Well, it's the New Year, and time to get the discussion going. Thanks to Peter Dlugos for his comments of January 6th and his provocative challenge to see whether non-propositional representations can be used in philosophy outside the two areas (philosophy of science and aesthetics) that I originally suggested.
First, he is quite right to emphasise that I intend non-propositional representations as supplements, rather than wholesale replacements for propositional representations. (#3 - here references are to Dlugos's numbered sections). But sometimes you can't do without pictures. Think of the well-known Gestalt diagrams that are used as reasons (arguments?) for the thesis that perceptual data has to be interpreted by the cognitive agent, and is not directly given to us. This line of reasoning would be completely ineffective unless actual examples, such as the famous duck/rabbit diagram, were given to us pictorially. Propositional descriptions just don't do it and I think could not be persuasive in the way the actual diagrams are. The same holds for many optical illusions that are used to convince us that inference is often used in perception. Perhaps more controversially, consider the often hopeless impasse between those in the philosophy of mind who deny the relevance of qualia to cognitive processing and those who insist it is crucial. Thinking myself that the latter is obviously right, it often seems that propositional arguments are hopeless as a way to get the point across. You have to get the information processors' attention directly, by inflicting pain on them for example. Now electronic philosophy can't do that (yet) but it can present its position directly via colour and auditory qualia in an electronic exchange.
What about more abstract areas of philosophy, which Dlugos quite rightly suggests (#4) are inherently resistant to non-propositional representations. It should at least be pointed out that mere abstractness does not preclude pictorial representations. Take something simple like complex numbers, which are generally thought of as abstract. These can standardly be represented pictorially by two-dimensional spaces. In fact a whole range of abstract mathematical objects are given pictorial representations. So the question has to be - is there something special about the nature of abstract philosophical concepts that prevents them from being given a pictorial representation, or is it just a lack of creativity that has left the propositional modes as the only vehicle? Has anybody got any good examples from the history of philosophy. or even better, suggestions of their own?