No matter how good the logic may be, you cannot rely on an argument which has certain falsity built into it. For a sound argument true premises are needed, as well as valid logic. The problem with contradictory premises is that they cannot both be true. If one is true, the other must be false, and vice versa. In other words, we can be certain that at least one of them must be false, and cannot therefore generate a sound argument.
Everything is mortal, and God is not mortal, so God is not everything.
(This might look like an argument against pantheism, but it is in fact an argument against common sense. Since the premises contradict each other, one must be false. This makes any conclusion unreliable.)
The fallacy is an interesting one because it permits the logic to be valid. It usually amazes non-logicians to hear that with inconsistent premises any conclusion, no matter how irrelevant, can be validly inferred. Logicians, however, do not use the word ‘valid’ to mean ‘sound’, If there is known falsity built in, as there must be with contradictory premises, then it matters not how good the logic is: the argument is not sound.
This is the fallacy which enables us to prove that the moon is made of green cheese. The proof is quite complicated, but quite fun:
We are given two premises, that milk is white, and milk is not white. If ‘milk is white’ is true, then it is also the case that ‘Either milk is white or the moon is made of green cheese’ is true. (This is correct.) Since we are also given that milk is not white, the second alternative must be true, namely that ‘the moon is made of green cheese’.
There is nothing wrong with the logic. The known falsity in the contradictory premises can be used to establish anything, including a rather smelly satellite.
It is difficult to use the fallacy of contradictory premises in everyday argument, because your audience will normally see that you are contradicting yourself. What you can do, however, is to use contradictions which are normally accepted in loose speech, and proceed to wrap them up in tight logic.
He’s a real professional[ but a bit of an amateur at times.
(It sounds acceptable enough, but remember that from it you can literally prove that the moon is made of green cheese.)
The above article is from the book How To Win Every Argument by Madsen Pirie. The article is only for educational and informative purposes to explain and understand formal logic and logical fallacies. It is a great book, definitely worth a read!