Sunday, February 14, 2016

Truth in Diagrams

Diagrams are fictions:

"The artist introduces a fiction; but it is not an arbitrary one; it exhibits affinities to which the mind accords a certain approval in pronouncing them beautiful, which if it is not exactly the same as saying that the synthesis is true, is something of the same general kind. The geometer draws a diagram, which if not exactly a fiction, is at least a creation, …" [CP 1.383]

So how is it that these fictions can be true or false?  To answer that question I think we have to look Peirce's notion of a metaphor which he defined as "representing a parallelism in something else" [CP 2.277].

The diagram is built on an analogy with its object.  The diagram runs from that analogy and its applications to the consequences that can be inferred from it; and as a metaphor, if it runs "parallel" to the object and its interactions, the diagram would be true.  The parallelism must be maintained in three respects: (1) a realistic analogy, (2) consistent inferences, and (3) corresponding consequences.  Something similar, I would venture, is going on with art as well.

Anyway, the catch in all this is the object.  Is it the object in all the obscurity of it’s secondness?  Or, is it an object constructed, more or less articulated, in thirdness?  This is a problem with metaphors in general.  If we say “this person’s a wolf” what’s the object we have in mind?  The animal in the wild?  Or, have we seen one staring blankly at us in a zoo?  Or, perhaps, it's a conglomeration of encyclopedia entries, school courses, or fairy tales?  We have these denotations and connotations for “wolf,” but most of us have no referent, no direct acquaintance with the animal itself.  Thus, the thirdness of those denotations and connotations become the referent, the object, on which our understanding and use of “wolf” is based, and the whole thing becomes an exercise in analytic viruosity.  The virtue of science, but not all that calls itself “science”, is that it demands a direct contact with the secondess of the object, both in applying the diagram and in testing its consequences.