JLRC: The meta-languages of interest here geometry, matter, number,
space
and time.
First, geometry.
Plane geometry terms: point, line, plane, closed surfaces, (triangles,
squares, pentagons,…)
Solid geometry - spheres, tetrahedrons, irregular forms (soccer balls
and the like).
Mathematical dimensionality, in its traditional form bridges plane and
solid geometry - 1,2,3,..,N.
Did CSP ever use traditional mathematical dimensionality in describing
logic?
Jon, John, Kirsti, List:
First, Ok, I found the passages. My source was Roberts, Existential
Graphs of CSP, p.26. Roberts cites 3.469 and 4.561.
Now to the philosophical issues and the perplexity of number theory as
matter. This post should be contrasted with FS views of the role of
diagrams in CSP’s writings.
John:
Since ammonia is a very small molecule with a small number of
electrical parts, 14 to be exact, it has been deeply studied from a
physical-mechanical perspective. The usual chemical representation is
as a planar figure,as a representation of empirical measurements.
Approximations from both quantum theory and molecular mechanics
suggest a ‘flattened” TETRAHEDRAL structure, not a plane. In gas
phase, the spectra data suggests that NH3 molecule flips back and
forth, above and below the plane of the nitrogen nucleus, much like an
umbrella flipping by strong wind.
Electrically, the 14 particles are distinguished as 4 nuclei and 10
electrons. The polar opposites (nuclei and electrons) are arranged in
a lattice like pattern to form an electro-neutral lattice like object.
Thus, from a modern chemical perspective, NH3 is more perplex than the
simple structure of introductory textbooks,.
But, CSP did not have access to such data and could not have taken it
into consideration. Nevertheless, the underlying concept of
representation of chemical structures as stationary objects remains
the same today, the same since Dalton’s precedence of 1806. It is
this stationary image of whole-part relations that give chemistry its
scientific identity and CSP’s logic of the particular.
This stationarity of representation of numbers is, of course, one of
the critical mathematical and philosophical separations of CSP’s
logic from modern physical thought, where “to be is to be a
variable”.
Kirsti:
May I re-align your wording a bit?
My purpose is mainly to align the logics in terms of Tarski’s
meta-languages, but I will not address that here.
The meta-languages of interest here geometry, matter, number, space
and time.
First, geometry.
Plane geometry terms: point, line, plane, closed surfaces, (triangles,
squares, pentagons,…)
Solid geometry - spheres, tetrahedrons, irregular forms (soccer balls
and the like).
Mathematical dimensionality, in its traditional form bridges plane and
solid geometry - 1,2,3,..,N.
Did CSP ever use traditional mathematical dimensionality in describing
logic?
A three dimensional tetrahedron plays a critical role in the extension
of chemical thought as a mode of "filling space”. (This concept has
deep inferences and deeper implications!)
Compare, ammonia (NH3) with methane (CH4). The latter has five nuclei
and ten electrons. The five nuclei and eight of the ten electrons can
be arranged in a regular lattice-like perplex structure. The other two
electrons appear to be irregular in this geometric representation.
AS a consequence of these formula and similar formula, Nitrogen is
assigned a valence of three and carbon a valence of four. (It is that
simple!)
Methane is spatially represented as a tetrahedron with the carbon atom
IN THE GEOMETRIC SPATIAL CENTER. It is symmetric around the center
point of the carbon nucleus.
(The potential for planar asymmetry is intrinsic to the valence of
four of carbon and introduces the concept of “handedness" into
chemical thought. Again, this is another major distinction between the
conceptualization of physical and chemical thought as a consequence of
valence.)
CSP’s diagram, as shown by Roberts, is a diagram on a surface with a
central nitrogen and the three attached hydrogens as “spokes”,
forming a unity. It is not a directed graph (not a graph of
mathematical category theory.)
The intent of this brief post was to shed some light on why I found
the passage cited by Roberts of great interest and why I questioned
Jon’s enhancements to CSP’s artwork. I hope I succeeded.
Some of my generalizations in relation to certain weaknesses of
CSP’s style.
The philosophical conjecture is that CSP used number theory in many
ways, not just the simple arithmetic of addition, subtraction,
multiplication, division, roots and exponents. He sought to include
CHEMICAL number theory within his mathematical logic. As well as
chemical memory. His general approach to logic is characterized by his
efforts to do so. Latter, Lesniewski followed the percepts of CSP, but
Tarski rejected this logical style of thought and separated formal
logical terms into meta-languages (see: Malatesta, The Primary Logic,
199. Modern chemical and biological logic follow both the Poles. The
notation of the perplex number system captures the Lesniewski - Tarski
duality.
This is the "difference that makes a difference” and separates CSP's
metaphysics of logic from other formal logics, other systems of
beliefs about the nature of thought, such as those proposed by FS.
Cheers
Jerry
By the way, these remarks are a further example of my simplistic
metaphysics:
_THE UNION OF UNITS UNIFIES THE UNIT_y.
On Apr 5, 2016, at 3:50 AM, kirst...@saunalahti.fi wrote:
John & al
I have a suggestion for what is missing. By mistake, I sent my
suggestion only to Jerry. But perhaps you and Jon are interested in
it, as well. - So I'll copy my note below:
Jerry,
I have not studied this particular triad CSP has presented. - BUT
two-dimensional diagrams never present triadicity to completion.
Tree dimensions are needed. And even then TIME is needed as the
fourth dimension, IF any reaction is to be grasped as a process.
