Arnold:
On Apr 29, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote:
In Vol IV
of the Collected Papers (and, I would guess, throughout the New
Elements of
Mathematics, a copy of Eisele's edition of which I would dearly
love to
get!) he goes to considerable lengths in exploring the role that the
mathematics of transitive phenomena plays in grounding higher-order
mathematical systems. Indeed, the importance of transitive
phenomena in
Peirce has recently been discussed briefly on the list. In short,
we may
well find that the very notion of a Symbol System involves
transitivities,
and that Peirce very thoroughly investigated this relation (as, of
course, =
a
species of the Logic of Relations!!).
Yes, I concur, the transitive relation is of utmost important in
continuous mathematics. But not necessarily in discrete
mathematics. Symbols may be used in either, often with belief in
"substitution" of numbers into variables.
The relations of a chemical bond create an ordering within a chemical
"word" but the chemical numbers are not transitive in the sense of
classical mathematics, ie, if a is greater than b, and if b is
greater than c, then a is greater than c. The table of elements uses
numbers in two senses, the vertical columns and the horizontal rows.
This well established fact lies at the heart of chemical logic, along
with electrical concepts. Indeed, one might say that chemical logic
is the logic of electricity.
I have read only a fraction of Peirce's works, often searching for
understanding on exactly how he fit his degree in chemistry into his
logic. Thus far, it appears more as an influence rather than a
basis. His use of drawing have some connection with the chemical
notion of functional groups or "chemical radicals." At this point in
time, much of medicine and biology is being rationalized, not in
terms of mathematics or physics, but in terms of chemical logic,
structures, and chemical symbols.
Thus, the open question to the list is, How does Peirce's work relate
to biology and medicine? Certainly some relation must exist, but how
is it expressed in symbols? Classes? Categories? Types? Subjects?
Objects? Predicates? Copula?
Cheers
Jerry
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