# If unproven premises lead to a valid conclusion, could this be a coincidence?

Suppose that one has a bunch of unproven premises, which lead to a valid conclusion. Instead of this proving that the premises are true, could it be a coincidence that the conclusion is true, not dependent on the truth of the premises?

• You can prove 1+1=2 from the Continuum Hypothesis, so yes. Commented Feb 6 at 23:27
• There are quite a few issues here. When you say 'valid conclusion' do you mean that the argument is valid, or the conclusion is a valid sentence? And why would you be trying to prove the premises are true? The point of a valid argument is to prove the conclusion is true, provided the premises are. If you are asking can a valid argument have premises that are irrelevant to the conclusion, then yes. At least in classical logic. Commented Feb 7 at 1:45
• P1: If I am a wizard, the Sun rose this morning. P2: I am a wizard. C: The Sun rose this morning. Commented Feb 7 at 2:15
• Does this answer your question? Do premises need to be true?
– g s
Commented Feb 7 at 3:01

Premise 1: Socrates is a cat

Premise 2: all cats are greek philosophers

Conclusion: Socrates is a greek philosopher

Premise 1 and 2 are very unproven yet the conclusion is correct. So clearly, one can reach true conclusions with false premises.

Now, the exact probability that premises are wrong but coincidentally happen to lead to a true conclusion depends on each specific case, so it's difficult to give a general answer to your question, but it suffice to say that reasoning backward is unsound to warrant caution.

Actually, there is no shortage of example for people happening to be right for the wrong reason. It happens often that someone who makes a lot of poor predictions ends up being right once on a while. Political analysts and pundits are quite adept at this. Faith healers also come to mind.

• Probability does not exist mind independently. There is no such thing as “the exact probability that premises are wrong”. Commented Feb 7 at 13:26
• @Baby_philosopher so the probability that a a given atom of cesium 137 emit a beta particle depends on my thoughts about it? Commented Feb 7 at 13:32
• There is no “probability” for a given atom decaying. No one knows when a given atom of cesium 137 will decay. All we know is that historically, we have observed groups of atoms decaying at a constant rate. But we already have a term for that: it’s called historical frequency Commented Feb 7 at 13:37
• What is the historical frequency of a premise being true? Commented Feb 7 at 13:38
• @Baby_philosopher that you don't know the probability changes nothing to the probability itself. Also, "we don't know" is precisely my point so your objection is not only misguided but also irrelevant. Commented Feb 7 at 23:34