Subject: Re: peirce-l digest: May 11, 2006
From: Gary Richmond <[EMAIL PROTECTED]>
Date: Tue, 16 May 2006 09:05:38 -0400
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[off-list]
Hi Ben,
Hey, what happened to your feedback on my paper? Anyhow, probably
best=20
since I made some significant changes yesterday. BUT, will you be=20
available to edit and Springer-ize it in a week or so? Please let
me=20
know so that if you can't I can set up contingency plans. If you
can, I=20
think it will pretty much be in the form I sent it to you in (but
let's=20
see what my reviewers think . .).
Below my signature are some key quotes from the CP on valency, the
first =
my favorite, but all of them, I think, relevant. No time now to
select=20
passages or even re-read them (I will do this later in the week=20
perhaps), but I thought you might find them valuable for the
present=20
discussion. Anyhow, the diagrammatic figures don't seem to be=20
reproducing from the eCP--I'll have to look into that later because
in=20
one place Peirce diagrams tons of valency diagrams not unlike some
of=20
those that appear in the slide show I wrote, you produced and which=20
rather "prove" in the way that diagram observation can the
"reduction=20
thesis" (which has now a strict mathematical proof by J. Hereth
Correia =
which I expect will be published in the ICCS proceedings this
summer,=20
but can't say for certain; I have the paper, but it's mainly heavy
duty=20
mathematics and the author has given permission for distribution
yet.=20
Karl-Erich Wolff, however, assumes me that the mathematics is sound).
Of course, as already mentioned, I find the most interesting
secondary=20
source on this to be Ketner, especially his 'Peirce's "Most Lucid
and=20
Interesting Paper": An Introduction to Cenopythagoreanism" and
several=20
other papers included as Appedix II to A Thief of Peirce. I don't
agree=20
with all of his philosophical points (one crucial one in
particular, but =
no time to get into that now--it's "catch up" time), but this is
where=20
he lays out "valency analysis" (his own expressions) based on
"clues=20
from MS 482." He notes that Peirce "gave the system no special
name" but =
that he, Ketner, "attempted to be consistent with what I take
Peirce's=20
insights to have been." (all the short quotes are from page 196 of
A=20
Thief of Peirce).
I was pleased to see your post to Peirce-l as I'd begun to worry
about=20
you a little. But let me know about the paper as one wants a
keynote to=20
look especially good :-)
Best,
Gary
ONE KEY PASSAGE
Peirce: CP 1.289 Cross-Ref:++
289. A reader may very intelligently ask, How is it possible
for an=20
indecomposable element to have any differences of structure? Of
internal =
logical structure it would be clearly impossible. But of external=20
structure, that is to say, structure of its possible compounds,
limited=20
differences of structure are possible; witness the chemical
elements, of =
which the "groups," or vertical columns of Mendel=E9eff's table,
are=20
universally and justly recognized as ever so much more important
than=20
the "series," or horizontal ranks in the same table. Those columns
are=20
characterized by their several valencies, thus:
He, Ne, A, Kr, X are medads ({m=E9den} none + the patronymic
=3D {id=E9=
s}).
H, L [Li], Na, K, Cu, Rb, Ag, Cs,-,-, Au, are monads;
G [Gl], Mg, Ca, Zn, Sr, Cd, Ba, -,-, Hg, Rd [Ra], are dyads;
B, Al, Sc, Ga, Y, In, La, -, Yb, Tc [Tl], Ac are triads;
C, Si, Ti, Ge, Zr, Sn, Co [Ce], -, -, Pc [Pb], Th, are tetrads;
N, P, V, As, Cb, Sb, Pr [Nd], -, Ta, Bi, Po [Pa], are properly=20
pentads (as PCL[5], though owing to the junction of two pegs they
often=20
appear as triads. Their pentad character is particularly required
to=20
explain certain phenomena of albumins); O, S, Cr, Se, Mo, Te, Nd
[Sm],=20
-, W, -, U, are properly hexads (though by junction of bonds they=20
usually appear as dyads);
F, Cl, Mn, Br, -, I, are properly heptads (usually appearing as
monad=
s);
Fe, Co, Ni, Ru, Rh, Pd, -, -, -, Os, Tr [Ir], Pt, are octads;
(Sm,=20
Eu, Gd, Er, Tb, Bz [?], Cl [Ct], are not yet placed in the table.)
