Certainty

Certainty, as an intentional state, must be attributed to interlocutors whose participation in the conversation includes "I am certain that ...".  It may be provisionally attributed, with the relevant Kripkean caveats, to other things and people to which/whom we find it practically necessary to attribute intentional states.

A completely private state of certainty is as unintelligible as a completely private conception of the meaning of "I am certain".  So, therefore, must a completely private state of being certain and correct be unintelligible.

This might be quite a disturbing idea to anyone drawn to philosophy as a cure for paranoid anxieties about the reliability of their interlocutors.

It is also catastrophic for any program of constructing epistemological fundamentals from private experiences.

However, it does allow a perspective on some of what is involved in actually being certain and correct:  Someone who says something correct, but is not certain about it, cannot fully understand what it is that they have said.  If I said "I believe it is the case that ~(p&~p), but I'm not sure", then I could not be said to understand the law of non-contradiction.