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

Exactitude is not truth.

The fact that a great many people believe something is no guarantee of its truth.

It is wrong for a man to say that he is certain of the objective truth of any proposition unless he can produce evidence which logically justifies that certainty.

intellectual capacity is no guarantee against being dead wrong.

[...] provability is a weaker notion than 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.

An urgent wish is no guarantor of a sound solution.

...the fact that a conclusion does not follow from its putative premise is not sufficient to show that it is false.

Le vrai peut quelquefois n'être pas vraisemblable.
(At times truth may not seem probable)

Seriousness is no more a guarantee of truth, insight, authenticity or probity, than humour is a guarantee of superficiality and stupidity.

[...] we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise, although most of the time these reasons cannot be known to us.

Widespread acceptance of an idea is not proof of its validity.

Reality is not always probable, or likely.