Peirce: CP 1.290 Cross-Ref:++
290. So, then, since elements may have structure through
valency, I=20
invite the reader to join me in a direct inspection of the valency
of=20
elements of the phaneron. Why do I seem to see my reader draw back?
Does =
he fear to be compromised by my bias, due to preconceived views?
Oh,=20
very well; yes, I do bring some convictions to the inquiry. But let
us=20
begin by subjecting these to criticism, postponing actual
observation=20
until all preconceptions are disposed of, one way or the other.
Peirce: CP 1.291 Cross-Ref:++
291. First, then, let us ask whether or not valency is the sole=20
formal respect in which elements of the phaneron can possibly vary.
But=20
seeing that the possibility of such a ground of division is
dependent=20
upon the possibility of multivalence, while the possibility of a=20
division according to valency can in nowise be regarded as a result
of=20
relations between bonds, it follows that any division by variations
of=20
such relations must be taken as secondary to the division according
to=20
valency, if such division there be. Now (my logic here may be
puzzling,=20
but it is correct), since my ten trichotomies of signs,+1 should
they=20
prove to be independent of one another (which is to be sure, highly=20
improbable), would suffice to furnish us classes of signs to the
number o=
f
310 =3D (32)5 =3D (10-1)5 =3D 105 - 5.104
+ 10.103 - 10.102
+ 5.10 - 1
=3D 50000
+ 9000
+ 49
=3D 59049
(Voil=E0 a lesson in vulgar arithmetic thrown in to boot!), which=20
calculation threatens a multitude of classes too great to be=20
conveniently carried in one's head, rather than a group
inconveniently=20
small, we shall, I think, do well to postpone preparations for
further=20
divisions until there be prospect of such a thing being wanted.
Peirce: CP 1.292 Cross-Ref:++
292. If, then, there be any formal division of elements of the=20
phaneron, there must be a division according to valency; and we may=20
expect medads, monads, dyads, triads, tetrads, etc. Some of these,=20
however, can be antecedently excluded, as impossible; although it
is=20
important to remember that these divisions are not exactly like the=20
corresponding divisions of Existential Graphs,+1 which have
relation=20
only to explicit indefinites. In the present application, a medad
must=20
mean an indecomposable idea altogether severed logically from every=20
other; a monad will mean an element which, except that it is
thought as=20
applying to some subject, has no other characters than those which
are=20
complete in it without any reference to anything else; a dyad will
be an =
elementary idea of something that would possess such characters as
it=20
does possess relatively to something else but regardless of any
third=20
object of any category; a triad would be an elementary idea of
something =
which should be such as it were relatively to two others in
different=20
ways, but regardless of any fourth; and so on. Some of these, I
repeat,=20
are plainly impossible. A medad would be a flash of mental=20
"heat-lightning" absolutely instantaneous, thunderless,
unremembered,=20
and altogether without effect. It can further be said in advance,
not,=20
indeed, purely a priori but with the degree of apriority that is
proper=20
to logic, namely, as a necessary deduction from the fact that there
are=20
signs, that there must be an elementary triad. For were every
element of =
the phaneron a monad or a dyad, without the relative of teridentity
+2=20
(which is, of course, a triad), it is evident that no triad could
ever=20
be built up. Now the relation of every sign to its object and=20
interpretant is plainly a triad. A triad might be built up of
pentads or =
of any higher perissad elements in many ways. But it can be proved
--=20
and really with extreme simplicity, though the statement of the
general=20
proof is confusing -- that no element can have a higher valency
than thre=
e.
