Stephen CR, Gary F, and Kirsti, I also received some offline comments, which I'll start with. And I'm including a slightly revised copy of CSPsciences.jpg.
Anon
Might it be useful to label/annotate the relationships and have a legend which describes the motivations behind the divisions via the labels?
Certainly. That diagram shows the top level of the classification. The dotted lines show the dependencies Peirce mentioned. But it's very hard to squeeze more detail into the interstices. It took me several iterations to find a way to minimize the line crossings. As an overview, I'd recommend that diagram (or something like it). But I'd draw more detailed diagrams for each of the three branches. Anon
Why did you put logic in two different locations?
In EP 2.259, Peirce wrote "Mathematics may be divided into (a) the Mathematics of Logic, (b) the Mathematics of Discrete series, and (c) the Mathematics of Continua and pseudo-continua." But in EP 2.260, he wrote "Logic is the theory of self-controlled, or deliberate, thought; and as such, must appeal to ethics for its principles." That distinction is critical, but it's buried in a mass of verbiage. The diagram highlights the distinction. Anon
Why did you include informal theories in mathematics?
In the mathematical branch, there are so many modern versions that I lumped them all in "Formal Theories". I also added "Informal Theories" to emphasize the point that formalism is not a prerequisite for the "diagrammatical reasoning" in mathematical thinking. Modern mathematicians, in fact, sometimes emphasize that premature formalization can be an *obstacle* to discovery -- because it may force thought into channels that distract attention from the central problem. George Polya's _How to Solve It_ is a good example. Stephen
My own effort... leads me to elevate ethics and aesthetics from their lower place and turn them into the second and third elements of a root triad (icon index symbol) which I term Reality Ethics and Aesthetics in that order.
I sympathize. Normative science deserves a more prominent role in philosophy teaching and research. It certainly deserves more attention. But in that diagram, I wanted to show that mathematics and phenomenology are the only two sciences that do not depend on any other sources. Normative science depends on them. Gary F.
If I made any kind of logic a branch of mathematics, I'd call it "formal logic" as Peirce did...
Good point. I made that change in CSPscience.jpg. The quotation from the "Minute Logic" (CP 4.240) is important. It should be cited in any discussion of the classification. As far as I know, Peirce never used to term 'informal mathematics'. I realize that diagrams, for Peirce, embody forms (icons). But modern mathematicians would call his diagrammatical reasoning informal. I used the term 'informal theories' as a "sop" to the Cerberus that guards the halls of mathematics. Gary
I think at the very top I might put "Inquiry" instead of "Knowledge," but it's not a change I'd fight for.
In my first version, I put "The Sciences" at the top. One reason why I chose 'knowledge' is that I plan to use the diagram for some discussions in Ontolog Forum, where most people know very little about Peirce. But 'knowledge representation' is a common term. Peirce thought in diagrams, and it's a pity that he didn't draw more to illustrate his own writings. CSPsciences.jpg is just one. But many more would be useful to highlight other aspects. Kirsti
Which cycle do you mean, John? I was talking about cyclical arithmetic
I was discussing the cycle of reasoning in Peirce's logic of pragmatism. The diagram of that cycle appears as Figure 7 on page 31 of http://www.jfsowa.com/pubs/signproc.pdf . This is another example of the way Peirce could have used diagrams to clarify his explanations. It's a pity that Ogden and Richards, not Peirce, are always cited for "the meaning triangle". John
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
