The Ontological--Cognitive Representation Calculus

Volume One of: A Calculus of Representation.

This two-volume calculus of representation develops a framework carried since the 1980s: a notation that keeps what there is and how it is grasped on the page at the same time, instead of collapsing either into the other. The first volume sets the notation down, and finds it already present - unremarked, and six centuries apart - in Ockham and in Frege. The second sets it in motion, and asks what a record of an inquiry still holds once the inquiry has changed its mind.

They are taught apart, to different ends, by different people: Ockham on a thing and the concept that covers it, Frege on an object and the way it is given to us. The claim made here is that they are one failure seen from two sides.

Think of representation as a relation running from what there is to how it is grasped. Such a relation can fail to be a one-to-one correspondence in exactly two directions, and each direction already has a name. Fail in the first and you have a universal. Fail in the second and you have a sense. What this book builds is a notation that keeps both on the page at once instead of collapsing them into one - and it gives assertion a place of its own, as a third thing that is neither truth nor content.

It derives nothing. There is no proof system here and no transformation rules. What it offers instead is the ability to state ordinary difficulties that are otherwise merely reportable: the man who takes the morning star and the evening star for two different bodies, the reader gripped by a novel, the science that turned out to be wrong. The usual apparatus leaves two options - convict somebody of inconsistency, or let the object take the damage. A notation that separates the two places lets one say what happened.