ON LOGICAL VALENCY
Peirce: CP 3.470 Cross-Ref:++
470. But beyond this point the analogy ceases to be striking.
In=20
fact, the analogy with the ruling theory of chemical compounds
quite=20
breaks down. Yet I cannot resist the temptation to pursue it. After
all, =
any analogy, however fanciful, which serves to focus attention upon=20
matters which might otherwise escape observation is valuable. A
chemical =
compound might be expected to be quite as much like a proposition
as=20
like an algebraical invariant; and the brooding upon chemical
graphs has =
hatched out an important theory in invariants.+1 Fifty years ago,
when I =
was first studying chemistry, the theory was that every compound=20
consisted of two oppositely electrified atoms or radicles; and in
like=20
manner every compound radicle consisted of two opposite atoms or=20
radicles. The argument to this effect was that chemical attraction
is=20
evidently between things unlike one another and evidently has a=20
saturation point; and further that we observe that it is the
elements=20
the most extremely unlike which attract one another. [Julius]
Lothar=20
Meyer's curve having for its ordinates the atomic volumes of the=20
elements and for its abscissas their atomic weights tends to
support the =
opinion that elements strongly to attract one another must have
opposite =
characters +1; for we see that it is the elements on the steepest=20
downward slopes of that curve which have the strongest attractions
for=20
the elements on the steepest upward inclines. But when chemists
became=20
convinced of the doctrine of valency, that is, that every element
has a=20
fixed number of loose ends, and when they consequently began to
write=20
graphs for compounds, it seems to have been assumed that this=20
necessitated an abandonment of the position that atoms and radicles=20
combine by opposition of characters, which had further been
weakened by=20
the refutation of some mistaken arguments in its favor. But if
chemistry =
is of no aid to logic, logic here comes in to enlighten chemistry.
For=20
in logic, the medad must always be composed of one part having a=20
negative, or antecedental, character, and another part of a
positive, or =
consequental, character; and if either of these parts is compound
its=20
constituents are similarly related to one another. Yet this does
not, at =
all, interfere with the doctrine that each relative has a definite=20
number of blanks or loose ends. We shall find that, in logic, the=20
negative character is a character of reversion in this sense, that
if=20
the negative part of a medad is compound, its negative part has, on
the=20
whole, a positive character. We shall also find, that if the
negative=20
part of a medad is compound, the bond joining its positive and
negative=20
parts has its character reversed, just as those relatives
themselves have=
=2E+2
Peirce: CP 3.471 Cross-Ref:++
471. Several propositions are in this last paragraph stated
about=20
logical medads which now must be shown to be true. In the first
place,=20
although it be granted that every relative has a definite number of=20
blanks, or loose ends, yet it would seem, at first sight, that
there is=20
no need of each of these joining no more than one other. For
instance,=20
taking the triad
"-- kills -- to gratify --," why may not the three loose ends all
join=20
in one node and then be connected with the loose end of the monad
"John=20
is --" as in Figure 3 making the proposition "John it is that kills
what =
is John to gratify what is John"? The answer is, that a little
exercise=20
of generalising power will show that such a four-way node is really
a=20
tetradic relative, which may be expressed in words thus, "-- is=20
identical with -- and with -- and with --"; so that the medad is
Figure 4
really equivalent to that of Figure 4, which corresponds to prussic
acid =
as shown in Figure 5.
Figure 5
Thus, it becomes plain that every node of bonds is equivalent to a=20
relative; and the doctrine of valency is established for us in logic
FROM THE SIMPLEST MATHEMATICS (THE MANY VALENCY DIAGRAMS WHICH
FOLLOW=20
THIS PASSAGE ARE NOT REPRODUCIBLE IN MY PROGRAM
Peirce: CP 4.308 Cross-Ref:++
308. Trichotomic mathematics is not quite so fundamentally
important =
as the dichotomic branch; but the need of a study of it is much
greater, =
its applications being most vital and its difficulties greater than
the=20
dichotomic. Nevertheless, it has received hardly any direct
attention.=20
The permutations of three letters have, of course, been noticed,
along=20
with other permutations. The theory of the cubic equation is fully
made=20
out; along with those of plane and twisted cubic curves. There is
also=20
an algebra of novenions. In addition, considerable studies have
been=20
made in a particular province of trichotomic mathematics by
logicians,=20
without their recognizing the triadic character of the subject.
