As regards the indefinite article there are
probably
no exceptions to our rule at all for us to remark, apart from obsolete formulas like Ein edler Rath ['Councillor'].
Gottlob-Frege-Posthumous-Writings
The plus sign does not mean the same as 'and'.
In the sentences '3 and 5 are odd', '3 and 5 are factors of 15 other than 1' we cannot substitute '2 and 6' or '8' for '3 and 5'.
On the other hand, '2 + 6' or '8' are always substitutable for '3 + 5'.
It is therefore incorrect to say' 1 and 1 is 2' instead of 'the sum of 1 and 1 is 2'.
It is wrong to say 'number is just so many ones'; and if we say 'units' for 'ones', if anything we magnify the error by confusing units with one, even though verbally there is a gain in smoothness.
Our feeling for language warns us against the form 'ones' for good reason.
If we say 'units' instead, we merely get round the prohibition.
? ? ~
On Concept and Object
In a series of articles in this Quar- terly on intuition and its psychical elaboration, Benno Kerry has several times referred to my Grundlagen der Arithmetik and other works of mine, sometimes agreeing and sometimes disagreeing with me. I cannot but be pleased at this, and I think the best way I can show my appreciation is to take up the discussion of the points he contests. This seems to me all the more necessary, because his op- position is at least partly based on a misunderstanding, which might be
1 Until his death in 1889 Benno Kerry was Privatdozent in Philosophy at the University of Strasburg.
The dispute with Kerry relates to Kerry's eight articles Uber Anschauung und ihre psychische Verarbeitung in the Vierteijahrsschrift fiir wissenschaftliche Philosophie:" (1885), pp. 433-493, 10 (1886), pp. 419-467, 11 (1887), pp. 53-
116, 11 (1887), pp. 249-307, l3 (1889), pp. 71-124, l3 (1889), pp. 392-419, 14 (1890), pp. 317-353, 15 (1891), pp. 127-167. In the second and fourth articles Kerry had gone into Frege's views in particular detail. -The piece for the NachlajJ is obviously a preliminary draft of the article Ober Begriff und Gegenstand, which nppeared in 1892. The latter is printed on the left with the original pagination, with the corresponding passages of the piec~ from the NachlajJ on the right (ed. ).
Translators' note: For the article Uber Begriff und Gegenstand we have taken over the translation by Peter Geach published in Translations from the Philosophical Writings of Gottlob Frege, ed. Geach and Black, pp. 42-55 (Blackwell 1960), both because we are largely in agreement with it and because it has been so widely read and quoted from. Where the wording of the draft agrees with that of the published article, we have relied heavily on the Geach translation, though we have departed from it in several places, mainly in order to remain consistent with the renderings we have adopted elsewhere of certain terms-here notably 'bedeuten' and 'Bedeutung'. Again such a departure has been necessary in places where the agreement in wording extends only to part of a Nentence.
We have chosen not to adhere to the format of the German text in presenting the draft as if both it and the criticism of Biermann were about the concept of number. The fact that they were both found, unseparated, in a folder under the heading 'On the Concept of Number' seems to us no good reason for the German editors' lay- out.
We should like to express our grateful thanks to Professor P. T. Geach for Jlc:rmitting us to make use of his translation in this way.
[A criticism ofKerry]I
87
? ? 88 On Concept and Object
shared by others, of what I say about the concept; and because, even apart from this special oc- casion, the matter is important and difficult enough for a more thorough treatment than seemed to me suit- able in my Grundlagen.
The word 'concept' is used in various ways; its sense is sometimes psychological, sometimes logical, and sometimes perhaps a confused mixture of both. Since this licence exists, it is natural to restrict it by requiring that when once a usage is adopted it shall be maintained. What I decided was to keep strictly to a purely logical use; the question whether this or that use is more appropriate is one that I should like to leave on one side, as of minor importance. Agreement about the mode of expression will easily be reached when once it is recognized that there is something that deserves a special term.
It seems to me that Kerry's misunderstanding results from his unintentionally confusing his own usage of the word 'concept' with mine. This readily gives rise to contradictions, for which my usage is not to blame.
[193] Kerry contests what he calls my definition of 'concept'. I would remark, in the first place, that my
I turn now to consider, as briefly as possible, the objections which B. Kerry* has brought against my definitions.
He begins by contesting what he calls my definition of a concept, and there is no doubt that here he is
* Uber Anschauung und ihre psy- chische Verarbeitung in der Viertel- jahrschrift fiir wissenschaftliche Philosophie, Volume Xl, No. 3, pp.
249 IT.
? explanation is not meant as a proper definition. One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance. What is simple cannot be decomposed, and what is logically simple cannot have a proper definition. Now something logically simple is no more given us a t the outset than most of the chemical elements are; it is reached only by means o f scientific work. I f some- thing has been discovered that is simple, or at least must count as simple for the time being, we shall have to coin a term for it, since language will not originally contain an expression that exactly answers. On the introduction of a name for something logically simple, a definition is not possible; there is nothing for it but to lead the reader or hearer, by means of hints, to understand the words as is intended.
Kerry wants to make out that the distinction between concept and object is not absolute. 'In a previous passage,' he says, 'I have myself expressed the opinion that the relation between the content of the concept and the concept-object is, in u certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being a concept and of being an object are mutually ex-
touching on a crucial point, perhaps the most important one in the whole issue. The first thing to say is that my explanation is not meant as a proper definition. One cannot define everything, any more than one can decompose every chemical substance. To do either presupposes that we are dealing with something composite. In many cases one has to be satisfied with leading the reader, by means of hints, to understand the word as it is intended.
On Concept and Object 89
The difference of opinion con- cerns the distinction between con- cept* and object. Kerry would like to make out that it is not absolute. 'In a previous passage,' he says, 'we have ourselves expressed the opinion that the relation between the concept-content and the concept- object is, in a certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being an
* In my paper Funktion und Begriff (Jena 1891) I called a concept a function whose value is always a truth-value, and this could be taken as a definition. But in that case the difficulty which, as I am trying to show, arises for the con- cept, arises for the function too.
? ? ? 90 On Concept and Object
elusive. The latter view no more object and being a concept are follows from the former than it mutually exclusive. The latter view
would follow, if, e. g. , the relation of father and son were one that could not be further reduced, that a man could not be at once a father and a son (though of course not, e. g. , father of the man whose son he was). '
Let us fasten on this simile. If there were, or had been beings that were fathers but could not be sons, such beings would obviously be quite different in kind from all men who are sons. Now it is something like this that happens here. The concept (as I understand the word) is predicative. *
On the other hand, a name of an object, a proper name, is quite incapable of being used as a grammatical predicate. This admit- tedly needs elucidation, otherwise it might appear false. Surely one can just as well assert of a thing that it is Alexander the Great, or is the number four, or is the planet Venus, as that it is green or is a mammal? [194]. If anybody thinks this, he is not distinguishing the usages o f the word 'is'. In the last two examples it serves as a copula, as a mere verbal sign of predication. (In this sense the
*It is, in fact, the reference of a grammatical predicate.
no more follows from the former than it would follow if, say, the relation of father and son were one that could not be further reduced, that a man could not be at once a father and a son (though of course not e. g. father of the man whose son he was). ' 1
Let me fasten on this simile. If there were, or had been, beings that were fathers, though they were so constituted by nature that they could not be sons, such beings would be obviously quite different in kind from all men who are sons. Now something like this happens here.
