One, Two, Three: Fundamental Categories of Thought

1.369-372      G-c.1885-1
1.376-378      G-c.1885-1


  369. Kant, the King of modern thought, it was who first
remarked the frequency in logical analytics of trichotomics or
threefold distinctions. It really is so; I have tried hard and
long to persuade myself that it is only fanciful, but the facts
will not countenance that way of disposing of the phenomenon.
Take any ordinary syllogism:

  * From "One, Two, Three: Fundamental Categories of Thought and of
Nature," c. 1885. This paper does not seem to form part of "A Guess at the
Riddle," but is here inserted to take the place of the unwritten section 2 of the
original work.
|p194

All men are mortal,
Elijah was a man;
Therefore, Elijah was mortal.

There are here three propositions, namely, two premisses and
a conclusion; there are also three terms, man, mortal, and
Elijah. If we transpose one of the premisses with the
conclusion, denying both, we obtain what are called the indirect
figures of syllogism; for example

All men are mortal,
But Elijah was not mortal;
Therefore, Elijah was not a man.

Elijah was not mortal,
But Elijah was a man;
Therefore, some men are not mortal.

Thus, there are three figures of ordinary syllogism. It is true
there are other modes of inference which do not come under
any of these heads; but that does not annul the fact that we
have here a trichotomy. Indeed, if we examine by itself what
is by some logicians called the fourth figure, we find that it also
has three varieties related to one another as the three figures
of ordinary syllogism. There is an entirely different way of
conceiving the relations of the figures of syllogism; namely, by
means of the conversion of propositions. But from that point
of view also, the same classes are preserved. DeMorgan* has
added a large number of new syllogistic moods which do not
find places in this classification. The reasoning in these is of
a peculiar character and introduces the principle of dilemma.
Still, regarding these dilemmatic reasonings by themselves,
they fall into three classes in a precisely similar manner.
Again, I have shown ** that the probable and approximate
inferences of science must be classified on the very same principles,
being either Deductions, Inductions, or Hypotheses. Other
examples of threes in logic are statements of what is actual,
what is possible, and what is necessary; the three kinds of
forms, Names, *** Propositions, and Inferences ; **** affirmative,
negative, and uncertain answers to a question. One very
important triad is this: it has been found that there are three

 * Formal Logic, ch. 8. See also 2.568.
 ** See vol. 2, bk. III, chs. 2 and 5.
 *** Or Terms, but see 372.
 **** Or Arguments.|p195

kinds of signs which are all indispensable in all reasoning; the
first is the diagrammatic sign or icon, which exhibits a
similarity or analogy to the subject of discourse; the second is the
index, which like a pronoun demonstrative or relative, forces the
attention to the particular object intended without describing
it; the third [or symbol] is the general name or description which
signifies its object by means of an association of ideas or
habitual connection between the name and the character signified.
  370. But there is one triad in particular which throws a
strong light on the nature of all the others. Namely, we find it
necessary to recognize in logic three kinds of characters, three
kinds of facts. First there are singular characters which are
predicable of single objects, as when we say that anything is
white, large, etc. Secondly, there are dual characters which
appertain to pairs of objects; these are implied by all relative
terms as "lover," "similar," "other," etc. Thirdly, there are
plural characters, which can all be reduced to triple characters
but not to dual characters. Thus, we cannot express the fact
that A is a benefactor of B by any descriptions of A and B
separately; we must introduce a relative term. This is
requisite, not merely in English, but in every language which might
be invented. This is true even of such a fact as A is taller than
B. If we say, " A is tall, but B is short," the conjugation " but "
has a relative force, and if we omit this word the mere
collocation of the two sentences is a relative or dual mode of
signifying....
  371. Let us now consider a triple character, say that A
gives B to C. This is not a mere congeries of dual characters.
It is not enough to say that A parts with C, and that B receives
C. A synthesis of these two facts must be made to bring them
into a single fact; we must express that C, in being parted with
by A, is received by B. If, on the other hand, we take a
quadruple fact, it is easy to express as a compound of two triple
facts.... We are here able to express the synthesis of the two
facts into one, because a triple character involves the
conception of synthesis. Analysis involves the same relations as
synthesis; so that we may explain the fact that all plural facts
can be reduced to triple facts in this way. A road with a fork
in it is the analogue of a triple fact, because it brings three
termini into relation with one another. A dual fact is like a
|p196

road without a fork; it only connects two termini. Now, no
combination of roads without forks can have more than two
termini; but any number of termini can be connected by roads
which nowhere have a knot of more than three ways. See the

