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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

Can Deduction for a Valid Argument produce the wrong conclusion?

The Principle of Explosion (show below) is stipulated to be valid inference even though (when translated into a syllogism) it is the non-sequitur error.

Proposition A is True.
Proposition A is False.
Therefore B
https://en.wikipedia.org/wiki/Principle_of_explosion

Translated into a syllogism:

All A are True
No A are True
Therefore B

It is categorically impossible to show
(a) That the above translation is incorrect.
(b) How the above two categorical propositions entail B.
https://en.wikipedia.org/wiki/Categorical_proposition

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

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

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

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

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