List, Jeff, Jon, Ben, Clark:
Jeff’s questions are well-posed. It seems to me that the logic of the
questions, from a physical-chemical perspective of the 21 st Century, is rather
straight forward. Without going into any detail, this question is closely
related to the reasons that I have devoted several years of work in developing
the perplex number system to describe the “Carnap'ian” physical functors for
the logic of chemistry and biology. In the CSP quote, the underlying
linguistic issue is how are meanings related to signs of “the atomic weight of
oxygen” and time? In the 1930’s, Carnap crisply distinguishes the concept of
a Proper Name from a position in an ordered sequence. Clearly, “Oxygen” is a
proper name and time is an ordered sequence. (see: The Logical Syntax of
Language, 1937, pages 11-35.)
Clark, this post may provide you some clues on how the perplex number system is
related to physical foundations of the theory of perplex systems / quantum
chemistry.
> On Feb 25, 2017, at 12:31 AM, Jeffrey Brian Downard <[email protected]>
> wrote:
>
>>> JD: I'm wondering if anyone can explain in greater detail what Peirce is
>>> suggesting in this passage in making the comparison between the atomic
>>> weight of oxygen and the continuity of Time--or if anyone knows of clear
>>> reconstructions of what he is doing in the secondary literature?
On 2/23/2017 10:28 PM, Jon Alan Schmidt wrote:
> Kelly Parker discusses the same passage on pages 116-117 of The Continuity of
> Peirce's Thought.
> Time, the standard of continuity, is the "most perfect" continuum in
> experience, but should not be taken as an absolutely perfect continuum. The
> perfect true continuum is only described hypothetically in mathematics.
> Peirce observed that time is in all likelihood not "quite perfectly
> continuous and uniform in its flow (CP 1.412). Phenomenological time does
> exhibit the properties of infinite divisibility and immediate connection, but
> is probably not best conceived as an unbroken and absolutely regular thread.
> The only constant we have noted in time is the regularity of development or
> change, but change is not smooth. Changes differ from one another. The
> "regular" phenomenon of change consists, on closer examination, of numerous
> (perhaps infinite) parallel courses of development with different patterns
> and histories that interweave and diverge.
From: Benjamin Udell <[email protected] <mailto:[email protected]>>
Sent: Friday, February 24, 2017 8:06 AM
To: [email protected] <mailto:[email protected]>
Subject: Re: [PEIRCE-L] Cyclical Systems and Continuity
Decades ago a topological singularity theorist told me that the theory provided
ways to distinguish points that one would think were not distinguishable (or
discernible). For example, think of a string that loops over itself on the
floor, or a curve that loops through itself on a plane. The point of
self-intersection is a point with "multiplicity two", since it corresponds to
two different points along the curve. They both correspond to a single point on
the plane (or floor). They are ordered, one coming earlier or later than the
other, depending the direction in which the points along the curve are ordered.
First, the argument that Ben reports is, from a physical perspective, flawed.
A crossing of a strands of string could not be in the same plane. In my
opinion, this is typical example of useless metaphors in mathematics. Hubris?
See texts on knot theory for a modern perspective.
Secondly, I would note that the CSP used the term “the atomic weight of
oxygen”.
During CSP lifespan, the notion of “atomic weight” and “valence" were the basis
for the chemical table of elements. At that time, the chemical table of
elements consisted of seven columns. The physical structure of atoms was not
known. CSP (1898?) believed in the Boscovich (1711-1787) theory of atoms with
the compositions of ALL atoms from the SAME undefined parts. The non-integer
values of the atomic weights of different elements were a consequence of the
compositions of the undefined parts, according to Boscovich.
Nevertheless, each chemical element was an existential quantifier that was a
ratio of real numbers within the Daltonian structure of molecules. Thus, the
tension between a real number as an atomic weight and a real number as a
duration of time. Yet, atoms are proper names. Discrete objects. So, what is
the illation between a discrete object and a real number?
This conundrum, along with many others, is resolved by the physical notation
for the perplex number system that is based on the units of electrical charge
as discrete integers. Mass (that is, atomic weights) is merely a correlate to
charge in the perplex logic of valence and the labelled bipartite graphs that
express illative and copulative structures of chemical molecules.
Valence is a functor that assigns contiguity to pairs of atoms in a chemical
bond. (EMPHASIS is on the contiguity of adjacent atoms and NOT on continuity of
matter or mass!) The pragmatic quali-signs of valence are the indexical values
of copulative pair of atoms as well as the predicates of the attributes of the
molecule necessary to generate the dicisign for the ampliative arguments of
emergence.
The statement:
> Phenomenological time does exhibit the properties of infinite divisibility
> and immediate connection, but is probably not best conceived as an unbroken
> and absolutely regular thread.
makes sense in that the predicative functor of time is infinitely divisible but
the copulative functor of “atomic weight” is not divisible.
Thus, CSP correctly noted the distinctions between the copulative and
predicative logics of the chemical sciences and their role in forming chemical
symbols, logical arguments and legisigns. Thus, the statement cited by Jeff is
“reasonable” from a historical perspective. It requires both historical
perspective and symbolic competencies to interpret the sinsigns of “the atomic
weight of oxygen".
Cheers
Jerry
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