Ediwina, Jon AS, Jeff JBD, List
I changed the subject line to clarify and emphasize the distinction. ET: the distinction between pure and applied mathematics is very fuzzy. I'd suspect it's the same in phenomenology. But I do support and agree with [Jeff's] agenda of using both mathematics and phenomenology to function within a pragmatic interaction with the world. For both subjects, the distinction is precise. JAS highlighted Peirce's distinction, which applies to both mathematics and phenomenology: JAS: It is incontrovertible that according to Peirce in CP 3.559 (and elsewhere), the mathematician frames a pure hypothesis without inquiring or caring whether it agrees with the actual facts or not. Yes, of course. That distinction is the greatest power of mathematics: it is independent of whatever may exist in our universe or any other. It gives us the freedom to create new things that never existed before. The only constraints are physical, not mental. That point is also true of phenomenology. For both fields, there is no limitation on what anyone may imagine -- or on what anyone may invent. As an example, consider the game of chess. Before anyone carved the wooden pieces, the rules of chess were the axioms of a pure mathematical theory, for which there were no applicable facts. But then, somebody (or perhaps a group of people) imagined a kind of game that did not yet exist. They discussed the possibilities, debated various options, and finally agreed to the axioms (rules) and the designs for physical boards and pieces. Before they played the game, there were no facts that corresponded to the mathematical theory or to anybody's perceptions. The tests of existence and accuracy are determined by the normative sciences, especially methodeutic. For inventions, the only limitations are the available physical resources to construct them. JBD: For my part, I'd like to get clearer on how the pure phenomenological theory is supposed to support and guide the applied activities--such as the activities of identifying possible sources of observational error, correcting for those errors, framing productive questions, exploring informal diagrammatic representations of the problems, measuring the phenomena, formulating plausible hypotheses, and generating formal mathematical models of the hypothetical explanations. Those issues depend on the normative sciences, especially methodeutic. The special sciences depend on phenomenology for the raw data and on mathematics for forming hypotheses. Then they require the normative sciences for testing and evaluating the hypotheses. In pure math, the variables do not refer to anything in actuality. In applied math, one or more of the variables are linked (via indexes) to something that exists or may exist in actuality. Those indexes are derived and tested by methodeutic. John
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