Peirce: CP 4.308 Cross-Ref:++
A trichotomic mathematics entirely free from any dichotomic
element=20
appears to be impossible. For how is the mathematician to take a
step=20
without recognizing the duality of truth and falsehood? Hegel and
others =
have dreamed of such a thing; but it cannot be. Trichotomic
mathematics=20
will therefore be a 2X3 affair, at simplest.
Peirce: CP 4.309 Cross-Ref:++
309. I will begin this topic by a glance at some of the=20
logico-mathematical generalities, without being too scrupulous
about=20
excluding higher numbers than three.
Peirce: CP 4.309 Cross-Ref:++
The most fundamental fact about the number three is its
generative=20
potency.+1 This is a great philosophical truth having its origin
and=20
rationale in mathematics. It will be convenient to begin with a
little a =
priori chemistry.+2 An atom of helion, neon, argon, xenon, crypton,=20
appears to be a medad (if I may be allowed to form a patronymic
from=20
{m=E9den}). Argon gives us, with its zero valency, the one single type
A.
Supposing H, L, Na, Ag, etc. and F, Cl, Br, I to have strictly unit=20
valency (which appears not to be true; at least, not for the
halogens),=20
then they afford only the two types
H-H H-F,
if these can be called two.
Peirce: CP 4.309 Cross-Ref:++
Assuming G (glucinum), etc. with O, S, etc., to have valency 2=20
(certainly not true), they might give an endless series of
saturated=20
rings, by themselves.).
SOURCE UNCERTAIN
Peirce: CP 5.469 Cross-Ref:++
=A72. THE VALENCY OF CONCEPTS +2
469. I begin, then, with the first idea that it seems desirable
to=20
call to your attention. Everybody is familiar with the useful,
though=20
fluctuating and relative distinction of matter and form; and it is=20
strikingly true that distinctions and classifications founded upon
form=20
are, with very rare exceptions, more important to the scientific=20
comprehension of the behaviour of things than distinctions and=20
classifications founded upon matter. Mendel=E9eff's classification
of the=
=20
chemical elements, with which all educated men are, by this time,=20
familiar, affords neat illustrations of this, since the
distinctions=20
between what he calls "groups," that is to say, the different
vertical=20
columns of his table, consists in the elements of one such "group"=20
entering into different forms of combination with hydrogen and with=20
oxygen from those of another group; or as we usually say, their=20
valencies differ; while the distinctions between what he calls the=20
"series," that is, the different horizontal rows of the table,
consist=20
in the less formal, more material circumstance that their atoms
have,=20
the elements of one "series," greater masses than those of the
other.=20
Now everybody who has the least acquaintance with chemistry knows
that,=20
while elements in different horizontal rows but the same vertical
column =
always exhibit certain marked physical differences, their chemical=20
behaviours at corresponding temperatures are quite similar; and all
the=20
major distinctions of chemical behaviour between different elements
are=20
due to their belonging to different vertical columns of the table.
