The Principle of Explosion is the Non Sequitur Error

peteolcott

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Aug 27, 2019, 12:27:23 PM8/27/19

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When-so-ever symbolic logic diverges from the deductive logical inference
symbolic logic errs. The Principle of Explosion is one place where symbolic
logic diverges from the deductive logical inference, thus the Principle of
Explosion is erroneous.

https://en.wikipedia.org/wiki/Formal_fallacy
The non-sequitur error occurs in every logical inference where the truth
of the conclusion does not depend upon the truth ALL of the premises.

https://en.wikipedia.org/wiki/Principle_of_explosion
The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ),
"from falsehood, anything (follows)", or ex contradictione (sequitur)
quodlibet (ECQ), "from contradiction, anything (follows)"), or the
principle of Pseudo-Scotus, is the law of classical logic, intuitionistic
logic and similar logical systems, according to which any statement
can be proven from a contradiction.

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Copyright 2019 Pete Olcott All rights reserved

"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

peteolcott

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Aug 27, 2019, 12:34:52 PM8/27/19

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On 8/27/2019 11:27 AM, peteolcott wrote:
> When-so-ever symbolic logic diverges from the deductive logical inference
> symbolic logic errs. The Principle of Explosion is one place where symbolic
> logic diverges from the deductive logical inference, thus the Principle of
> Explosion is erroneous.
>
> https://en.wikipedia.org/wiki/Formal_fallacy
> The non-sequitur error occurs in every logical inference where the truth
> of the conclusion does not depend upon the truth ALL of the premises.
>
> https://en.wikipedia.org/wiki/Principle_of_explosion
> The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ),
> "from falsehood, anything (follows)", or ex contradictione (sequitur)
> quodlibet (ECQ), "from contradiction, anything (follows)"), or the
> principle of Pseudo-Scotus, is the law of classical logic, intuitionistic
> logic and similar logical systems, according to which any statement
> can be proven from a contradiction.
>

Below is a formal proof of the principle using symbolic logic
Step Proposition Derivation
1 P Assumption
2 ~P Assumption
3 P V Q Disjunction introduction (1)
4 Q Disjunctive syllogism (2,3)

The error is at step 4 we are falsely assuming that P & ~P derives ~P
where in actuality P & ~P derives FALSE.

peteolcott

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Aug 27, 2019, 2:24:45 PM8/27/19

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On 8/27/2019 11:27 AM, peteolcott wrote:

> When-so-ever symbolic logic diverges from the deductive logical inference
> symbolic logic errs. The Principle of Explosion is one place where symbolic
> logic diverges from the deductive logical inference, thus the Principle of
> Explosion is erroneous.
>
> https://en.wikipedia.org/wiki/Formal_fallacy
> The non-sequitur error occurs in every logical inference where the truth
> of the conclusion does not depend upon the truth ALL of the premises.
>

https://www.thoughtco.com/what-is-a-non-sequitur-1691437
A non sequitur is a fallacy in which a conclusion does not
follow logically from what preceded it. Also known as irrelevant
reason and fallacy of the consequent.