As mentioned before, ``Pat knows Mike's telephone number'' is written
We can write ``Pat knows Mike's telephone number is 333-3333''
where K(P,Q) is the proposition that denot(P) knows the proposition Q and Concept1(``333-3333'') is some standard concept of that telephone number.
The two ways of expressing knowledge are somewhat interdefinable, since we can write
Here asserts that A is a constant, i.e. a concept such that we are willing to say that P knows X if he knows it equals A. This is clear enough for some domains like integers, but it is not obvious how to treat knowing a person.
Using the standard concept function Concept1, we might replace (41) by
with similar meaning.
(41) and (42) express a denotational definition of Know in terms of K. A conceptual definition seems to require something like
where Concept2 is a suitable function from things to concepts and may not be available for all sorts of objects.