Argumentum ad Logicam

"The Fallacy Fallacy"

Argumentum ad logicam basically says that, even though an arguer uses a false or faulty argument to try to prove a premise, their argument could still be correct. 

Also known as "The Fallacy Fallacy," this lapse in logic uses the following form:

Argument A for the Conclusion C is false; therefore, Conclusion C is also false. 

Honestly, the argument can be 100% wrong even though the conclusion remains correct.

All Birds Can Fly

Example:

PERSON 1: "All crows are birds. All birds can fly. Therefore, all crows can fly."

PERSON 2: "Wait, ostriches are birds, and they can't fly. Because your logic is faulty, so is your conclusion. Clearly, crows can't fly."

Example: 

Alternate-Universe Galileo: The Earth revolves around the Sun because the Earth is trying to hide from the Moon." 

If he had said this, he would've been correct that the Earth revolved around the Sun but incorrect in his reasoning. Regardless of how disastrous his logic was, it can't override the factual conclusion. It would be fallacious of anyone to argue that the Earth doesn't revolve around the Sun because Alternate-Universe Galileo used faulty logic to determine that it does so.

Example: 

For centuries, it was believed by mathematicians that the proposition known as "Fermat's last theorem" was true, yet it took over 300 years for anyone to actually prove it. In the meantime, many invalid arguments were presented for it. If the conclusion had been dismissed simply because nobody could figure out the logic for why it was true, we'd be missing out on the truth.

They were right, they just struggled to logically explain why. Their struggles still didn't make the conclusion wrong.