Maps: Assumptions Made

Maps are one of the most common, and intuitively understandable, instances of diagrams.  And, if you compare the aerial photograph of the region around my boyhood home on the left with a road map of the same region below, you can see a clear example of the abstraction involved with a diagram. As Peirce put it: Diagrams are "a skeleton representation of the relations concerned in the problem before the mind's eye in a schematic shape." [CP3.556]  The map, in this case, has abstracted, selected and simplified, the relationships (roads) between the indices (towns) for the purpose driving in the region. And, doing this requires certain assumptions; assumptions as to what is "important" if nothing else.

The tendency, however, is to take these assumptions for granted. Milton Friedman [in "The Methodology of Positive Economics"] writes:

"… to suppose that hypotheses have not only 'implications' but also 'assumptions' and that the conformity of these 'assumptions' to 'reality' is a test of the validity of the hypothesis different from or additional to the test by implications. This widely held view is fundamentally wrong and productive of much mischief. [p. 14]

We rarely can afford the luxury of a "test by implications," that is of actually applying the diagram and then finding out it didn't work. More often we need to make a judgment prior to using the diagram as to whether it is appropriate for the situation and our purposes. Even the road map above, as functional as it may be for driving, is missing important information and perhaps making other inappropriate assumptions for, say, hiking. The hiker using this diagram and leaving it to be tested solely by the inferences that can be made from it may find him or herself in a very difficult situation.

More generally, though, I think saying we should not be concerned with assumptions is to say we should no longer be concerned with philosophy. For philosophy — before it became the chauvinistic and sectarian thing it is today — was concerned with just that: the assumptions a diagram, a conceptual system, or a set of beliefs might make; what others assumptions could be made; and what alternative systems might then be possible. Philosophy at the turn of the century did not consider questions within a minute domain of specialization, limiting itself to calculations within a given diagram. Philosophy was the discipline that considered questions regarding diagrams in general.