Re: review of Moore's Peirce edition

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 jerry_lr_chandler <at> mac.com ---------
    Date: Fri, 03 Feb 2012 21:30:44 -0500
    From: Jerry LR Chandler <jerry_lr_chandler <at> mac.com>
Reply-To: Jerry LR Chandler <jerry_lr_chandler <at> mac.com>
Subject: Re: [peirce-l] review of Moore's Peirce edition
      To: Irving <ianellis <at> IUPUI.EDU>, PEIRCE-L <at> LISTSERV.IUPUI.EDU

> 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 jerry_lr_chandler <at> mac.com -----

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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