Edwina, Gary F, List,
ET: Thank you for this excellent post... I'd like to note that I think a key problem with the arguments over 'where does mathematics or phaneroscopy fit into this process' is the old issue of the differentiation of Mind and Matter and their relations. ET: I feel that De Tienne separates the two in a Cartesian method - and slots each into a separate time and place. But Peirce, with his hylomorphic synechism doesn't separate the two and therefore, the one is always informing and analyzing the other. I think the quotes and outline you have provided show this quite clearly. The other issue is HOW Mind portrays our world to us - and your answer is: diagrams. That's a separate issue...and well argued by your comments. Those are important issues, which Peirce had resolved in a way that is consistent with Aristotle's response to Plato. Mathematical forms are real in the sense that they are independent of anything that anybody may think about them. The forms (or diagrams that represent them) are discovered, not invented by mathematicians, but they exist in actuality only when embodied. That embodiment may be on paper, in a computer, or in our neurons. GF: why [do] you bother to repeat all this, since its all been said before and nobody has questioned any of it. The only question I have is why you insert phaneroscopy in your new subject line, as there is nothing in the entire post about phenomenology/phaneroscopy in particular, because there is nothing in it that differentiates phaneroscopy from Peirce's thought in general. First, I am delighted that we all agree on the central role of diagrams in Peirce's thought. But Gary R did question it by accusing me of putting too much emphasis on diagrams -- because, as he said, diagrams are the foundation of my research on conceptual graphs. I wanted to emphasize that I learned the importance of diagrams from Peirce. GF: Its a good summary of the role of diagrams in Peirces thought, but it does nothing to explain the unique role of phaneroscopy in his classification of sciences or in his philosophy. Second, I wanted to emphasize that the central role of phaneroscopy is the transition from experience to diagrams. Contrary to ADT's slide 25, there is no transition out of mathematics, since diagrams can (a) relate experience to any pattern or structure of any branch of science or common sense, (b) allow mathematics and formal logic to be applied to any and every representation of 1-ness, 2-ness, and 3-ness, and (c) furnish all the data required for the normative sciences to evaluate the truth or relevance of hypotheses (guesses) to other diagrams from memories, reading, or dialogues with other people. GF: What does make [phaneroscopy] unique is precisely the subject of the current slow read of ADTs slides. Third, I have read each of the slides from ADT's original and from each of the transcriptions. I believe that he has made many important points. But as I showed about slide 25, he could have made his presentation more precise and more general if he had recognized the role of diagrams. In short, phaneroscopy is the process of mapping experience to diagrams that can be interpreted by all later sciences. The normative sciences evaluate them by the criteria of esthetics, ethics, and truth. Finally, ADT's phrase "the rest of us" suggested that Peirce's mathematics is inadequate to support common sense. Yet every textbook from elementary school to the most advanced research is illustrated with diagrams, which could be mapped to and from EGs. In particular, the diagrams that linguists use to represent the syntax and semantics of ordinary languages have a direct mapping to and from EGs. I also believe that some kinds of diagrams can even represent the exotic languages that Dan Everett has studied. For reference, I put the nine quotations from my previous note and my nine brief summaries in the file http://jfsowa.com/peirce/diagrams.txt John
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