Consider this real-life sentence:
- Once your dog knows what "sit" means, he will be happy to please you.
- The dog knows what "sit" means.
- The dog knows that "sit" means ....
Now it could be that this is something special about meaning, that we simply say that someone or something knows what something means provided simply that he, she or it grasps it, without him, her or its having to know any semantic proposition. But I've also toyed with the idea that when we say "x knows what/where/when n V" (where "n" is a noun and "V" is a verb), this should not be analyzed as attributing to x knowledge of the relevant proposition of the form <n V m>. (In the above case, n is a word and "V" is "means".)
Sam was Gettiered in his coming to believe that 9x8=72. His innumerate teacher was saying "7x10=70, and 9x8=70, too", and Sam heard it as "7x10=70, and 9x8=72." And Sam never acquired any other relevant evidence. Then Sam does not know that 9x8=72. But maybe we should say that Sam knows what 9x8 is. For it doesn't seem right to say Sam doesn't know what 9x8 is.
Or suppose Spike has just heard a genuinely powerful argument for external world scepticism. It hasn't made him lose his beliefs, but the argument provided a defeater for his knowledge. So Spike doesn't know he has ten fingers, though he correctly believes it. It doesn't seem right to say Spike doesn't know how many fingers he has (i.e., what the number of his fingers is, to put it in the form I used above).
There is another possibility. It could be that to know what/where/when n V does require knowing that n V m for an appropriate m, but that we use "doesn't know what/where/when" to indicate something stronger than the denial of this knowledge.
I am not very secure in my intuitions about Sam and Spike, actually.
