- Care to make any of this more precise?
[The above] formula, for example?
Yes, it will take some care to make it all more precise, and I’ve cared enough to work on it when I get a chance. I initially came to Peirce’s 1865–1866 lectures in grad school from the direction of graph-&-group theory in connection with a 19th century device called a “table of marks”, out which a lot of work on group characters and group representations developed.
A table of marks for a transformation group is an incidence matrix with in the cell if fixes and otherwise. I could see Peirce’s formula was based on a logical analogue of those incidence matrices so that gave me at least a little stable ground to inch forward on.
The development of Peirce’s information formula is discussed in my ongoing study notes, consisting of selections from Peirce’s 1865–1866 Lectures on the Logic of Science and my commentary on them.