Peirce: CP 5.469 Cross-Ref:++
This illustration has much more pertinence to pragmatism than=20
appears at first sight; since my researches into the logic of
relatives=20
have shown beyond all sane doubt that in one respect combinations
of=20
concepts exhibit a remarkable analogy with chemical combinations;
every=20
concept having a strict valency. (This must be taken to mean that
of=20
several forms of expression that are logically equivalent, that one
or=20
ones whose analytical accuracy is least open to question, owing to
the=20
introduction of the relation of joint identity, follows the law of=20
valency.) Thus, the predicate "is blue" is univalent, the predicate=20
"kills" is bivalent (for the direct and indirect objects are,
grammar=20
aside, as much subjects as is the subject nominative); the
predicate=20
"gives" is trivalent, since A gives B to C, etc. Just as the
valency of=20
chemistry is an atomic character, so indecomposable concepts may be=20
bivalent or trivalent. Indeed, definitions being scrupulously
observed,=20
it will be seen to be a truism to assert that no compound of
univalent=20
and bivalent concepts alone can be trivalent, although a compound
of any =
concept with a trivalent concept can have at pleasure, a valency
higher=20
or lower by one than that of the former concept. Less obvious, yet=20
demonstrable, is the fact that no indecomposable concept has a
higher=20
valency. Among my papers are actual analyses of a number greater
than I=20
care to state.+1 They are mostly more complex than would be
supposed.=20
Thus, the relation between the four bonds of an unsymmetrical
carbon=20
atom consists of twenty-four triadic relations. Careful analysis
shows=20
that to the three grades of valency of indecomposable concepts=20
correspond three classes of characters or predicates. Firstly come=20
"firstnesses," or positive internal characters of the subject in
itself; =
secondly come "secondnesses," or brute actions of one subject or=20
substance on another, regardless of law or of any third subject;
thirdly =
comes "thirdnesses," or the mental or quasi-mental influence of one=20
subject on another relatively to a third. Since the demonstration
of=20
this proposition is too stiff for the infantile logic of our time
(which =
is rapidly awakening, however), I have preferred to state it=20
problematically, as a surmise to be verified by observation. The
little=20
that I have contributed to pragmatism (or, for that matter, to any
other =
department of philosophy), has been entirely the fruit of this
outgrowth =
from formal logic, and is worth much more than the small sum total
of=20
the rest of my work, as time will show.
Benjamin Udell wrote:
Jerry,
Gary Richmond's view doesn't technically contradict Gary F.'s
statements=
, since Gary F.'s statements were qualified by the possibility of
somebod=
y's producing evidence, though Gary F. obviously seemed doubtful
about th=
e idea of the chemical "connection." I felt kind of doubtful too,
though =
I myself have been aware of people's calling Peirce's theory about
monads=
, dyads, & triads, a "valency" theory. Actually I wish I'd asked
Gary Ric=
hmond about it when he included the "valency theory" language in a
presen=
tation which he wrote & which I produced for him in PowerPoint
http://mem=
bers.door.net/arisbe/menu/library/aboutcsp/pr-main.htm#richmond .
At the=
time, I just kind of assumed vaguely...well, I don't know what I
was thi=
nking. I was thinking about how I was making the presentation look
kind o=
f "spacy" and the closing theme from the old Fireball XL5 TV show
was muc=
h in my mind. I'm so deep sometimes. Anyway, if Gary R. says that
Peirce =
made the chemistry connection explicit in some passages in his
writings, =
then I'd assume that Peirce did so.=20
Of course, those would be some interesting passages to read!
Unfortunate=
ly, Gary R. has been very busy lately. But I'll ask him later
because I'm=
curious to read them too. I've been kind of busy myself, or I'd
have res=
ponded sooner. I started off writing a reply to Jim Piat and it got
so lo=
ng that I may never send it.
The Reduction Thesis is: All relations of more than three elements
are r=
educible to triadic relations, but triadic relations are not
reducible to=
dyadic and monadic relations.
Best, Ben Udell
=20
[Ben] Off-list, Gary Richmond, who's quite busy, sent me this:
66~~~~~~~~~~
Chemistry expresses itself in Peirce's valency theory (the term
is no=
t his but Ken Ketner's who hasn't been given enough credit yet for
his wo=
rk in this area, something you hinted hadn't been developed in
Pierce, et=
c.). In any event, see the reduction thesis at work in organic
chemistry =
here: http://en.wikipedia.org/wiki/Organic_nomenclature=20
=20
Trichotomy, the reduction thesis, the development of EGs, etc. all
come =
from Peirce's knowledge of and work in chemistry. In some writings
he mak=
es this explicit.
=20
~~~~~~~~~~99
=20
=20
[Jerry] This is a curious paragraph.
It is too terse for me to understand it.
The first sentence is ambiguous to me.
In particular, what is the reference for the term, "reduction
thesis" i=
n this context?
Chemical names are assigned on the basis of a constructive
thesis, as s=
tudy of the indicated web address will indicate.
This post apparently contradicts Gary F.'s views.
Can someone untangle the intended communication?
=20
=20
Cheers
Jerry
=20
