Robert M, Gary F, List, Before saying anything else, I'll remind everybody of two points: (1) theorematic reasoning is a special case of diagrammatic reasoning. (2) In Peirce's classification of the sciences, there is a two-way flow of information: every science (including every branch of philosophy) depends on mathematics for its methods of reasoning, and mathematical discovery is inspired by patterns found in all the special sciences. I strongly agree with Robert about the following quotation: CSP> "mathematics meddles with every other science without exception. There is no science whatever to which is not attached an application of mathematics..." (CP 1.245) GF> The relevance to John's original post, as i see it, is this: if theorematic reasoning is only a mathematical procedure, it leaves out the experiential element of Peirce's methodology and his pragmatism. I want to include everything. I cited Eisele's article because she was emphasizing the same points as Robert. And she would certainly agree with CP 1.245. Re imaginary vs actual: Diagrammatic reasoning applies to all experiences in the phaneron in exactly the same way. The past is known only by memory, which is notoriously error prone. The future is imaginary until the instant it becomes actual. And the present is fleeting. Therefore, any kind of planning for the future (including the very next step anyone is about to perform) involves a mixture of memory, perception, and imagination. Any diagrammatic reasoning about causality would relate perception (actual) and memory (past) to an action (imaginary future). As Peirce said many times, the meaning of any general is a would-be -- in the imaginary future. John
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