The concept-as I understand the word-is predicative even in cases where we speak of a subject- concept. For instance, the sentence 'All mammals are warm-blooded' says the same as 'Whatever is a mammal is warm-blooded'. On the other hand, a name of an object-a proper name-is quite incapable of being used as a grammatical predi- cate. This may strike one as false if one does not distinguish between a proper name's occurring as only part of a predicate, which is cer- tainly possible, and its being itself the whole predicate, which is not pos- sible. One can assert of a thing that it is green or is a mammal; but one cannot in the same way assert of a thing that it is Alexander the Great, or is the number four, or is Venus.
1 Vjschr. f wissensch. Philosophie 11 ( 1887), p. 272 (ed. ).
? ? ? German word ist can sometimes be replaced by the mere personal suffix: cf. dies Blatt ist griin and dies Blatt griint. ) We are here saying that something falls under a concept, and the grammatical predicate stands for this concept. In the first three examples, on the other hand, 'is' is used like the 'equals' sign in
In order to see this, it is of course necessary to distinguish the two uses of the word 'is'. For in the first cases it serves as a copula, as a mere auxiliary indicating that we have a statement, and is sometimes then replaceable by the mere verb ending: e. g. 'dieses Blatt ist griin' ['this grass is green'], 'dieses Blatt griint' [lit. 'this grass greens']. Here one is saying that something falls under a concept. The grammatical predicate means this concept. In the second cases, the word 'is' is used like the equals sign in arithmetic, to express an equation. * Let us consider the following example: in the sentence 'That is Saturn' we have two proper names for the same object. For the word 'that', together with an appropriate pointing gesture, must here be construed as a proper name (in the logical sense) i. e. as a sign for an object. I am not here asserting the meaning of the word 'Saturn' of the object I am pointing to; if that were so, I should be asserting an object of itself, which would be nonsensical- one just cannot assert an object of
* I use the word 'equal' and the sign '=' in the sense 'the same as', 'not different from'. Cf. E. Schroder,
Vorlesungen iiber die Algebra der Logik (Leipzig 1890), Vol. 1, ? 1, especially p. 127 & p. 128. Schroder, however, is to be criticized for not here distinguishing two fundamentally different relations; the relation of an object to a concept it falls under, and the sub- ordination of one concept to
arithmetic, equation. *
to express
an
*I use the word 'equal' and the symbol '=' in the sense 'the same as', 'no other than', 'identical with'. Cf. E. Schroeder, Vorlesungen ueber die Algebra der Logik (Leipzig
On Concept and Object 91
1890), Vol. 1, ? 1. Schroeder must
however be criticized for not dis-
tinguishing two fundamentally dif-
ferent relations; the relation o f an
object to a concept it falls under,
and the subordination of one con-
cept to another. His remarks on
the Vollwurzel are likewise open
to objection. Schroeder's symbol ~ another. His discussion of the does not simply take the place of the Vollwurzel is likewise open to objec- copula. tion.
? ? ? 92
On Concept and Object
In the sentence 'The mor- ning star is Venus', we have two proper names, 'morning star' and 'Venus', for the same object. In the sentence 'the morning star is a planet' we have a proper name, 'the morning star', and a concept-word, 'planet'. So far as language goes, no more has happened than that 'Venus' has been replaced by 'a planet'; but really the relation has become wholly different. An equation is reversible; an object's falling under a concept is an irre- versible relation. In the sentence 'the morning star is Venus', 'is' is ob- viously not the mere copula; its content is an essential part of the predicate, so that the word 'Venus' does not constitute the whole of the predicate. * One might say instead: 'the morning star is no other than V enus'; what was previously im- plicit in the single word 'is' is here set forth in four separate words, and
* Cf. my Grundlagen, ? 66, footnote.
*Cf. my Grundlagen, ? 57.
something-. The 'is' is not the mere copula, but is to be compared with a word like 'griint', in which the verb ending by itself takes the place of the copula, whilst the stem gives the actual content. * The content of the predicate is not comprised in the word 'Saturn' alone; an essential part of it is contained in the word 'is', or at least has to be added in thought. As the logical predicate we may Sftke, say: no other than Saturn. I t is ~is which is predicated here and not just Saturn. Saturn is an object, no other than Saturn is a concept.
? ? only as an object. Kerry, too, would probably not wish to dispute that there is something of this kind. But this would mean admitting a dis- tinction, which it is very important recognize, between what can occur only as an object, and everything else. And this distinction would not he effaced even if it were true, as Kerry thinks it is, that there are concepts that can also be objects.
concept, and Kerry himself surely does not wish to dispute that this is possible either. But this means ad- mitting a distinction, which it is of fundamental importance to rec- ognize, between what, by its very nature, can occur only as an object, and everything else. And this dis- tinction would not be effaced even if it were true, as Kerry thinks it is, that there are concepts that can also be objects. Now there are in fact cases which seem to support this
On Concept and Object
93
in 'is no other than' the word 'is'
now really is the mere copula. What
is predicated here is thus not Venus
but no other than Venus. These
words stand for a concept; admit-
tedly only one object falls under
this, but such a concept must still
always be distinguished from the
object. * We have here a word
'Venus' that can never be a proper
predicate [195] although it can form
part of a predicate. The reference**
of this word is thus something that something making its appearance can never occur as a concept, but only as an object, never as a
There are, indeed, cases that seem
to support his view. I myself have
indicated (in Grundlagen, ? 53, ad view. I myself have pointed out
jin. ) that a concept may fall under a higher concept-which, however, must not be confused with one concept's being subordinate to 11nother. Kerry does not appeal to this; instead, he gives the following example: 'the concept "horse" is a concept easily attained', and thinks that the concept 'horse' is an object, in fact one of the objects that fall under the concept 'concept easily at-
* Cf. my Grundlagen, ? 51.
** Cf. my paper, 'On Sense and Reference' (Ueber Sinn und Be- deutung), shortly to appear in the Zeitschriftfiir Phi! . und phi! . Kritik.
