Assessing the Consequences

Peirce describes working with diagrams as follows:

"It is by manipulating on paper, or in the fancy, formulæ or other diagrams — experimenting on them, experiencing the thing. Such experience alone evolves the reason hidden within us and as utterly hidden as gold ten feet below ground — and this experience only differs from what usually carries that name in that it brings out the reason hidden within and not the reason of Nature, as do the chemist's or physicist's experiments." [CP 4.86]

He seems to have in mind the self-contained axiomatic diagrams, such as geometry or logic, and the "experimentation" he describes occurs within the diagram itself. It does not involve experience outside the diagram.  We might add new indices or relations to a map, to a steamboat pilot's knowledge, or to the sciences of chemistry and physics, but that would not be done working only within those diagrams.  It would be done by applying them to experience and measuring the inferences made against experience.  The diagram would be tied to experience both fore and aft as it were, and it is a peculiarity of axiomatic diagrams, not diagrammatic thinking in general, that they can cast off those lines and set sail.  And even having set sail, those axiomatic diagrams must be able to dock again, to measure their results against experience now and then.  Where there is an objective or axiomatic consistency on the input-side of diagrams, there is a consistency derived from assessing their inferences on the output-side.

This not to say diagrammatic thinking is necessarily experimental.  Any of Peirce's means of fixing beliefs — tenacity, authority, discussion, and/or experimentation — can be used to measure the consequences being inferred from a diagram, and thereby assess the diagram itself.  Even within the experimental means there are any number of criteria — truth, utility, beauty, goodness — that can be and have been applied.  This is just to say there is a measure in using the diagram that has a bearing on the structuring of the diagram itself.