I once asked whether we only believe statements when we think of them. Now I am asking a similar but different question, about knowledge rather than belief. Do we only know statements when we are actively thinking of them?
It seems that in an orthodox sense or use of 'knowledge' it is not the case that we only know statements - know that specific statements are true - when and while we are thinking of them.
On an orthdox view:
there are numberless things that I know, such as that there are Maoris in New Zealand, or that Plato wrote the Phaedo, which at any given time lie unconsidered in my memory. I have the knowledge, but it lies dormant, though ready for use. At any time during the waking day it might be brought to mind, with understanding and assent, and then it is no longer dormant: what was there potentially is now actualised. (Justin Gosling, 'Mad, Drunk or Asleep?: Aristotle's Akratic', Phronesis, Vol. 38, No. 1 (1993), pp. 98-104: 98.)
It might be better to say that we do not cease to know that S is p - know the truth of that statement - when and while the statement is not present to mind but rather that our knowledge of the truth of the statement on such occasions is dormant or latent.
If we reject this, we face a problem. To hold that we cease to know when we cease to think creates the following difficulty. Suppose I know at t1 that S is p - I know the truth of this statement. Suppose also that at t2 I am asleep and am not thinking of the statement. If we say that because I am not thinking of it, I do not know it - my knowledge has passed out of existence - then how are we to explain that on waking at t3 I again know that S is p, that I know the truth of this statement? If my knowledge has passed out of existence at t2 how can it pass back into existence at t3?
Put the point like this. At t3 my knowledge has come into existence ex nihilo. This is because (a) my knowledge at t1 is irrelevant to explain, and can certainly have no causal or other continuity with, my knowledge at t3 since my knowledge at t1 has no existence; and because (b) my knowledge cannot ex hypothesi derive from t2 since this was when and while I was not thinking of the relevant statement. Ex nihilo can be rejected only if we can introduce some knowledge-creating factor that supervenes at t3. But what could this be?
On these grounds I am reluctant to accept that we know statements - know that they are true - only when we think of them.