Jerry, List,
The papers in CP 3&4 are some of the first works of Peirce
that I studied most intently from the late (19)60s on, and
they are a big part of what drove me back into mathematics
and grad school after a long detour through psychology and
philosophy, just so I could learn enough logic and math to
get a clue what Peirce was talking about. But having gone
through the rigors of that, I find that deciphering Peirce
is relatively easy, at least, compared to most other folks,
since a preponderance of the logic that mathematicians and
computer scientists actually use today is derived, however
waywardly and often without acknowledgement, from Peirce's
own formalisms and philosophy of notation.
Have to break for lunch, will try to get to the rest later.
Jon
On 2/13/2015 12:15 PM, Jerry LR Chandler wrote:
List, Jon:
Jon, a central problem of deciphering CSP logic of relatives
in assigning meaning to the terms he uses as compared to how
logic-mathematical terms are used today.
Your interpretations of his meanings are only one of many
possible meanings, and, as you are well aware, we often
differ on such matters.
Taking dual individual relatives, for instance,
we may arrange them all in an infinite block, thus,
A:A A:B A:C A:D A:E etc.
B:A B:B B:C B:D B:E etc.
C:A C:B C:C C:D C:E etc.
D:A D:B D:C D:D D:E etc.
E:A E:B E:C E:D E:E etc.
etc. etc. etc. etc. etc. etc.
In the same way, triple individual relatives
may be arranged in a cube, and so forth.
The table of pairs and triples of terms in THIS paper
are ORDER relations in a plane or cube.
The interpretation as a "set" is a reduction of meaning from "ordered symbols"
to "members of a set" (for example, Venn diagrams). Nothing wrong with such
a the reduction of meaning to a simpler meaning, it is just that it is
a different meaning.
The reason we differ is clear to me. I insist that CSP was educated as a
chemist
and that he would, THEREFORE, use a logic which was consistent with the logic of
chemistry as it was known in his time. Set theory is not adequate to represent
the polar opposites of electricity as used in the chemical dualism of mass and
electricity. During the period of 1860-1900, the logic of chemistry changed
dramatically and CSP notion of relatives also changed. Compare his use of
chemical terminology in the 1860/1870's with that in his long paper
C.S. Peirce (1897 Jan.), "The Logic of Relatives", The Monist, v. VII, n. 2 pp.
161-217.
The interpretation I gave is consistent with his usage of the term "relative"
in this paper in the discussion of the bonding of logical terms in a medad.
Perhaps we are merely looking at his changes of meaning of "relative" with time.
As the above paper shows, the transition of meanings of the term "relative" from
a chemical relative to a logical relative to a mathematical relative are subtle.
As mathematics is taught today, there are literally dozens of different meanings
for the notion of a "relation" as a logical operation. The reader of
mathematical
texts must select the logic operation signified by the term "relation" from a
set
of terms used in context of that text.
On a different but adjacent topic, it should be noted that the treatment of
the six ways to express the ORDER relation between three terms, A, B, and C,
is analogous to a general mathematical structure of a group. The order of
three of the six sentences express a group rotation operation on a triangle
and the other three sentences express a reflection in the plane. Thus, the
concept of a mathematical group provides simple logical diagrams to express
differences in the grammatical order of these "relative?" terms.
Cheers
Jerry
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