John, thanks for clarifying, I guess our perspectives are not so different as I thought. But I still think that Peirce's did not have to wait until 1911 to "integrate every aspect of his philosophy" with EGs; I think they co-evolved with those other aspects, philosophical problems being reflected in EGs and vice versa. In fact that's the main reason I'm taking a close look at EGs in the context of the Lowell lectures.
The direct quote I should have included as a statement of your position was from your Thursday post: "Among the implications: The sharp distinction between "formal logic", which is part of mathematics, from logic as a normative science and the many studies of reasoning in linguistics, psychology, and education." Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 3-Nov-17 15:02 On 11/3/2017 10:38 AM, <mailto:g...@gnusystems.ca> g...@gnusystems.ca wrote: > For you, formal logic is a branch of mathematics; for us, though... It's always a bad idea to make claims about anyone else's thoughts, contemporary or historical. It's best to quote their exact words. As for me, I completely agree with Peirce: formal logic is pure mathematics, normative logic is part of the normative sciences, applied logic is part of any system of reasoning in philosophy or any branch of science, and many aspects of logic may be studied by linguists, psychologists, and educational psychologists. > if EGs are relegated entirely to the realm of pure mathematics, we > lose the experiential element of their meaning. I completely agree. I would never say that. > This is why I don't find it helpful to consider the Lowell > presentation of EGs as merely a crude and confused form of more recent > developments in mathematics. I agree. I never said that. All I said is that the 1903 and 1906 versions were early stages in his way of thinking about EGs. They contained too much excess baggage that created obstacles in the "way of inquiry". By discarding the irrelevant details, the 1911 version enabled him to integrate every aspect of his philosophy. See "Peirce's magic lantern of thought" by Pietarinen: <http://www.helsinki.fi/science/commens/papers/magiclantern.pdf> http://www.helsinki.fi/science/commens/papers/magiclantern.pdf On p. 7, Pietarinen quotes from a later part of the letter to Kehler that contains Peirce's 1911 version of EGs. The following quotation begins with the part that Ahti quoted and continues with a bit more: > In great pains, I learned to think in diagrams, which is a much > superior method [to algebraic symbols]. I am convinced there is a far > better one, capable of wonders, but the great cost of the apparatus > forbids my learning it. It consists in thinking in stereoscopic > moving pictures. Of course, one might substitute the real objects > moving in sold space; and that might not be so unreasonably costly. > (NEM 3:191) I don't believe that it's an accident that Peirce mentioned 3D or even 4D (3D + time) in the same letter in which he introduced EGs. His 1911 semantics can accommodate such things in EGs. John
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