(Grundlagen, ? 53 to the end) that a concept may fall under a higher concept which, however, is not to be confused with one concept's being subordinate to another. Kerry does not appeal to this; instead, he gives the following example: 'the concept "horse" is a concept easily attained', and thinks that the concept 'horse' is an object, in fact one of the ob-
Thus, as we see, we have here the case of
jects that fall
under the
concept
? ? ? 94 On Concept and Object
tained'. Quite so; the three words 'the concept "horse"' do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I g a v e - that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept word. *
Kerry holds that no logical rules can be based on linguistic dis- tinctions; but my own way of doing this is something that nobody can avoid who lays down such rules at all; for we cannot come to an under- standing with one another apart from language, and so in the end we must always rely on other people's understanding words, inflexions, and sentence-construction in essentially the same way as ourselves. As I said before, I was not trying to give a definition, but only hints; and to this end I appealed to the general feeling for the German language. It is here very much to my advantage that there is such good accord between the linguistic distinction and the real one.
As regards the indefinite article there are probably no exceptions to our rule at all for us to remark, apart from obsolete formulas like Ein edler Rath ['Councillor']. The matter is not so simple for the definite article, especially [ 196] in the plural; but then my criterion does not relate to this case. In the singular, so far as I can see, the matter is doubtful only when a singular takes the place of a plural, as in the sentence 'the Turk besieged
* Grundlagen, ? 51; 66, footnote; ? 68, footnote on p. 80.
'concept easily attained'. Quite so; the three words 'the concept "horse"' do designate an object, but for that very reason they do not designate a concept in the sense in which I am using the word. This is in full accord with the criterion I gave-that the singular definite ar- ticle always indicates an object, whereas the indefinite article accom- panies a concept-word. * Now it is true that Kerry holds that no logical prescriptions can be based on lin- guistic distinctions; but proceeding as I do, this is something that nobody can possibly avoid who lays down such prescriptions; for you cannot make yourself understood apart from language, and so in the
end you must always rely on the reader or hearer's understanding words, inflexions and sentence- construction as you do yourself. As was said, I was not trying to give a definition, but only hints; and to this end I appealed to the general feeling for the German language; for my criterion relates directly only to the German language. I t is here very much to my advantage that the linguistic distinction accords so well with the real one. As regards the indefinite article there are, I should say, no exceptions to our rule at all to remark, apart from the archaic form 'Ein edler Rat' [Councillor], which here and there is still in official use. If the article in the plural can be replaced by 'all' and the meaning is that the statement is to hold of each individual member of the class, then we have a concept-
* My Grundlagen, ? 51; ? 66, footnote; ? 68, footnote on p. 80.
? ? ? Vienna', 'the horse is a four-legged animal'. These cases are so easily recognizable as special ones that the value of our rule is hardly impaired by their occurrence. It is clear that in the first sentence 'the Turk' is the proper name of a people. The second sentence is probably best regarded as expressing a universal judgement, say 'all horses are four- legged animals' or 'all properly con- stituted horses are four-legged animals'; these will be discussed later. ?
word (e. g. die Pferde sind pflanzen- fressende Tiere). 1 On the other hand, the phrase 'the Romans' in the sentence 'The Romans conquered Gaul' is to be regarded as a proper
name, for here we are not saying of each Roman that he has conquered Gaul; we are speaking of the Roman people, which is to be regarded logically as an object. There are also cases in which the singular is used in the sense of the plural--e. g. 'The horse is a herbivorous animal'. This case is so easily recognizable as an exception, that the value of our criterion is hardly impaired by it. (If the grammatical subject is a concept word, the sentence can be trans- formed into one in which the subject occurs predicatively with the in- definite article--e. g. 'If something is a horse, then it is a herbivorous animal'. The fuller account given in the Grundlagen makes it clear, I think, what I have in mind. )
? Nowadays people seem inclined to exaggerate the scope of the state- ment that different linguistic expres- sions are never completely equiva- lent, that a word can never be exactly translated into another lan- guage. One might perhaps go even further, and say that the same word is never taken in quite the same way even by men who share a language. I will not enquire as to the measure of truth in these statements; I would only emphasize that nevertheless different expressions quite often have something in common, which I call the sense, or in the special case
On Concept and Object 95
1 In the German sentence the word 'die' is the plural form of the definite article. The natural English translation would be 'Horses are herbivorous animals' (trans. ).
? ? ? 96 On Concept and Object
Kerry calls my criterion un- suitable; for surely, he says, in the sentence 'the concept that I am now talking about is an individual con- cept' the name composed of the first eight words stands for a concept; but he is not taking the word 'concept' in my sense, and it is not in what I have laid down that the contradiction lies. But nobody can require that my mode of expression shall agree with Kerry's.
It must indeed be recognized that we are here confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept,* whereas e. g. , the [197]
of sentences, the thought. In other words, we must not fail to recognize that the same sense, the same thought, may be variously ex- pressed; thus the difference does not here concern the sense, but only the apprehension, shading, or colouring of the thought, and is irrelevant for logic. It is possible for one sentence
to give no more and no less infor- mation than another; and, for all the multiplicity of languages, mankind has a common stock of thoughts. If all transformation of the expression were forbidden on the plea that this would alter the content as well, logic would simply be crippled; for the task of logic can hardly be perfor- med without trying to recognize the thought in its manifold guises. Moreover, all definitions would then have to be rejected as false.
* A similar 'thing happens when we say as regards the sentence 'this
Therefore when Kerry says that my criterion does not meet the case, claiming that in the sentence 'The concept that I am now talking about is an individual concept' the name composed of the first eight words surely means a concept, the contra- diction does not lie in what I have laid down; it obtains between the sense I attach to the word 'concept' and that adopted by Kerry. But nobody can require that my stipulations shall be in accord with Kerry's mode of expression, but only that they be consistent in them- selves. True, we cannot fail to recognize that we are here confron- ted by an awkwardness of language, which I admit is unavoidable, if we assert 'the concept horse is not a concept',* whereas, e. g. the city of Berlin is a city, and the volcano
*A similar thing happens when we say 'In the sentence "this rose is red", the grammatical predicate "red" belongs to the subject "this rose"'. Here the four words 'the grammatical predicate "red"' are not a grammatical predicate, but a subject. By the very act of explicitly calling it a grammatical predicate in this way, we deprive it of this property.
? ? ? city of Berlin is a city, and the volcano Vesuvius is a volcano. Language is here in a predicament that justifies the departure from custom. The peculiarity of our case is indicated by Kerry himself, by means of the quotation-marks around 'horse'; I use italics to the same end. There was no reason to mark out the words 'Berlin' and 'Vesuvius' in a similar way. In logical discussions one quite often needs to assert something about a concept, and to express this in the form usual for such assertions-viz. to make what is asserted of the concept into the content of the grammatical predicate. Conse- quently, one would expect that the reference of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object,? or, speaking more precisely, represented by an object. We designate this object by pre- lixing the words 'the concept'; e. g.
'The concept man is not empty'.
