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Copytext 1
On a New List of Categories
Charles S. Peirce
Proceedings of the American Academy of Arts and Sciences 7 (1868), 287-298.
Sec. 1. 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.
Sec. 2. 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.
Sec. 3. 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 subject, nor in a subject, and accordingly is identical with the conception of substance.
Sec. 4. 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.
Sec. 5. The terms "prescision" and "abstraction," which 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 prescision 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, 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 prescision, 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.
Prescision 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.
Sec. 6. The facts now collected afford 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 elementary 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 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.
Sec. 7. 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 distinguished, 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." 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.
Sec. 8. 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.
Sec. 9. 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 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.
Sec. 10. 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, 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.
Sec. 11. 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 Interpretant),
SUBSTANCE
The three intermediate conceptions may be termed accidents.
Sec. 12. 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 an other.
Sec. 13. 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.
Sec. 14. 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 imputed 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.
Sec. 15. 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 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 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,
1) Symbols which directly determine only their grounds or imputed qualities, and are thus but sums of marks or terms;
2) Symbols which also independently determine their objects 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,
3) 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 arguments.
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 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, P', P, P, and P';
S is P', P, P, and P':
[Ergo,] S is M.
Here the first premiss amounts to this, that "P', P, P, and P'" 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.
S', S, S, and S' are taken as samples of the collection M;
S', S, S, and S' are P:
[Ergo,] All M is P.
Hence the first premiss amounts to saying that "S', S, S, and S'" is an index of M. Hence the premisses are an index of the conclusion.
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 symbol 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.
Notes
1. This agrees with the author of De Generibus et Speciebus, Ouvrages Inedits d'Abelard, p. 528. Return to text.
2. Herbart says: "Unsre saemmtlichen Gedanken lassen sich von zwei Seiten betrachten; theils als Thaetigkeiten unseres Geistes, theils in Hinsicht dessen, was durch sie gedacht wird. In letzterer Beziehung heissen sie Begriffe, welches Wort, indem es das Begriffene bezeichnet, zu abstrahiren gebieted von der Art und Weise, wie wir den Gedanken empfangen, produciren, oder reproduciren moegen." But the whole difference between a concept and an external sign lies in these respects which logic ought, according to Herbart, to abstract from. Return to text.
Copytext 2
Charles S. Peirce
On a New List of Categories
Proceedings of the American Academy
of Arts and Sciences 7 (1868), pp. 287-298.
Specially Formatted for On-Line Presentation by
Joseph Ransdell
See below for legal/scholarly status of document.
Click on "editorial notes" in the panel to the left for an
editorial preface to the document.
(CP1.545, W2.49)
§1. 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.
[CP1.546]
§2. 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.
(CP1.547)
§3. 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, or 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 subject, nor in a subject, and
accordingly is identical with the conception of
substance.
(CP1.548)
§4. 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 (W2.50) 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.
(CP1.549)
§5. The terms "prescision" and "abstraction," which
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 prescision 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
essences of terms, and only draws a distinction in
meaning. Dissociation is that separation which, 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 prescision,
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 (W2.51) 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.
Prescision 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
premises 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.
(CP1.550)
§6. The facts now collected afford 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 elementary 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 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 (W2.52) subjective elements of
consciousness which cannot be securely inferred from
the objective elements.
(CP1.551)
§7. 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
distinguished, 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." Embodying blackness is the equivalent of
black.<1> 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, (W2.53) 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.
(CP1.552)
§8. 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.
(CP1.553)
§9. The occasion of reference to a correlate is
obviously by comparison. This act has not been
suficiently 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) the likeness of
the other. Again, suppose we think of a murderer as
being in relation to a murdered person; in this case 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 out 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, (W2.54) 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.
(CP1.554)
§10. 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, 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.
(CP1.555)
§11. 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
Interpretant),
SUBSTANCE.
(W2.55)
The three intermediate conceptions may be termed
accidents.
(CP1.556)
§12. 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 an other.
(CP1.557)
§13. Since no one of the categories can be
prescinded from those above it, the list of supposable
objects which they afford is,
What is.
Qualethat which refers to a ground,
Relatethat which refers to a ground
and correlate,
Representamenthat which refers to
ground, correlate, and interpretant.
It.
(CP1.558)
§14. A quality may have a special determination
which prevents its being prescinded from reference to a
correlate. Hence there are two kinds of relation.
1st. That of relates whose reference to a ground is
a prescindible or internal quality.
2nd. 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 imputed
quality. If the reference of a relate to its ground (W2.56)
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.
1st. Those whose relation to their objects is a mere
community in some quality, and these representations
may be termed Likenesses.
2nd. Those whose relation to their objects consists
in a correspondence in fact, and these may be termed
Indices or Signs.
3rd. 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.
(CP1.559)
§15. 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 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 (W2.57)concepts.<2> 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 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,
1°: Symbols which directly determine only their
grounds or imputed qualities, and are thus but sums
of marks or terms;
2°: Symbols which also independently determine
their objects 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,
3°: Symbols which also independently determine
their interpretants, and thus the minds to which they
appeal, by premising a proposition or propositions
which such a mind is to admit. These are arguments.
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 (W2.58) appearances) are therefore stated by
the proposition to be related to one another on the
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 premises form a representation
of the conclusion, because they indicate the
interpretant of the argument, or representation
representing it to represent its object. The premises
may afford a likeness, index, or symbol of the
conclusion. In deductive argument, the conclusion is
represented by the premises as by a general sign under
which it is contained. In hypotheses, something like
the conclusion is proved, that is, the premises form a
likeness of the conclusion. Take, for example, the
following argument:--
M is, for instance, P', P, P, and P';
S is P', P, P, and P':
[Ergo,] S is M.
Here the first premise amounts to this, that " P',
P, P, and P' " is a likeness of M, and thus the
premises are or represent a likeness of the conclusion.
That it is different with induction another example will
show.
S', S, S, and S' are taken as samples of the
collection M;
S', S, S, and S' are P:
[Ergo,] All M is P.
Hence the first premiss amounts to saying that " S',
S, S, and S' " is an index of M. Hence the
premisses are an index of the conclusion.
The other divisions of terms, propositions, and
arguments arise (W2.59) 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 symbol 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.<Note> 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.
FOOTNOTES
1 This agrees with the author of De Generibus et
Speciebus, Ouvrages Inédits d'Abélard, p. 528.
2 Herbart says: "Unsre sämmtlichen Gedanken lassen
sich von zwei Seiten betrachten; theils als Thätigkeiten
unseres Geistes, theils in Hinsicht dessen, was durch
sie gedacht wird. In letzterer 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 mögen." But the whole difference
between a concept and an external sign lies in these
respects which logic ought, according to Herbart, to
abstract from.
EDITORIAL NOTES
Note (Ransdell): The grammar of the sentence to
which this note is appended, though formally
impeccable, makes it unnecessarily difficult to
understand and it can seem to be ungrammatical. I
suggest that it can be slightly reworded as follows:
"This is an imperfect view of the application which the
conceptions -- which, according to our analysis, are the most
fundamental conceptions -- find in the sphere of logic."
