Chemistry Reference
In-Depth Information
6.4 Peirce
'
s Logic of Relations
Athletes in team-sports often refer to
—a cooperative spirit that
contributes to winning tight games. Chemical properties involve
relations
among
substances. Both as a science and as a practical art, chemistry characteristically
deals with relationships—arguably, focus on relationships is a
defining
feature of
chemistry. As a student of chemistry, and also as the son of one of America
good chemistry
'
'
s
leading mathematicians (Harvard Professor Benjamin Peirce), Charles Peirce had a
lively interest in the
logic of relations
: his pioneering work in this field made the
development of modern symbolic logic possible.
Each relation involves a number (n) of relata—it has an
'
adicity
.
Monadic
'
'
(n
¼
1) relations are
properties
(or
qualities
or
attributes
). Ordinary relations
'
'
'
'
'
'
are diadic (n
3). Relations with four or more relata are properly
considered as combinations of relations of lower adicity.
5
Peirce in 1885 and
Gottlieb Frege in 1879 independently introduced two innovations (quantification
and use of variables) that distinguish modern logic from its Aristotelian ancestor:
∃
¼
2) or triadic (n
¼
x
¼
for some x
;
8
y
¼
for all y
(and
Rxy
¼
x bears relation R to y
). Peirce
'
s innova-
tions were recognized by leading logicians before 1890, but Frege
'
s work was
overlooked until Bertrand Russell called attention to it in 1910.
Some relations are symmetric so that
Rxy
Ryx
. But, if John loves Mary,
Mary may or may not love John. Relation
Rxy
sometimes is reducible (so that
Rxy
¼
Px
+
Qy
) but diadic relationships are not generally reducible to (decompos-
able into) combinations of monadic properties (
Rxy
¼
Px
+
Qy
). The same is true for
triadic relationships. Peirce cited an analogy between chemical valence and
the logic of relatives: “A chemical atom is quite like a relative in having a definite
number of loose ends or
6¼
corresponding to the blanks of the
relative” (CP: 3.469). He developed a Method of graphically representing logical
relationships including the logic of relatives. This
unsaturated bonds,
'
'
Method of Existential Graphs
'
was not well-received by contemporary logicians but later had important applica-
tions in digital computation.
6
'
5
Peirce wrote as if he had a rigorous proof of this, but never published such a proof. Presently-
known proofs are not straight-forward.
6
Peirce developed an approach to experience that explicitly avoided mechanistic explanation: he
called this
'
Phaneroscopy.
'
This method was analogous to Phenomenology, developed indepen-
dently by Edmund Husserl at roughly the same time. Peirce distinguished three modes of being—
the three Phaneroscopic Categories. “Firstness is the mode of being of that which is such as it is,
positively and without reference to anything else. Secondness is the mode of being of that which is
such as it is, with respect to a second [item] but regardless of any third [item]. Thirdness is the
mode of being of that which is such as it is in bringing a second [item] and a third [item] in relation
to one another” (CP 8.328). A certain color, say fire-engine-red, would be a First. Firsts are
potentials—many things might or might not be red. Any bipolar interaction, say some percipient
detecting red, illustrates secondness. Struggle and resistance are usual features of Seconds.
Seconds correspond to actuality—entities are Seconds. A percipient interpreting red as a stop-
signal would constitute a Third. Thirdness corresponds to generality—laws, purposes, and inten-
tions are Thirds (Short
2007
, 60-90).