Here the first three words are to be regarded as a proper name,? ? which can no more be used predicatively than 'Berlin' or 'Vesuvius'. When we
rose is red': The grammatical pre- dicate 'is red' belongs to the subject 'this rose'. Here the words 'The grammatical predicate "is red"' are not a grammatical predicate but a subject. By the very act of explicitly calling it a predicate, we deprive it of this property.
? Cf. my Grundlagen, p. X.
? ? I call anything a proper name if it is a sign for an object.
Vesuvius is a volcano. Language is here in a predicament that justifies the departure from what we nor- mally say. The peculiarity of our case is indicated by Kerry himself by means of the quotation-marks around 'horse'. (We have used italics here to the same end. ) There was no reason to mark out the words 'Berlin' and 'Vesuvius' in a similar way above. In logical dis- cussions one quite often needs to assert something about a concept,? and to express this in the gram- matical form usual for such state- ments, so that what is asserted becomes the content of the gram- matical predicate. Consequently, one would expect the concept to be the content of the grammatical subject; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or, speak- ing more precisely: an object that is connected with it in accordance with a rule must be substituted for it, and it is this object we designate by an expression of the form 'the concept x'. (Cf. p. X of my Grundlagen. )
? When we say 'All men are mortal', we do not assert mortality of the concept man, but we sub- ordinate the concept mortal to the latter concept. [This is obviously a slip on Frege's part; what he means of course is that we subordinate the concept man to the concept mortal (trans. ). l
On Concept and Object 97
? ? 98 On Concept and Object
say 'Jesus falls under the concept man', then, setting aside the copula, the predicate is:
'someone falling under the concept
man'
and this means the same as: 'a man'.
But the phrase
'the concept man'
is only part of this predicate. Somebody might urge, as
against the predicative nature of the concept, that nevertheless we speak of a subject-concept. But even in such cases, e. g. in the sentence
'all mammals have red blood'
we cannot fail to recognize the pre- dicative nature? of the concept; for we can say instead:
[198] 'whateverisamammal has red blood'
or:
? What I call here the predicative nature of the concept is just a special case of the need of supple- mentation, the 'unsaturatedness', that I gave as the essential feature of a function in my work Function und Begriff (Jena, 1891). I t was there scarcely possible to avoid the ex- pression 'the functionflx)', although there too the difficulty arose that what this expression stands for is not a function.
'if anything is a mammal, then it has red blood'.
So the phrase 'the concept horse' must be regarded as a proper name, which can no more be used pre?
? ? ? When I wrote my Grundlagen der Arithmetik, I had not yet made the Jistinction between sense and reference;? and so, under the expres- sion 'a possible content of judge- ment, I was combining what I now Jesignate by the distinctive words 'thought' and 'truth-value'. Conse- quently, I no longer entirely approve of the explanation I then gave (op. cit. p. 77), as regards its wording; my view is, however, still essentially the same.
dicatively than can, say, 'Berlin' or 'Vesuvius'. If we say that Bucephalus falls under the concept horse, then the predicate here is clearly 'falling under the concept horse', and this has the same mean- ing as 'a horse'. But the phrase 'the concept horse' is only part of this predicate.
When I wrote my Grundlagen, I had not yet made the distinction between sense and meaning;? and so, under the expression 'content of possible judgement', I was combin- ing what I now distinguish by the words 'thought' and 'truth-value'. For this reason I no longer hold my choice of expressions in the second footnote t o p . 77 to be quite suitable, although in the main my view remains the same: a concept is essentially predicative in nature,? ? whilst the very opposite is true of an object, so that a proper name (sign or name of an object) can never contain the whole predicate.
? Cf. my paper Uber Sinn und Bedeutung in the Zeitschrift fiir Phi/. und Phi/. Kritik.
? ? What I have here called the predicative nature of a concept is just a special case of the need for supplementation or the un- saturatedness that I gave as being essential to a function in my paper Funktion und Begriff. It was there scarely possible to avoid the ex- pression 'the functionf(x)', although in that case too the difficulty arose that the meaning of the words 'the function f(x)' is not a function.
? Cf. my essay 'On Sense and Reference' in the Zeitschrift fiir Phi/. und phi/. Kritik.
On Concept and Object 99
? ? 100
On Concept and Object
We may say in brief, taking 'subject' and 'predicate' in the linguistic sense: A concept is the reference of a predicate; an object is something that can never be the whole reference of a predicate, but
[Continued on p. 105]
We may say in brief: a concept is what can be predicated. An object is what cannot be predicated, though something can be predicated of it. ?
? In his second article (p. 424) Kerry says 'By the number 4 we understand the result of additively combining 3 and 1. The concept- object answering to the concept given here is the individual number 4, a quite definite number in the natural number series. This object obviously bears just the marks named in its concept, and no other besides-provided we refrain, as we surely must, from counting as
propria of the object the infinitely many relations in which it stands to all other individual numbers: "the" 4 is likewise the result of additively combining 3 and 1. '
We must assume from this that Kerry calls the content of the words 'the result of additively combining 3 and 1' a concept. I would agree with him if there was no definite article before 'result'. I think he will claim the content of the quoted words, without the definite article, to be a concept too, so that in this respect there will be complete agreement between us. Now how, according to Kerry, would the concept which answers first to the whole phrase be distinguished from that which answers, secondly, to this phrase with the definite article omitted? The definite article does not add a new characteristic mark. What it does do is to indicate:
