Note. More drafty thoughts I’ll need to air out over the next few days.
The reader may share with the author a feeling of discontent at this juncture, attempting to reconcile the formal intentions of this inquiry with the cardinal contentions of experience. Let me try to express this difficulty in the form of a question: “What is the nature of the bond between form and content in experience, between the abstract formal categories and the concrete material contents that exist in experience?”
Here is the tentative answer that I will entertain, seeking to test its usefulness in this work. I take there to be a primitive category of “form-in-experience” that presently lacks a compact name but that from the standpoint of a given agent often passes from the “structure of experience” to the “experience of structure”.
My personal definition of mathematical understanding has long been expressed in the chiasmatic figure of speech: “the form of experience and the experience of form”. This is not the place to argue for the virtues of this concept, but I thought it would clarify a few points to share it here.