Try imagining the diagram in a three-dimensional space. - Triadicity
is not about triangles (as defined in plane geometry) ). - Then you
will end up with a tetraed.
Any tetraed has FOUR turning points, four edges, as well as four
triangular planes. Projective geometry is thus needed in order to
present a diagram showing the hidden one, too.
And then the dimension of TIME. - Phillip J. Davis & Reuben Hersh
(1980) in 'Mathematical Experience' deal with some of the
mathematical problems involved. (They do not understand triadicity,
unfortunately).
Best wishes,
Kirsti
John Collier kirjoitti 5.4.2016 07:41:
Thanks for the context, Jerry. I am not familiar with the passage,
but
it does seem, by your account, to be peculiar at best. I would agree
that the standard representation of NH3 puts all of the nodes (the
endpoints, or perhaps the branches, representing hydrogen atoms and
the centre the nitrogen atom). This is a structure of relations, and
I
see no reason why it would need to be interpreted as a third. That
is
quite unlike the triple relation of the sign, unless we are missing
something here, I have no idea what it might be. Your explanation
seems plausible to me, given Peirce's (near) obsession with threes,
but it is also such an obvious error that I can't help but wonder if
we are missing something.
John Collier
Professor Emeritus and Senior Research Associate
University of KwaZulu-Natal
http://web.ncf.ca/collier [1]
-----Original Message-----
From: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com]
Sent: Tuesday, 05 April 2016 6:24 AM
To: Peirce List
Subject: Re: [PEIRCE-L] Re: Systems Of Interpretation
Jon, John:
Thanks, Jon.
The question I raised was in order to seek alternative
interpretations of CSP’s
diagram of a chemical structure, ammonia. (NH3)
He showed it as a triad. The nitrogen atom was in the middle of the
three
hydrogens, each at the end of a spoke. NOT a triangle.
But, the chemical atoms are all of the nature and co-exist as
relatives. So,
four atoms but only a triad.
Why?
My feeling is that CSP wanted a triad so that he made one.
This is not a satisfactory inquiry into a diagrammatic assertion.
Cheers
Jerry
On Apr 3, 2016, at 5:04 PM, Jon Awbrey <jawb...@att.net> wrote:
Peircers,
Questions about the meaning of the “central hub” in the
“three-spoked”
picture of an elementary sign relation have often come up, just
recently among Jerry Chandler's questions and a question Mary
Libertin
asked on my blog.
Maybe the answer I gave there can help to clear that up:
http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%E2
[2]
%80%A2-5/#comment-32800
The central “spot”, as Peirce called it [in his logical
graphs], is
located on a different logical plane, since it is really a
place-holder for the whole sign relation or possibly for the
individual triple. Normally I would have labeled it with a letter
to
indicate the whole sign relation, say L, or else the individual
triple, say ℓ = (o, s, i).
Regards,
Jon
On 3/31/2016 1:24 PM, Jon Awbrey wrote:
Post : Systems Of Interpretation • 5
http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%e
[3]
2%80%a2-5/
Date : March 31, 2016 at 10:24 am
Subthread:
MB:http://permalink.gmane.org/gmane.science.philosophy.peirce/18534
[4]
EVD:http://permalink.gmane.org/gmane.science.philosophy.peirce/18540
[5]
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/18552
[6]
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18553
[7]
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18554
[8]
Mike, Val, Jerry, List,
Here is the revised edition of my last comment on the order
issue.
(I am hoping I can get to the rest of Jerry's questions
eventually.)
Figure 2. An Elementary Sign Relation (and see attached)
https://inquiryintoinquiry.files.wordpress.com/2016/03/awbrey-awbrey-
[9]
1999-elementary-sign-relation.gif
An elementary sign relation is an ordered triple (o, s, i).
It is called ''elementary'' because it is one element of a sign
relation L ⊆ O × S × I, where O is a set of objects, S is a
set of
signs, and I is a set of interpretant signs that are collectively
called the ''domains'' of the relation.
But what is the significance of that ordering?
In any presentation of subject matter we have to distinguish the
natural order of things from the order of consideration or
presentation in which things are taken up on a given occasion.
The natural order of things comes to light through the discovery
of
invariants over a variety of presentations and representations.
That type of order tends to take a considerable effort to reveal.
The order of consideration or presentation is often more
arbitrary,
making some aspects of the subject matter more salient than
others
depending on the paradigm or perspective one has chosen.
In the case of sign relations, the order in which we take up the
domains O, S, I or the components of a triple (o, s, i) is wholly
arbitrary so long as we maintain the same order throughout the
course
of discussion.
Regards,
Jon
--
academia: http://independent.academia.edu/JonAwbrey [10]
my word press blog: http://inquiryintoinquiry.com/ [11]
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[1] http://web.ncf.ca/collier
[2]
http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%E2
[3]
http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%e
[4] http://permalink.gmane.org/gmane.science.philosophy.peirce/18534
[5] http://permalink.gmane.org/gmane.science.philosophy.peirce/18540
[6] http://permalink.gmane.org/gmane.science.philosophy.peirce/18552
[7] http://permalink.gmane.org/gmane.science.philosophy.peirce/18553
[8] http://permalink.gmane.org/gmane.science.philosophy.peirce/18554
[9]
https://inquiryintoinquiry.files.wordpress.com/2016/03/awbrey-awbrey-
[10] http://independent.academia.edu/JonAwbrey
[11] http://inquiryintoinquiry.com/
[12] http://www.cspeirce.com/peirce-l/peirce-l.htm