1. That there is such a result.
2. That there is only one such. From what I have said in my Grundlagen, from ? 45 up to and
? On Concept and Object 101
[Footnote* top. 100 continued] including ? 53, there can be no doubt that no further characteristic marks are ascribed to our concept in these two sentences, but that proper- ties are asserted of it. Incidentally, I am sorry that Kerry is at such pains to blur afresh the distinction I wisely drew between the uses of the words 'property' and 'characteristic mark'- a distinction that alone makes it possible to achieve com- plete clarity concerning the fallacy in the ontological proof of the existence o f God. Therefore the sentence 'There is a result of ad- ditively combining 3 and 1' no more ascribes a further characteristic mark to the concept result of ad- ditive/y combining 3 and 1 than the existence, which is asserted in the sentence 'There is a God', is a characteristic mark of the concept God. What is here said of existence holds also for oneness. So we might well arrive at Kerry's view that the words 'the result of additively com- bining 3 and 1' mean the same concept as the words 'result o f additively combining 3 and 1'; for how else are concepts to be dis- tinguished if not by their charac- teristic marks or the way in which they are formed? The distinction between the two expressions would then be similar to that between 'Berlin' and 'the city of Berlin'. These both designate the same object. It is just that the latter happens in addition to remind us of certain properties. However it soon becomes clear that our two ex- pressions do not mean the same, as we should have to suppose they did if we wished to construe them as designations of concepts; unless one
wished to maintain that there was a further way of distinguishing con- cepts other than through their
? 102 On Concept and Object
[Footnote* top. 100 continued]
characteristic marks and mode of formation. When Kerry says 'By the number 4 we understand the result of additively combining 3 and 1', this is obviously meant to be a definition. A definition is always a logical identity. The sentence 'The number 4 is nothing other than the result of additively combining 3 and 1' would have the same sense. Thus this sentence does not claim to assert that the number 4 falls under the concept result o f additively combining 3 and 1, as does 'The number 4 is a result of additively combining 3 and 1'. This latter cannot be construed as a logical identity, as a definition, because it leaves it open whether there may not be something else which is also a result of this operation, and because it has a sense only if it has previously been established what the words 'the
number 4' designate. This can only be fixed by a logical identity to the effect that the same thing is to be understood by the words 'the num- ber 4', whose sense we know because the meanings of its parts and of the grammatical forms em- ployed are known to us. I t is, accordingly, clear that the definite article makes an essential con- tribution to the sense of our sentence and that the position here is conse- quently quite different from what it is in the case of 'The capital of the German Empire is the city of Ber- lin', where if you leave out 'the city of' you are only suppressing a quali- fication which is incidental to the sense. Thus I see no alternative but to deny that the words 'the result of additively combining 3 and 1' mean a concept, if one refuses to allow the possibility that concepts should be distinct from one another even through their characteristic marks
? ? On Concept and Object 103 [Footnote* top. 100 continued]
and mode of formation are the same. This alternative would be open to Kerry.
In fact Kerry seems to coun- tenance this possibility when he says on pp. 456 ff. 1 that the concept of a concept can contain the same characteristic marks as the concept itself. But there is no doubt that here again a property is being confused with a characteristic mark.
? ? ~
On Concept and Object
In a series of articles in this Quar- terly on intuition and its psychical elaboration, Benno Kerry has several times referred to my Grundlagen der Arithmetik and other works of mine, sometimes agreeing and sometimes disagreeing with me. I cannot but be pleased at this, and I think the best way I can show my appreciation is to take up the discussion of the points he contests. This seems to me all the more necessary, because his op- position is at least partly based on a misunderstanding, which might be
1 Until his death in 1889 Benno Kerry was Privatdozent in Philosophy at the University of Strasburg.
The dispute with Kerry relates to Kerry's eight articles Uber Anschauung und ihre psychische Verarbeitung in the Vierteijahrsschrift fiir wissenschaftliche Philosophie:" (1885), pp. 433-493, 10 (1886), pp. 419-467, 11 (1887), pp. 53-
116, 11 (1887), pp. 249-307, l3 (1889), pp. 71-124, l3 (1889), pp. 392-419, 14 (1890), pp. 317-353, 15 (1891), pp. 127-167. In the second and fourth articles Kerry had gone into Frege's views in particular detail. -The piece for the NachlajJ is obviously a preliminary draft of the article Ober Begriff und Gegenstand, which nppeared in 1892. The latter is printed on the left with the original pagination, with the corresponding passages of the piec~ from the NachlajJ on the right (ed. ).
Translators' note: For the article Uber Begriff und Gegenstand we have taken over the translation by Peter Geach published in Translations from the Philosophical Writings of Gottlob Frege, ed. Geach and Black, pp. 42-55 (Blackwell 1960), both because we are largely in agreement with it and because it has been so widely read and quoted from. Where the wording of the draft agrees with that of the published article, we have relied heavily on the Geach translation, though we have departed from it in several places, mainly in order to remain consistent with the renderings we have adopted elsewhere of certain terms-here notably 'bedeuten' and 'Bedeutung'. Again such a departure has been necessary in places where the agreement in wording extends only to part of a Nentence.
We have chosen not to adhere to the format of the German text in presenting the draft as if both it and the criticism of Biermann were about the concept of number. The fact that they were both found, unseparated, in a folder under the heading 'On the Concept of Number' seems to us no good reason for the German editors' lay- out.
We should like to express our grateful thanks to Professor P. T. Geach for Jlc:rmitting us to make use of his translation in this way.
[A criticism ofKerry]I
87
? ? 88 On Concept and Object
shared by others, of what I say about the concept; and because, even apart from this special oc- casion, the matter is important and difficult enough for a more thorough treatment than seemed to me suit- able in my Grundlagen.
The word 'concept' is used in various ways; its sense is sometimes psychological, sometimes logical, and sometimes perhaps a confused mixture of both. Since this licence exists, it is natural to restrict it by requiring that when once a usage is adopted it shall be maintained. What I decided was to keep strictly to a purely logical use; the question whether this or that use is more appropriate is one that I should like to leave on one side, as of minor importance. Agreement about the mode of expression will easily be reached when once it is recognized that there is something that deserves a special term.
It seems to me that Kerry's misunderstanding results from his unintentionally confusing his own usage of the word 'concept' with mine. This readily gives rise to contradictions, for which my usage is not to blame.
[193] Kerry contests what he calls my definition of 'concept'. I would remark, in the first place, that my
I turn now to consider, as briefly as possible, the objections which B. Kerry* has brought against my definitions.
He begins by contesting what he calls my definition of a concept, and there is no doubt that here he is
* Uber Anschauung und ihre psy- chische Verarbeitung in der Viertel- jahrschrift fiir wissenschaftliche Philosophie, Volume Xl, No. 3, pp.
249 IT.
? explanation is not meant as a proper definition. One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance. What is simple cannot be decomposed, and what is logically simple cannot have a proper definition. Now something logically simple is no more given us a t the outset than most of the chemical elements are; it is reached only by means o f scientific work. I f some- thing has been discovered that is simple, or at least must count as simple for the time being, we shall have to coin a term for it, since language will not originally contain an expression that exactly answers. On the introduction of a name for something logically simple, a definition is not possible; there is nothing for it but to lead the reader or hearer, by means of hints, to understand the words as is intended.
Kerry wants to make out that the distinction between concept and object is not absolute. 'In a previous passage,' he says, 'I have myself expressed the opinion that the relation between the content of the concept and the concept-object is, in u certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being a concept and of being an object are mutually ex-
touching on a crucial point, perhaps the most important one in the whole issue. The first thing to say is that my explanation is not meant as a proper definition. One cannot define everything, any more than one can decompose every chemical substance. To do either presupposes that we are dealing with something composite. In many cases one has to be satisfied with leading the reader, by means of hints, to understand the word as it is intended.
On Concept and Object 89
The difference of opinion con- cerns the distinction between con- cept* and object. Kerry would like to make out that it is not absolute. 'In a previous passage,' he says, 'we have ourselves expressed the opinion that the relation between the concept-content and the concept- object is, in a certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being an
* In my paper Funktion und Begriff (Jena 1891) I called a concept a function whose value is always a truth-value, and this could be taken as a definition. But in that case the difficulty which, as I am trying to show, arises for the con- cept, arises for the function too.
