Talking about different forms (or maybe dimensions?) of knowledge as 'person-form', 'content-form', 'tool-form' seems rather like Aristotelian causality, where cause has a material-aspect, a formal-aspect, an agency-aspect and a purpose-aspect. Do these relate? If they do, then there's a line of thinking we can go down...
1. agency-aspect of causation <==> person-form of knowledge
2. material-aspect of causation <==> tool-form of knowledge
3. formal-aspect of causation <==> content-form of knowledge
4. purpose-aspect of causation <==> ??? purpose-form of knowledge ??? (what is knowledge for?)
I'm not sure about this. Maybe too abstract.
"To know something is to know what causes it" - Aristotle (in the Posteria Analytics)
I think if I'm pursuing a theory of 'double-description' of knowledge, then Aristotle basically says that to know a cause is to become aware of a number of descriptions of different aspects of cause. That seems similar to what I'm saying.
I would say "To know anything is to have a number of different descriptions of that knowledge."
Are the descriptions of knowledge the causes of knowledge?
Maybe. This is very hard stuff and my brain hurts slightly! (how do I know..?)
It's interesting to think about the 'purpose' of knowledge. Let's say, for example, that the purpose of knowledge is to 'do good'. How does that relate to the surgeon almost accidentally killing a patient? What we would say is that the language game the surgeon plays has an ethical dimension related to the purpose of what he or she does. This ethical dimension helps to coordinate the language game along with the other knowledge-forms.
Going back to the classroom where the surgeon might have learnt his skills (or rather the language game), the safer language games that the students play will be coordinated by the teacher of the surgeon who reveals a person-form of knowledge, uses a tool-form, and a content-form... against the background of a purpose-form? or an ethical-form? I wonder if this isn't to do with the authenticity of the teacher.
This is interesting because it means that we need to consider 'bad' teaching, 'bad' ethics and 'bad' knowledge...