John, Jeff, List, We seem to have consensus that Peirce's phenomenology makes observations based on direct experience and draws upon mathematical principles to analyze whatever appears into its elements, to arrive at a very general theory which he calls the "Doctrine of Categories." Without mathematics, it could accomplish nothing; without experience, it would have nothing to apply mathematical principles to, and again would accomplish nothing.
Logic as semiotics inherits this characteristic form from phenomenology in the form of the Dicisign, as Frederik Stjernfelt has shown in Natural Propositions: iconic signs, often diagrammatic, must be combined with indexical signs in order to convey information - the icons signify the form, and the indices the subject matter of the informational sign, i.e. the identity of its object. I think John's account below is one expression of this consensus. But there is one point in it that I must take issue with. John says, "The special sciences depend on phenomenology for the raw data and on mathematics for forming hypotheses." But we have previously agreed that in Peirce's hierarchy of sciences, each science depends on those above it for principles, while the higher levels can and often do get their raw data from those below. Since phenomenology is above the special sciences in the hierarchy, they should be drawing theoretical principles from it, not "raw data." I believe that this is indeed the case, and gave an example above of how semiotics "inherits" categorial principles from phenomenology. On the other hand, since phenomenology/phaneroscopy observes anything that can appear "to the mind," it can draw some "raw data" from special sciences. But what makes phaneroscopy distinctive, and places it before everything in the hierarchy of sciences except mathematics, is the kind of attention it deploys in its observations. "Its task requires and exercises a singular sort of thought, a sort of thought that will be found to be of the utmost service throughout the study of logic" (CP2.197). As Peirce says to James in the 1904 letter previously quoted, "Psychology, you may say, observes the same facts as phenomenology does. No. It does not observe the same facts. It looks upon the same world; - the same world that the astronomer looks at. But what it observes in that world is different." Phenomenological observation is, we might say, looking for the mathematical essence of experiencing itself. It can do this because it does not draw upon any theoretical framework developed by the later sciences such as semiotic or astronomy. D.S. Kothari says "The simple fact is that no measurement, no experiment or observation is possible without a relevant theoretical framework." What sets phenomenology apart from (and above) all other positive sciences is that the only theoretical framework it employs is from mathematics, and a very pure kind of mathematics which is free of any prior application to normative or special sciences. For instance, it employs "dichotomic mathematics," (which Peirce referred to as "the simplest mathematics") to arrive at the concept of Secondness, which is the basis of the subject/object distinction in philosophy of mind; and Peirce was clear that phenomenology does not assume this distinction but reveals its experiential basis by applying that mathematical framework. If any scientific observation could be called "phenomenology" - which seems to be John's idea in what he has said up to now about phenomenology/phaneroscopy - there would be no need to practice it as the "primal positive science", as Peirce called it. This is the one point where I think John's description below needs to be modified. Gary f. From: peirce-l-requ...@list.iupui.edu <peirce-l-requ...@list.iupui.edu> On Behalf Of John F. Sowa Sent: 28-Aug-21 20:28 To: peirce-l@list.iupui.edu Subject: [PEIRCE-L] Pure math & phenomenology (was Slip & Slide 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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