? ? ? 90 On Concept and Object
elusive. The latter view no more object and being a concept are follows from the former than it mutually exclusive. The latter view
would follow, if, e. g. , the relation of father and son were one that could not be further reduced, that a man could not be at once a father and a son (though of course not, e. g. , father of the man whose son he was). '
Let us fasten on this simile. If there were, or had been beings that were fathers but could not be sons, such beings would obviously be quite different in kind from all men who are sons. Now it is something like this that happens here. The concept (as I understand the word) is predicative. *
On the other hand, a name of an object, a proper name, is quite incapable of being used as a grammatical predicate. This admit- tedly needs elucidation, otherwise it might appear false. Surely one can just as well assert of a thing that it is Alexander the Great, or is the number four, or is the planet Venus, as that it is green or is a mammal? [194]. If anybody thinks this, he is not distinguishing the usages o f the word 'is'. In the last two examples it serves as a copula, as a mere verbal sign of predication. (In this sense the
*It is, in fact, the reference of a grammatical predicate.
no more follows from the former than it would follow if, say, the relation of father and son were one that could not be further reduced, that a man could not be at once a father and a son (though of course not e. g. father of the man whose son he was). ' 1
Let me fasten on this simile. If there were, or had been, beings that were fathers, though they were so constituted by nature that they could not be sons, such beings would be obviously quite different in kind from all men who are sons. Now something like this happens here.
The concept-as I understand the word-is predicative even in cases where we speak of a subject- concept. For instance, the sentence 'All mammals are warm-blooded' says the same as 'Whatever is a mammal is warm-blooded'. On the other hand, a name of an object-a proper name-is quite incapable of being used as a grammatical predi- cate. This may strike one as false if one does not distinguish between a proper name's occurring as only part of a predicate, which is cer- tainly possible, and its being itself the whole predicate, which is not pos- sible. One can assert of a thing that it is green or is a mammal; but one cannot in the same way assert of a thing that it is Alexander the Great, or is the number four, or is Venus.
1 Vjschr. f wissensch. Philosophie 11 ( 1887), p. 272 (ed. ).
? ? ? German word ist can sometimes be replaced by the mere personal suffix: cf. dies Blatt ist griin and dies Blatt griint. ) We are here saying that something falls under a concept, and the grammatical predicate stands for this concept. In the first three examples, on the other hand, 'is' is used like the 'equals' sign in
In order to see this, it is of course necessary to distinguish the two uses of the word 'is'. For in the first cases it serves as a copula, as a mere auxiliary indicating that we have a statement, and is sometimes then replaceable by the mere verb ending: e. g. 'dieses Blatt ist griin' ['this grass is green'], 'dieses Blatt griint' [lit. 'this grass greens']. Here one is saying that something falls under a concept. The grammatical predicate means this concept. In the second cases, the word 'is' is used like the equals sign in arithmetic, to express an equation. * Let us consider the following example: in the sentence 'That is Saturn' we have two proper names for the same object. For the word 'that', together with an appropriate pointing gesture, must here be construed as a proper name (in the logical sense) i. e. as a sign for an object. I am not here asserting the meaning of the word 'Saturn' of the object I am pointing to; if that were so, I should be asserting an object of itself, which would be nonsensical- one just cannot assert an object of
* I use the word 'equal' and the sign '=' in the sense 'the same as', 'not different from'. Cf. E. Schroder,
Vorlesungen iiber die Algebra der Logik (Leipzig 1890), Vol. 1, ? 1, especially p. 127 & p. 128. Schroder, however, is to be criticized for not here distinguishing two fundamentally different relations; the relation of an object to a concept it falls under, and the sub- ordination of one concept to
arithmetic, equation. *
to express
an
*I use the word 'equal' and the symbol '=' in the sense 'the same as', 'no other than', 'identical with'. Cf. E. Schroeder, Vorlesungen ueber die Algebra der Logik (Leipzig
On Concept and Object 91
1890), Vol. 1, ? 1. Schroeder must
however be criticized for not dis-
tinguishing two fundamentally dif-
ferent relations; the relation o f an
object to a concept it falls under,
and the subordination of one con-
cept to another. His remarks on
the Vollwurzel are likewise open
to objection. Schroeder's symbol ~ another. His discussion of the does not simply take the place of the Vollwurzel is likewise open to objec- copula. tion.
? ? ? 92
On Concept and Object
In the sentence 'The mor- ning star is Venus', we have two proper names, 'morning star' and 'Venus', for the same object. In the sentence 'the morning star is a planet' we have a proper name, 'the morning star', and a concept-word, 'planet'. So far as language goes, no more has happened than that 'Venus' has been replaced by 'a planet'; but really the relation has become wholly different. An equation is reversible; an object's falling under a concept is an irre- versible relation. In the sentence 'the morning star is Venus', 'is' is ob- viously not the mere copula; its content is an essential part of the predicate, so that the word 'Venus' does not constitute the whole of the predicate. * One might say instead: 'the morning star is no other than V enus'; what was previously im- plicit in the single word 'is' is here set forth in four separate words, and
* Cf. my Grundlagen, ? 66, footnote.
*Cf. my Grundlagen, ? 57.
something-. The 'is' is not the mere copula, but is to be compared with a word like 'griint', in which the verb ending by itself takes the place of the copula, whilst the stem gives the actual content. * The content of the predicate is not comprised in the word 'Saturn' alone; an essential part of it is contained in the word 'is', or at least has to be added in thought. As the logical predicate we may Sftke, say: no other than Saturn. I t is ~is which is predicated here and not just Saturn. Saturn is an object, no other than Saturn is a concept.
? ? only as an object. Kerry, too, would probably not wish to dispute that there is something of this kind. But this would mean admitting a dis- tinction, which it is very important recognize, between what can occur only as an object, and everything else. And this distinction would not he effaced even if it were true, as Kerry thinks it is, that there are concepts that can also be objects.
concept, and Kerry himself surely does not wish to dispute that this is possible either. But this means ad- mitting a distinction, which it is of fundamental importance to rec- ognize, between what, by its very nature, can occur only as an object, and everything else. And this dis- tinction would not be effaced even if it were true, as Kerry thinks it is, that there are concepts that can also be objects. Now there are in fact cases which seem to support this
On Concept and Object
93
in 'is no other than' the word 'is'
now really is the mere copula. What
is predicated here is thus not Venus
but no other than Venus. These
words stand for a concept; admit-
tedly only one object falls under
this, but such a concept must still
always be distinguished from the
object. * We have here a word
'Venus' that can never be a proper
predicate [195] although it can form
part of a predicate. The reference**
of this word is thus something that something making its appearance can never occur as a concept, but only as an object, never as a
There are, indeed, cases that seem
to support his view. I myself have
indicated (in Grundlagen, ? 53, ad view. I myself have pointed out
jin. ) that a concept may fall under a higher concept-which, however, must not be confused with one concept's being subordinate to 11nother. Kerry does not appeal to this; instead, he gives the following example: 'the concept "horse" is a concept easily attained', and thinks that the concept 'horse' is an object, in fact one of the objects that fall under the concept 'concept easily at-
* Cf. my Grundlagen, ? 51.
