XPost: sci.math, sci.logic, comp.theory

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

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