{diagram}

figure, where I have drawn the termini as self-returning roads,
in order to introduce nothing beyond the road itself. Thus,
the three essential elements of a network of roads are road
about a terminus, roadway-connection, and branching; and in
like manner, the three fundamental categories of fact are, fact
about an object, fact about two objects (relation), fact about
several objects (synthetic fact).
  372. We have seen that the mere coexistence of two
singular facts constitutes a degenerate form of dual fact; and in
like manner there are two orders of degeneracy in plural facts,
for either they may consist in a mere synthesis of facts of which
the highest is dual, or they may consist in a mere synthesis
of singular facts. This explains why there should be three
classes of signs; for there is a triple connection of sign, thing
signiJied, cognition produced in the mind. There may be a mere
relation of reason between the sign and the thing signified; in
that case the sign is an icon. Or there may be a direct physical
connection; in that case, the sign is an index. Or there may be
a relation which consists in the fact that the mind associates
the sign with its object; in that case the sign is a name* [or
symbol]. Now consider the difference between a logical term,
a proposition, and an inference. A term is a mere general
description, and as neither icon nor index possesses generality,
it must be a name; and it is nothing more. A proposition is
also a general description, but it differs from a term in that it
purports to be in a real relation to the fact, to be really
determined by it; thus, a proposition can only be formed of the
conjunction of a name and an index. An inference, too,
contains a general description....
  * Cf. 369.
  376. The ordinary doctrine is open to a variety of
objections from the very point of view from which it was first
delineated. First, desire certainly includes an element of
pleasure quite as much as of will. Wishing is not willing; it is
a speculative variation of willing mingled with a speculative
and anticipatory feeling of pleasure. Desire should therefore
be struck out of the definition of the third faculty, leaving it
mere volition. But volition without desire is not voluntary;
it is mere activity. Consequently, all activity, voluntary or
not, should be brought under the third faculty. Thus
attention is a kind of activity which is sometimes voluntary and
sometimes not so. Second, pleasure and pain can only be
recognized as such in a judgment; they are general predicates
which are attached to feelings rather than true feelings. But
mere passive feeling, which does not act and does not judge,
which has all sorts of qualities but does not itself recognize
these qualities, because it does not analyze nor compare -- this
is an element of all consciousness to which a distinct title ought
to be given. Third, every phenomenon of our mental life is
more or less like cognition. Every emotion, every burst of
passion, every exercise of will, is like cognition. But
modifications of consciousness which are alike have some element in
common. Cognition, therefore, has nothing distinctive and
cannot be regarded as a fundamental faculty. If, however, we
ask whether there be not an element in cognition which is
neither feeling, sense, nor activity, we do find something, the
faculty of learning, acquisition, memory and inference,
synthesis. Fourth, looking once more at activity, we observe that
the only consciousness we have of it is the sense of resistance.
We are conscious of hitting or of getting hit, of meeting with a
fact. But whether the activity is within or without we know

  * A number of manuscript pages seem to be missing here. 376-8 from "One,
Two, Three: Fundamental Categories of Thought and Nature," have been
substituted for them.
|p200

only by secondary signs and not by our original faculty of
recognizing fact.
  377. It seems, then, that the true categories of
consciousness are: first, feeling, the consciousness which can be included
with an instant of time, passive consciousness of quality,
without recognition or analysis; second, consciousness of an
interruption into the field of consciousness, sense of resistance, of an
external fact, of another something; third, synthetic
consciousness, binding time together, sense of learning, thought.
  378. If we accept these [as] the fundamental elementary
modes of consciousness, they afford a psychological
explanation of the three logical conceptions of quality, relation, and
synthesis or mediation. The conception of quality, which is
absolutely simple in itself and yet viewed in its relations is seen
to be full of variety, would arise whenever feeling or the
singular consciousness becomes prominent. The conception of
relation comes from the dual consciousness or sense of action
and reaction. The conception of mediation springs out of the
plural consciousness or sense of learning.