** Cf. my paper, 'On Sense and Reference' (Ueber Sinn und Be- deutung), shortly to appear in the Zeitschriftfiir Phi! . und phi! . Kritik.
(Grundlagen, ? 53 to the end) that a concept may fall under a higher concept which, however, is not to be confused with one concept's being subordinate to another. Kerry does not appeal to this; instead, he gives the following example: 'the concept "horse" is a concept easily attained', and thinks that the concept 'horse' is an object, in fact one of the ob-
Thus, as we see, we have here the case of
jects that fall
under the
concept
? ? ? 94 On Concept and Object
tained'. Quite so; the three words 'the concept "horse"' do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I g a v e - that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept word. *
Kerry holds that no logical rules can be based on linguistic dis- tinctions; but my own way of doing this is something that nobody can avoid who lays down such rules at all; for we cannot come to an under- standing with one another apart from language, and so in the end we must always rely on other people's understanding words, inflexions, and sentence-construction in essentially the same way as ourselves. As I said before, I was not trying to give a definition, but only hints; and to this end I appealed to the general feeling for the German language. It is here very much to my advantage that there is such good accord between the linguistic distinction and the real one.
As regards the indefinite article there are probably no exceptions to our rule at all for us to remark, apart from obsolete formulas like Ein edler Rath ['Councillor']. The matter is not so simple for the definite article, especially [ 196] in the plural; but then my criterion does not relate to this case. In the singular, so far as I can see, the matter is doubtful only when a singular takes the place of a plural, as in the sentence 'the Turk besieged
* Grundlagen, ? 51; 66, footnote; ? 68, footnote on p. 80.
'concept easily attained'. Quite so; the three words 'the concept "horse"' do designate an object, but for that very reason they do not designate a concept in the sense in which I am using the word. This is in full accord with the criterion I gave-that the singular definite ar- ticle always indicates an object, whereas the indefinite article accom- panies a concept-word. * Now it is true that Kerry holds that no logical prescriptions can be based on lin- guistic distinctions; but proceeding as I do, this is something that nobody can possibly avoid who lays down such prescriptions; for you cannot make yourself understood apart from language, and so in the
end you must always rely on the reader or hearer's understanding words, inflexions and sentence- construction as you do yourself. As was said, I was not trying to give a definition, but only hints; and to this end I appealed to the general feeling for the German language; for my criterion relates directly only to the German language. I t is here very much to my advantage that the linguistic distinction accords so well with the real one. As regards the indefinite article there are, I should say, no exceptions to our rule at all to remark, apart from the archaic form 'Ein edler Rat' [Councillor], which here and there is still in official use. If the article in the plural can be replaced by 'all' and the meaning is that the statement is to hold of each individual member of the class, then we have a concept-
* My Grundlagen, ? 51; ? 66, footnote; ? 68, footnote on p. 80.
? ? ? Vienna', 'the horse is a four-legged animal'. These cases are so easily recognizable as special ones that the value of our rule is hardly impaired by their occurrence. It is clear that in the first sentence 'the Turk' is the proper name of a people. The second sentence is probably best regarded as expressing a universal judgement, say 'all horses are four- legged animals' or 'all properly con- stituted horses are four-legged animals'; these will be discussed later. ?
word (e. g. die Pferde sind pflanzen- fressende Tiere). 1 On the other hand, the phrase 'the Romans' in the sentence 'The Romans conquered Gaul' is to be regarded as a proper
name, for here we are not saying of each Roman that he has conquered Gaul; we are speaking of the Roman people, which is to be regarded logically as an object. There are also cases in which the singular is used in the sense of the plural--e. g. 'The horse is a herbivorous animal'. This case is so easily recognizable as an exception, that the value of our criterion is hardly impaired by it. (If the grammatical subject is a concept word, the sentence can be trans- formed into one in which the subject occurs predicatively with the in- definite article--e. g. 'If something is a horse, then it is a herbivorous animal'. The fuller account given in the Grundlagen makes it clear, I think, what I have in mind. )
? Nowadays people seem inclined to exaggerate the scope of the state- ment that different linguistic expres- sions are never completely equiva- lent, that a word can never be exactly translated into another lan- guage. One might perhaps go even further, and say that the same word is never taken in quite the same way even by men who share a language. I will not enquire as to the measure of truth in these statements; I would only emphasize that nevertheless different expressions quite often have something in common, which I call the sense, or in the special case
On Concept and Object 95
1 In the German sentence the word 'die' is the plural form of the definite article. The natural English translation would be 'Horses are herbivorous animals' (trans. ).
? ? ? 96 On Concept and Object
Kerry calls my criterion un- suitable; for surely, he says, in the sentence 'the concept that I am now talking about is an individual con- cept' the name composed of the first eight words stands for a concept; but he is not taking the word 'concept' in my sense, and it is not in what I have laid down that the contradiction lies. But nobody can require that my mode of expression shall agree with Kerry's.
It must indeed be recognized that we are here confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept,* whereas e. g. , the [197]
of sentences, the thought. In other words, we must not fail to recognize that the same sense, the same thought, may be variously ex- pressed; thus the difference does not here concern the sense, but only the apprehension, shading, or colouring of the thought, and is irrelevant for logic. It is possible for one sentence
to give no more and no less infor- mation than another; and, for all the multiplicity of languages, mankind has a common stock of thoughts. If all transformation of the expression were forbidden on the plea that this would alter the content as well, logic would simply be crippled; for the task of logic can hardly be perfor- med without trying to recognize the thought in its manifold guises. Moreover, all definitions would then have to be rejected as false.
* A similar 'thing happens when we say as regards the sentence 'this
Therefore when Kerry says that my criterion does not meet the case, claiming that in the sentence 'The concept that I am now talking about is an individual concept' the name composed of the first eight words surely means a concept, the contra- diction does not lie in what I have laid down; it obtains between the sense I attach to the word 'concept' and that adopted by Kerry. But nobody can require that my stipulations shall be in accord with Kerry's mode of expression, but only that they be consistent in them- selves. True, we cannot fail to recognize that we are here confron- ted by an awkwardness of language, which I admit is unavoidable, if we assert 'the concept horse is not a concept',* whereas, e. g. the city of Berlin is a city, and the volcano
*A similar thing happens when we say 'In the sentence "this rose is red", the grammatical predicate "red" belongs to the subject "this rose"'. Here the four words 'the grammatical predicate "red"' are not a grammatical predicate, but a subject. By the very act of explicitly calling it a grammatical predicate in this way, we deprive it of this property.
