Can Deduction for a Valid Argument produce the wrong conclusion?
In classical logic, intuitionistic logic and similar logical systems, the principle of explosion... 'from contradiction, anything [follows]' https://en.wikipedia.org/wiki/Principle_of_explosion
The Principle of Explosion (show below) is stipulated to be valid inference even though (when translated into a syllogism) is the non-sequitur error.
Socrates is a man.
Socrates is not a man.
Therefore, Socrates is a butterfly.
The conclusion does not follow from the premises, thus the non-sequitur error.
To eliminate this issue we can redefine a valid argument as:
An argument is deductively valid iff the conclusion is a necessary consequence of all of its premises. (This makes every argument with contradictory premises invalid).
© 2024 polcott