wrote:
> CORRECT REASONING DERIVES TRUTH
> When-so-ever truth preserving operations are applied to an initial set
> of expressions of (formal or natural) language derive another expression
> of language as a necessary consequence then reasoning is correct.

Shut up moron.

On 3/10/2022 6:53 PM, Richard Damon wrote:
> On 3/10/22 11:29 AM, olcott wrote:
>> CORRECT REASONING DERIVES TRUTH
>> When-so-ever truth preserving operations are applied to an initial set
>> of expressions of (formal or natural) language derive another
>> expression of language as a necessary consequence then reasoning is
>> correct.
>>
>> Furthermore when-so-ever the above process is applied to an initial
>> set of expressions of (formal or natural) language that are known to
>> be true (such as Haskell Curry elementary theorems) then we know that
>> the derived expression of language is true.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>> Each of the two paragraphs above constitute proofs in correct
>> reasoning, they are comparable to valid argument and a sound argument
>> in deductive inference. Anything that diverges from the above model is
>> not construed as a proof in correct reasoning.
>>
>> Correct reasoning differs from deductively valid inference in that the
>> conclusion must be a necessary consequence of its premises, thus the
>> principle of explosion is not allowed.
>>
>> 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. Otherwise, a deductive argument
>> is said to be invalid.
>>
>> A deductive argument is sound if and only if it is both valid, and all
>> of its premises are actually true. Otherwise, a deductive argument is
>> unsound. https://iep.utm.edu/val-snd/
>>
>> Principle of explosion
>> In classical logic, intuitionistic logic and similar logical systems,
>> the principle of explosion (Latin: ex falso [sequitur] quodlibet,
>> 'from falsehood, anything [follows]';
>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>
> My first thought on this is you have hamstrung your logic with this
> restriction and won't be able to build logical deductions.
>
> If A -> B is only an acceptable deduction of B necessarily follows from
> A, this implies that if Not A is True, that B can not be True either.
>
> Thus proving A -> B is a valid inference rule requires either proving A
> or proving A <-> B (B is true, if and only if A)
>
> My guess is this means your logic system will become mostly just a toy.
>
> Feel free to try to actually PROVE that you can build an actual reach
> logic system with this rule.

My response to you has been posted in sci.logic

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer