New List of Categories (Grand Logic)
1.545-559 G-1867-1c
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ON A NEW LIST OF CATEGORIES
# 1. ORIGINAL STATEMENT*
545. This paper is based upon the theory already
established, that the function of conceptions is to reduce the
manifold of sensuous impressions to unity and that the validity of
a conception consists in the impossibility of reducing the
content of consciousness to unity without the introduction of it.
546. This theory gives rise to a conception of gradation
among those conceptions which are universal. For one such
conception may unite the manifold of sense and yet another
may be required to unite the conception and the manifold to
which it is applied; and so on.
547. That universal conception which is nearest to sense
is that of the present, in general. This is a conception, because
it is universal. But as the act of attention has no connotation
at all, but is the pure denotative power of the mind, that is
to say, the power which directs the mind to an object, in
contradistinction to the power of thinking any predicate of
that object -- so the conception of what is present in general,
which is nothing but the general recognition of what is
contained in attention, has no connotation, and therefore no proper
unity. This conception of the present in general, of IT in
general, is rendered in philosophical language by the word
" substance " in one of its meanings. Before any comparison or
discrimination can be made between what is present, what is
present must have been recognized as such, as it, and
subsequently the metaphysical parts which are recognized by
abstraction are attributed to this it, but the it cannot itself
be made a predicate. This it is thus neither predicated of a
* The first section of this chapter was published with this chapter heading in
the Proceedings of the American Academy of Arts and Sciences, vol. 7, May
1867, pp. 287-298. It was intended as ch. 1 of the Grand Logic of 1893 and as
Essay II of the Search for a Method, c. 1893.
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subject, nor in a subject, and accordingly is identical with the
conception of substance.
548. The unity to which the understanding reduces
impressions is the unity of a proposition. This unity consists in
the connection of the predicate with the subject; and,
therefore, that which is implied in the copula, or the conception of
being, is that which completes the work of conceptions of
reducing the manifold to unity. The copula (or rather the verb
which is copula in one of its senses) means either actually is or
would be, as in the two propositions, "There is no griffin,"
and "A griffin is a winged quadruped." The conception of
being contains only that junction of predicate to subject
wherein these two verbs agree. The conception of being,
therefore, plainly has no content.
If we say "The stove is black," the stove is the substance,
from which its blackness has not been differentiated, and the
is, while it leaves the substance just as it was seen, explains its
confusedness, by the application to it of blackness as a
predicate.
Though being does not affect the subject, it implies an
indefinite determinability of the predicate. For if one could
know the copula and predicate of any proposition, as " .....
is a tailed-man," he would know the predicate to be applicable
to something supposable, at least. Accordingly, we have
propositions whose subjects are entirely indefinite, as "There is a
beautiful ellipse," where the subject is merely something
actual or potential; but we have no propositions whose
predicate is entirely indeterminate, for it would be quite senseless
to say, "A has the common characters of all things," inasmuch
as there are no such common characters.
Thus substance and being are the beginning and end of all
conception. Substance is inapplicable to a predicate, and
being is equally so to a subject.
549. The terms 'precision" * and "abstraction," which
* Precision. (1) A high degree of approximation, only attainable by the
thorough application of the most refined methods of science.
(2) Its earlier meaning, still more or less used by logicians, is derived from
a meaning given to praecisio by Scotus and other scholastics: the act of
supposing (whether with consciousness of fiction or not) something about one
element of a percept, upon which the thought dwells, without paying any regard
to other elements. Precision implies more than mere discrimination, which
relates merely to the essence of a term. Thus I can, by an act of discrimination,
separate color from extension; but I cannot do so by precision, since I cannot
suppose that in any possible universe color (not color-sensation, but color
as a quality of an object) exists without extension. So with trianguarity and
trilaterality. On the other hand, precision implies much less than dissociation,
which, indeed, is not a term of logic, but of psychology. It is doubtful whether
a person who is not devoid of the sense of sight can separate space from color by
dissociation, or, at any rate, not without great difficulty; but he can, and, indeed,
does do so, by precision, if he thinks a vacuum is uncolored. So it is, likewise,
with space and tridimensionality.
Some writers called every description of abstraction by the name precision,
dividing precision into the real and the mental, and the latter into the negative
and the positive; but the better usage named these abstraction divided into real
and intentional, and the latter into negative (in which character from which
abstraction is made is imagined to be deniable of tfie subject prescinded) and
into precisive abstraction or precision, where the subject prescinded is supposed
(in some hypothetical state of things) without any supposition, whether
affirmative or negative, in respect to the character abstracted. Hence, the brocard:
abstrahentium non est mendacium (generally enunciated in connection with the
De A nima, lII, VII, 7) . Scotus (in II Physic., Expositio 20 textus 18) says: " Et si
aliquis dicat, quod Mathematici tunc faciunt mendacium: quia considerant ista,
quasi essent abstracta a motu, et materia; quae tamen sunt coniuncta materiae.
Respondet, quod non faciunt mendacium: quia Mathematicus non considerat,
utrum id, de quo demonstrat suas passiones, sit coniunctum materiae, vel
abstractum a materia." This is not the place to treat of the many interesting
logical, as well as psychological, discussions which have taken place concerning
precision, which is one of the subjects which the scholastics treated in a
comparatively modern way, although it leads directly to the question of nominalism
and realism. It may, however, be mentioned that Scotus in many places draws
a certain distinction variously designated by him and his followers (its nature
and application is perhaps made as clear as anywhere in the Opus Oxon. III,
xxii. qu. unica, " Utrum Christus fuerit homo in triduo," i. e. between the
crucifixion and the resurrection), which the Thomists mostly dispute. There is some
account of the matter in Chauvinus, Lexicon (2d ed.), under "Praecisio" . . .
Dictionary of Philosophy and Psychology, vol. 2, pp. 323-4, Macmillan Co.,
New York, edition of 1911.
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were formerly applied to every kind of separation, are now
limited, not merely to mental separation, but to that which
arises from attention to one element and neglect of the other.
Exclusive attention consists in a definite conception or
supposition of one part of an object, without any supposition of the
other. Abstraction or precision ought to be carefully
distinguished from two other modes of mental separation, which
may be termed discrimination and dissociation. Discrimination
has to do merely with the senses of terms, and only draws a
distinction in meaning. Dissociation is that separation which,
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in the absence of a constant association, is permitted by the
law of association of images. It is the consciousness of one
thing, without the necessary simultaneous consciousness of the
other. Abstraction or precision, therefore, supposes a greater
separation than discrimination, but a less separation than
dissociation. Thus I can discriminate red from blue, space from
color, and color from space, but not red from color. I can
prescind red from blue, and space from color (as is manifest
from the fact that I actually believe there is an uncolored space
between my face and the wall); but I cannot prescind color
from space, nor red from color. I can dissociate red from blue,
but not space from color, color from space, nor red from color.
Precision is not a reciprocal process. It is frequently the
case, that, while A cannot be prescinded from B, B can be
prescinded from A. This circumstance is accounted for as
follows. Elementary conceptions only arise upon the occasion
of experience; that is, they are produced for the first time
according to a general law, the condition of which is the
existence of certain impressions. Now if a conception does not
reduce the impressions upon which it follows to unity, it is a
mere arbitrary addition to these latter; and elementary
conceptions do not arise thus arbitrarily. But if the impressions
could be definitely comprehended without the conception, this
latter would not reduce them to unity. Hence, the impressions
(or more immediate conceptions) cannot be definitely
conceived or attended to, to the neglect of an elementary
conception which reduces them to unity. On the other hand, when
such a conception has once been obtained, there is, in general,
no reason why the premisses which have occasioned it should
not be neglected, and therefore the explaining conception may
frequently be prescinded from the more immediate ones and
from the impressions.
550. The facts now collected affard the basis for a
systematic method of searching out whatever universal elementary
conceptions there may be intermediate between the manifold of
substance and the unity of being. It has been shown that the
occasion of the introduction of a universal elemnentary
conception is either the reduction of the manifold of substance to
unity, or else the conjunction to substance of another
conception. And it has further been shown that the elements conjoined
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cannot be supposed without the conception, whereas the
conception can generally be supposed without these elements.
Now, empirical psychology discovers the occasion of the
introduction of a conception, and we have only to ascertain what
conception already lies in the data which is united to that of
substance by the first conception, but which cannot be
supposed without this first conception, to have the next conception
in order in passing from being to substance.
It may be noticed that, throughout this process,
introspection is not resorted to. Nothing is assumed respecting the
subjective elements of consciousness which cannot be securely
inferred from the objective elements.
551. The conception of being arises upon the formation of
a proposition. A proposition always has, besides a term to
express the substance, another to express the quality of that
substance; and the function of the conception of being is to
unite the quality to the substance. Quality, therefore, in its
very widest sense, is the first conception in order in passing
from being to substance.
Quality seems at first sight to be given in the impression.
Such results of introspection are untrustworthy. A proposition
asserts the applicability of a mediate conception to a more
immediate one. Since this is asserted, the more mediate
conception is clearly regarded independently of this circumstance,
for otherwise the two conceptions would not be distingu;shed,
but one would be thought through the other, without this
latter being an object of thought, at all. The mediate
conception, then, in order to be asserted to be applicable to the other,
must first be considered without regard to this circumstance,
and taken immediately. But, taken immediately, it transcends
what is given (the more immediate conception), and its
applicability to the latter is hypothetical. Take, for example, the
proposition, "This stove is black." Here the conception of this
stove is the more immediate, that of black the more mediate,
which latter, to be predicated of the former, must be
discriminated from it and considered in itself, not as applied to an
object, but simply as embodying a quality, blackness. Now this
blackness is a pure species or abstraction, and its application
to this stove is entirely hypothetical. The same thing is meant
by " the stove is black," as by " there is blackness in the stove."
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Embodying blackness is the equivalent of black. * The proof is
this. These conceptions are applied indifferently to precisely
the same facts. If, therefore, they were different, the one which
was first applied would fulfil every function of the other; so
that one of them would be superfluous. Now a superfluous
conception is an arbitrary fiction, whereas elementary
conceptions arise only upon the requirement of experience; so that a
superfluous elementary conception is impossible. Moreover,
the conception of a pure abstraction is indispensable, because
we cannot comprehend an agreement of two things, except as
an agreement in some respect, and this respect is such a pure
abstraction as blackness. Such a pure abstraction, reference
to which constitutes a quality or general attribute, may be
termed a ground.
Reference to a ground cannot be prescinded from being, but
being can be prescinded from it.
552. Empirical psychology has established the fact that
we can know a quality only by means of its contrast with or
similarity to another. By contrast and agreement a thing is
referred to a correlate, if this term may be used in a wider
sense than usual. The occasion of the introduction of the
conception of reference to a ground is the reference to a correlate,
and this is, therefore, the next conception in order.
Reference to a correlate cannot be prescinded from reference
to a ground; but reference to a ground may be prescinded from
reference to a correlate.
553. The occasion of reference to a correlate is obviously
by comparison. This act has not been sufficiently studied by
the psychologists, and it will, therefore, be necessary to adduce
some examples to show in what it consists. Suppose we wish
to compare the letters p and b. We may imagine one of them
to be turned over on the line of writing as an axis, then laid
upon the other, and finally to become transparent so that the
other can be seen through it. In this way we shall form a new
image which mediates between the images of the two letters,
inasmuch as it represents one of them to be (when turned over)
he likeness of the other. Again, suppose we think of a
murderer as being in relation to a murdered person; in this case
* This agrees with the author of "De Generibus et Speciebus," Ouvrages
In‚dits d'Abelard, p. 528, [edited by V. Cousin, Paris, 1836].
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we conceive the act of the murder, and in this conception it
is represented that corresponding to every murderer (as well
as to every murder) there is a murdered person; and thus we
resort again to a mediating representation which represents
the relate as standing for a correlate with which the mediating
representation is itself in relation. Again, suppose we look up
the word homme in a French dictionary; we shall find opposite
to it the word man, which, so placed, represents homme as
representing the same two-legged creature which man itself
represents. By a further accumulation of instances, it would
be found that every comparison requires, besides the related
thing, the ground, and the correlate, also a mediating
representation which represents the relate to be a representation of the
same correlate which this mediating representation itself
represents. Such a mediating representation may be termed an
interpretant, because it fulfils the office of an interpreter, who
says that a foreigner says the same thing which he himself says.
The term representation is here to be understood in a very
extended sense, which can be explained by instances better
than by a definition. In this sense, a word represents a thing
to the conception in the mind of the hearer, a portrait
represents the person for whom it is intended to the conception of
recognition, a weathercock represents the direction of the wind
to the conception of him who understands it, a barrister
represents his client to the judge and jury whom he influences.
Every reference to a correlate, then, conjoins to the
substance the conception of a reference to an interpretant; and
this is, therefore, the next conception in order in passing from
being to substance.
Reference to an interpretant cannot be prescinded from
reference to a correlate; but the latter can be prescinded
from the former.
554. Reference to an interpretant is rendered possible and
justified by that which renders possible and justifies
comparison. But that is clearly the diversity of impressions. If we
had but one impression, it would not require to be reduced
to unity, and would therefore not need to be thought of as
referred to an interpretant, and the conception of reference to
an interpretant would not arise. But since there is a manifold
of impressions, we have a feeling of complication or confusion,
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which leads us to differentiate this impression from that, and
then, having been differentiated, they require to be brought to
unity. Now they are not brought to unity until we conceive
them together as being ours, that is, until we refer them to a
conception as their interpretant. Thus, the reference to an
interpretant arises upon the holding together of diverse
impressions, and therefore it does not join a conception to the
substance, as the other two references do, but unites directly
the manifold of the substance itself. It is, therefore, the last
conception in order in passing from being to substance.
555. The five conceptions thus obtained, for reasons which
will be sufficiently obvious, may be termed categories. That is,
Being
Quality (reference to a ground)
Relation (reference to a correlate)
Representation (reference to an intcrpretant)
Substance
The three intermediate conceptions may be termed
accidents.
556. This passage from the many to the one is numerical.
The conception of a third is that of an object which is so related
to two others, that one of these must be related to the other
in the same way in which the third is related to that other.
Now this coincides with the conception of an interpretant.
An other is plainly equivalent to a correlate. The conception of
second differs from that of other, in implying the possibility of
a third. In the same way, the conception of self implies the
possibility of an other. The ground is the self abstracted from
the concreteness which implies the possibility of another.
557. Since no one of the categories can be prescinded from
those above it, the list of supposable objects which they afford
is
What is.
Quale (that which refers to a ground)
Relate (that which refers to ground and correlate)
Representamen (that which refers to ground, correlate,
and interpretant)
It
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558. A quality may have a special determination which
prevents its being prescinded from reference to a correlate.
Hence there are two kinds of relation.
First. That of relates whose reference to a ground is a
prescindible or internal quality.
Second. That of relates whose reference to a ground is an
unprescindible or relative quality.
In the former case, the relation is a mere concurrence of the
correlates in one character, and the relate and correlate are
not distinguished. In the latter case the correlate is set over
against the relate, and there is in some sense an opposition.
Relates of the first kind are brought into relation simply by
their agreement. But mere disagreement (unrecognized) does
not constitute relation, and therefore relates of the second kind
are only brought into relation by correspondence in fact.
A reference to a ground may also be such that it cannot be
prescinded from a reference to an interpretant. In this case it
may be termed an isnputed quality. If the reference of a relate
to its ground can be prescinded from reference to an
interpretant, its relation to its correlate is a mere concurrence or
community in the possession of a quality, and therefore the
reference to a correlate can be prescinded from reference to an
interpretant. It follows that there are three kinds of
representations.
First. Those whose relation to their objects is a mere
community in some quality, and these representations may be
termed likenesses. *
Second. Those whose relation to their objects consists in a
correspondence in fact, and these may be termed indices or
signs. **
Third. Those the ground of whose relation to their objects
is an imputed character, which are the same as general signs
and these may be termed symbols.
559. I shall now show how the three conceptions of
reference to a ground, reference to an object, and reference to an
interpretant are the fundamental ones of at least one universal
science, that of logic. Logic is said to treat of second intentions
* In later writings called "icons."
** In later writings an index is always taken to be but one of many kinds of
signs; a sign being understood in some sense similar to that given in 540.
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as applied to first.* It would lead me too far away from the
matter in hand to discuss the truth of this statement; I shall
simply adopt it as one which seems to me to afford a good
definition of the subject-genus of this science. Now, second
intentions are the objects of the understanding considered as
representations, and the first intentions to which they apply
are the objects of those representations. The objects of the
understanding, considered as representations, are symbols, that
is, signs which are at least potentially general. But the rules
of logic hold good of any symbols, of those which are written
or spoken as well as of those which are thought. They have no
immediate application to likenesses or indices, because no
arguments can be constructed of these alone, but do apply to
all symbols. All symbols, indeed, are in one sense relative to
the understanding, but only in the sense in which also all
things are relative to the understanding. On this account,
therefore, the relation to the understanding need not be
expressed in the definition of the sphere of logic, since it
determines no limitation of that sphere. But a distinction can be
made between concepts which are supposed to have no
existence except so far as they are actually present to the
understanding, and external symbols which still retain their
character of symbols so long as they are only capable of being
understood. And as the rules of logic apply to these latter as
much as to the former (and though only through the former,
yet this character, since it belongs to all things, is no
limitation), it follows that logic has for its subject-genus all symbols
and not merely concepts. ** We come, therefore, to this, that
logic treats of the reference of symbols in general to their
objects. In this view it is one of a trivium of conceivable
sciences. The first would treat of the formal conditions of
* See Peirce's definition in the Century Dicfionary (1889) Intention 8; also
Albertus Magnus, Meta. I,1,1, and Th. Aquinas, Meta. IV, 4, f. 43 v. A.
** Herbart says [Lehrbuch, 2 A., 1te Kap., # 34]: "Unsre sammtlichen Gedanken
lassen sich von zwei Seiten betrachten; theils als Thatigkeiten unseres Geistes,
theils in Hinsicht dessen, was durch sie gedacht wird. In letzerer Beziehung
heissen sie Begriffe, welches Wort, indem es das Begriffene bezeichnet, zu
abstrahiren gebietet von der Art und Weise, wie wir den Gedanken empfangen,
produciren oder reproduciren mogen." But the whole difference between a
concept and an external sign lies in these respects which logic ought, according
to Herbart, to abstract from.
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symbols having meaning, that is of the reference of symbols
in general to their grounds or imputed characters, and this
might be called formal grammar;* the second, logic,** would
treat of the formal conditions of the truth of symbols; and
the third would treat of the formal conditions of the force
of symbols, or their power of appealing to a mind, that is, of
their reference in general to interpretants, and this might be
called formal rhetoric.***
There would be a general division of symbols, common to
all these sciences; namely, into,
1ø. Symbols which directly determine only their grounds
or imputed qualities, and are thus but sums of marks or
terms;
2ø. Symbols which also independently determine their
obgects by means of other term or terms, and thus, expressing
their own objective validity, become capable of truth or
falsehood, that is, are propositions; and,
3ø. Symbols which also independently determine their
interpretants, and thus the minds to which they appeal, by
premissing a proposition or propositions which such a mind is
to admit. These are argurnents.
And it is remarkable that, among all the definitions of the
proposition, for example, as the oratio indicativa, as the
subsumption of an object under a concept, as the expression of
the relation of two concepts, and as the indication of the
mutable ground of appearance, there is, perhaps, not one in which
the conception of reference to an object or correlate is not the
important one. In the same way, the conception of reference
to an interpretant or third, is always prominent in the
definitions of argument.
In a proposition, the term which separately indicates the
object of the symbol is termed the subject, and that which
indicates the ground is termed the predicate. The objects
indicated by the subject (which are always potentially a
plurality -- at least, of phases or appearances) are therefore
stated by the proposition to be related to one another on the
* Later called Speculative Crammar or Stechiology.
** Later called Critical Logic or Critic.
*** Later called Speculative Rhetoric or Methodeutic.
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ground of the character indicated by the predicate. Now this
relation may be either a concurrence or an opposition.
Propositions of concurrence are those which are usually considered
in logic; but I have shown in a paper upon the classification of
arguments* that it is also necessary to consider separately
propositions of opposition, if we are to take account of such
arguments as the following:
Whatever is the half of anything is less than that of which
it is the half:
A is half of B;
A is less than B.
The subject of such a proposition is separated into two terms,
a "subject nominative" and an "object accusative."
In an argument, the premisses form a representation of the
conclusion, because they indicate the interpretant of the
argument, or representation representing it to represent its object.
The premisses may afford a likeness, index, or symbol of the
conclusion. In deductive argument, the conclusion is
represented by the premisses as by a general sign under which it is
contained. In hypotheses, something like the conclusion is
proved, that is, the premisses form a likeness of the conclusion.
Take, for example, the following argument:
M is, for instance, P1, P2, P3, and P4;
S is P1, P2, P3, and P4:
.-. S is M.
Here the first premiss amounts to this, that "P1, P2, P3,
and P4" is a likeness of M, and thus the premisses are or
represent a likeness of the conclusion. That it is different with
induction another example will show.
S1, S2, S3, and S4 are taken as samples of the collection M;
S1, s2, S3, and S4 are P:
.-. All M is P.
Hence the first premiss amounts to saying that "S1, S2,
S3, and S4" is an index of M. Hence the premisses are an
index of the conclusion.
* See vol. 2, bk. III, ch. 2.
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The other divisions of terms, propositions, and arguments
arise from the distinction of extension and comprehension. I
propose to treat this subject in a subsequent paper.* But I
will so far anticipate that as to say that there is, first, the direct
reference of a symbol to its objects, or its denotation; second,
the reference of the svmbol to its ground, through its object,
that is, its reference to the common characters of its objects,
or its connotation; and third, its reference to its interpretants
through its object, that is, its reference to all the synthetical
propositions in which its objects in common are subject or
predicate, and this I term the information it embodies. And
as every addition to what it denotes, or to what it connotes, is
effected by means of a distinct proposition of this kind, it
follows that the extension and comprehension of a term are in
an inverse relation, as long as the information remains the
same, and that every increase of information is accompanied
by an increase of one or other of these two quantities. It may
be observed that extension and comprehension are very often
taken in other senses in which this last proposition is not true.
This is an imperfect view of the application which the
conceptions which, according to our analysis, are the most
fundamental ones find in the sphere of logic. It is believed, however,
that it is sufficient to show that at least something may be
usefully suggested by considering this science in this light.