Young children seem to overextend a 'seeing = knowing rule' so that they neglect to notice that people gain knowledge from inferring as well as from seeing. Yet that cannot be a sufficient explanation of children's problems with conceptualizing knowledge, because rule underextension occurs in children's claims to know something that they have not seen (nor inferred). The two errors were studied together with pairs of children aged 4 and 5 years. Each child had their own box, items on the table were shared out into the boxes, and either both children, or neither, or one of them, looked in their own box. Children were asked if they and the other knew what was in each other's box; and were asked for explanations and predictions. About a quarter of the children showed full competence. In others, overextension and underextension occurred; yet almost all children explained that inference was involved in knowing, without bias towards giving such explanation more for self than for other. Error patterns were not predictable from a test for understanding the term 'know'. It is suggested that children have a framework conception of 'knowing' in which another's mind is treated as similar to own mind, but problems arise in implementing that insight before children manage to conceptualize constraints on knowledge.