Jerry,
Please explain what "chemical logic" may be, and how it relates if at
all, to mathematical logic on the one hand and whether it is not
somehow akin to the experimental logic of Mill or Dewey, or perhaps a
neurologically, electro-chemically based version of some sort of
psychologistic logic.
----- Message from [email protected] ---------
Date: Fri, 03 Feb 2012 21:30:44 -0500
From: Jerry LR Chandler <[email protected]>
Reply-To: Jerry LR Chandler <[email protected]>
Subject: Re: [peirce-l] review of Moore's Peirce edition
To: Irving <[email protected]>, [email protected]
Irving, List:
A belated reply to Irving's note on "Wissenschaften" and chemistry
and a few speculations about the origins of "logical rigor".
On Jan 27, 2012, at 7:32 PM, Irving wrote:
Jerry, Kirsti, list,
...
That being said, I for one suspect it is very much possible to
discuss logic and mathematics without bringing chemistry into the
discussion. For those interested in the axiomatization of
chemistry, or in employing group theory to study cristaline
structures, that of course is a different story altogether. But, as
a mathematician, I have no need to consider chemistry. My interest
in chemistry, as historian of mathematics extends only so far as
Cayley, Kempe, and Peirce were inspired by chemical diagrams to
treat logical relations graphically. ... But this is just my own
logico-mathematical orientation at play.
I certainly agree that nearly all mathematicians can do mathematics,
logicians can do logic and mathematical logicians can study the
history of logic without addressing the atomic numbers and the
particular graphic icons constructed by chemists to symbolize, index
and "icononize" material reality. Relative to the ancient history of
mathematics, the atomic number are not yet 100 years old and, of
course, the mathematics of molecular biology, now incubating in the
pregnant minds of biochemists, is yet to be fully born, although
biosemioticians are preparing to serve as midwives.
Further, I believe that academics have an inviolate obligation to
seek to answer the questions of interest to them (within the legal
confines of one's community.) I am reminded of a elderly
epidemiologist, who patiently explained to me that one expresses
one's personal values by WHAT one chooses to study and one's
professional values by HOW one studies it. Over the years, I have
audited about 2 dozen graduate level math courses; chemistry was not
mentioned in any of these, with one exception in a graph theory
class. Now, as a professional chemist, I know that chemistry is an
entangled mixture of mathematics and empiricism, grounded in the
atomic numbers and experimentation. I would add that the rigor of
chemical logic probably exceeds the rigor of mathematical logic
because chemists do not invoke irrational, transcendental, or
surrealistic numbers, chemists do not admit to imaginary numbers and
chemists demand proof in nature and as well in the mind. This is an
empirical logic or, better yet, a pragmatic logic that CSP understood
very well.
Within this framework, I study CSP's writings in search of a better
understanding of the relation between logic and chemistry, in search
of the encoding of chemistry in logic, and in search of the encoding
of logic in chemistry (the molecular neuro-sciences.) My
philosophical biases are well-known to regular readers of this list -
I am a hardcore realist.
My immediate goals have been strongly influenced by two colleagues -
category theorists Robert Rosen and Andree Ehresmann. Andree argues
that category theory is a suitable BASIS for mathematical biology /
complex systems theory (See "Memory Evolutive Systems" 2007?).
Robert Rosen spent an entire career studying his brand of molecular
biology, termed metabolic repair systems. Using category theory, he
concluded that formal mathematical logic LACKED the capacity to
symbolize natural systems. (See "Life Itself" 1991?)
The Rosen and Ehremann hypotheses are not exactly diametrically
opposed, but may be considered so for most practical purposes.
Through my participation in the Washington Evolutionary Systems
Society, I got to know both Robert and Andree as personal friends and
colleagues. These friendships fostered deep discussions of the
relationships between mathematics, logic and biology, more so with
Andree than Robert.
Thus, I come to CSP's writings with a trained eye on how and when the
sciences influence the works of a mathematician. The subtle
influences of chemical thinking AS IT STOOD in CSP lifetime, are
abundant in CSP writings. But, he wrote BEFORE the atomic numbers
were exactly measured and BEFORE the exact logical rigor of the
covalent chemical bond was established.
Thus, I ask, what prevents a formal theory of chemical logic that
would resolve the conundrums raised by the logics deployed by Rosen
and by Ehresmann? The importance of this question is twofold. A
formal logical theory of chemistry would be a significant advance in
understanding nature. Secondly, any formal theory of biology will be
derivative from a formal theory of chemistry. (This conclusion was
established experimentally by Watson and Crick about 60 years ago.)
It appears that to me that the concept of "formal" is entangled with
the pragmatic necessity to encode our thoughts into symbolic forms in
order to communicate. Thus, from a molecular biological perspective,
two forms of encodings are essential. One form (informed) from
atomic numbers to cellular dynamics. The second form, which I have
called exformative forms, motivates muscle actions (dynamic motions
of signal generation) that generate the symbolic expressions of logic
that are interpreted as "logical rigor".
Now to return to Moore's "Philosophy of Mathematics", I was pleased
with his descriptions of the selections he made, but rather
disappointed that he neglected to select those writings of CSP that I
consider the most important (from my biases, obviously.)
Cheers
Jerry
PS: BTW, I have often wondered if CSP's efforts to construct a
philosophy of continuity was not deeply influenced by his beliefs in
the individuality of atoms.
----- End message from [email protected] -----
Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info
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