[13] But it sometimes comes about that, when we have properly granted certain premisses, certain conclusions are derived from them that, though false, nonetheless follow from them. [14] What am I to do, then? Accept the false conclusion? [15] And how is that possible? Then should I say that I was wrong to accept the premisses? No, this isn’t permissible either. Or say: That doesn’t follow from the premisses? But that again isn’t permissible. [16] So what is one to do in such circumstances? Isn’t it the same as with debts? Just as having borrowed on some occasion isn’t enough to make somebody a debtor, but it is necessary in addition that he continues to owe the money and hasn’t paid off the loan; likewise, our having accepted the premisses isn’t enough to make it necessary for us to accept the inference, but we have to continue to accept the premisses.

...logical validity is not a guarantee of truth.

Just because an idea is true doesn't mean it can be proved. And just because an idea can be proved doesn't mean it's true.

But failure to disprove something is not a good reason to believe it.

No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavours to establish.

Just because something 'happens', because it is 'true', because the 'facts' are correct, does not ensure that it is the truth.

...no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish.

Just because a man has died for it, does not make it true.

If a conclusion is not poetically balanced, it cannot be scientifically true.

if you can’t prove something wrong, you can’t really prove it right either.

If I do not believe as you believe, it proves that you do not believe as I believe, and that is all that it proves.

Every conclusion supposes premises; these premises themselves either are self-evident and need no demonstration, or can be established only by relying upon other propositions, and since we can not go back thus to infinity, every deductive science, and in particular geometry, must rest on a certain number of undemonstrable axioms.

the futility of something is not always (in love and in politics) a sufficient argument against it.

It certainly is no proof that a man is inspired simply because he is right.