? ? ? city of Berlin is a city, and the volcano Vesuvius is a volcano. Language is here in a predicament that justifies the departure from custom. The peculiarity of our case is indicated by Kerry himself, by means of the quotation-marks around 'horse'; I use italics to the same end. There was no reason to mark out the words 'Berlin' and 'Vesuvius' in a similar way. In logical discussions one quite often needs to assert something about a concept, and to express this in the form usual for such assertions-viz. to make what is asserted of the concept into the content of the grammatical predicate. Conse- quently, one would expect that the reference of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object,? or, speaking more precisely, represented by an object. We designate this object by pre- lixing the words 'the concept'; e. g.
'The concept man is not empty'.
Here the first three words are to be regarded as a proper name,? ? which can no more be used predicatively than 'Berlin' or 'Vesuvius'. When we
rose is red': The grammatical pre- dicate 'is red' belongs to the subject 'this rose'. Here the words 'The grammatical predicate "is red"' are not a grammatical predicate but a subject. By the very act of explicitly calling it a predicate, we deprive it of this property.
? Cf. my Grundlagen, p. X.
? ? I call anything a proper name if it is a sign for an object.
Vesuvius is a volcano. Language is here in a predicament that justifies the departure from what we nor- mally say. The peculiarity of our case is indicated by Kerry himself by means of the quotation-marks around 'horse'. (We have used italics here to the same end. ) There was no reason to mark out the words 'Berlin' and 'Vesuvius' in a similar way above. In logical dis- cussions one quite often needs to assert something about a concept,? and to express this in the gram- matical form usual for such state- ments, so that what is asserted becomes the content of the gram- matical predicate. Consequently, one would expect the concept to be the content of the grammatical subject; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or, speak- ing more precisely: an object that is connected with it in accordance with a rule must be substituted for it, and it is this object we designate by an expression of the form 'the concept x'. (Cf. p. X of my Grundlagen. )
? When we say 'All men are mortal', we do not assert mortality of the concept man, but we sub- ordinate the concept mortal to the latter concept. [This is obviously a slip on Frege's part; what he means of course is that we subordinate the concept man to the concept mortal (trans. ). l
On Concept and Object 97
? ? 98 On Concept and Object
say 'Jesus falls under the concept man', then, setting aside the copula, the predicate is:
'someone falling under the concept
man'
and this means the same as: 'a man'.
But the phrase
'the concept man'
is only part of this predicate. Somebody might urge, as
against the predicative nature of the concept, that nevertheless we speak of a subject-concept. But even in such cases, e. g. in the sentence
'all mammals have red blood'
we cannot fail to recognize the pre- dicative nature? of the concept; for we can say instead:
[198] 'whateverisamammal has red blood'
or:
? What I call here the predicative nature of the concept is just a special case of the need of supple- mentation, the 'unsaturatedness', that I gave as the essential feature of a function in my work Function und Begriff (Jena, 1891). I t was there scarcely possible to avoid the ex- pression 'the functionflx)', although there too the difficulty arose that what this expression stands for is not a function.
'if anything is a mammal, then it has red blood'.
So the phrase 'the concept horse' must be regarded as a proper name, which can no more be used pre?
? ? ? When I wrote my Grundlagen der Arithmetik, I had not yet made the Jistinction between sense and reference;? and so, under the expres- sion 'a possible content of judge- ment, I was combining what I now Jesignate by the distinctive words 'thought' and 'truth-value'. Conse- quently, I no longer entirely approve of the explanation I then gave (op. cit. p. 77), as regards its wording; my view is, however, still essentially the same.
dicatively than can, say, 'Berlin' or 'Vesuvius'. If we say that Bucephalus falls under the concept horse, then the predicate here is clearly 'falling under the concept horse', and this has the same mean- ing as 'a horse'. But the phrase 'the concept horse' is only part of this predicate.
When I wrote my Grundlagen, I had not yet made the distinction between sense and meaning;? and so, under the expression 'content of possible judgement', I was combin- ing what I now distinguish by the words 'thought' and 'truth-value'. For this reason I no longer hold my choice of expressions in the second footnote t o p . 77 to be quite suitable, although in the main my view remains the same: a concept is essentially predicative in nature,? ? whilst the very opposite is true of an object, so that a proper name (sign or name of an object) can never contain the whole predicate.
? Cf. my paper Uber Sinn und Bedeutung in the Zeitschrift fiir Phi/. und Phi/. Kritik.
? ? What I have here called the predicative nature of a concept is just a special case of the need for supplementation or the un- saturatedness that I gave as being essential to a function in my paper Funktion und Begriff. It was there scarely possible to avoid the ex- pression 'the functionf(x)', although in that case too the difficulty arose that the meaning of the words 'the function f(x)' is not a function.
? Cf. my essay 'On Sense and Reference' in the Zeitschrift fiir Phi/. und phi/. Kritik.
On Concept and Object 99
? ? 100
On Concept and Object
We may say in brief, taking 'subject' and 'predicate' in the linguistic sense: A concept is the reference of a predicate; an object is something that can never be the whole reference of a predicate, but
[Continued on p. 105]
We may say in brief: a concept is what can be predicated. An object is what cannot be predicated, though something can be predicated of it. ?
? In his second article (p. 424) Kerry says 'By the number 4 we understand the result of additively combining 3 and 1. The concept- object answering to the concept given here is the individual number 4, a quite definite number in the natural number series. This object obviously bears just the marks named in its concept, and no other besides-provided we refrain, as we surely must, from counting as
propria of the object the infinitely many relations in which it stands to all other individual numbers: "the" 4 is likewise the result of additively combining 3 and 1. '
We must assume from this that Kerry calls the content of the words 'the result of additively combining 3 and 1' a concept. I would agree with him if there was no definite article before 'result'. I think he will claim the content of the quoted words, without the definite article, to be a concept too, so that in this respect there will be complete agreement between us. Now how, according to Kerry, would the concept which answers first to the whole phrase be distinguished from that which answers, secondly, to this phrase with the definite article omitted? The definite article does not add a new characteristic mark. What it does do is to indicate:
1. That there is such a result.
2. That there is only one such. From what I have said in my Grundlagen, from ? 45 up to and
? On Concept and Object 101
[Footnote* top. 100 continued] including ? 53, there can be no doubt that no further characteristic marks are ascribed to our concept in these two sentences, but that proper- ties are asserted of it. Incidentally, I am sorry that Kerry is at such pains to blur afresh the distinction I wisely drew between the uses of the words 'property' and 'characteristic mark'- a distinction that alone makes it possible to achieve com- plete clarity concerning the fallacy in the ontological proof of the existence o f God. Therefore the sentence 'There is a result of ad- ditively combining 3 and 1' no more ascribes a further characteristic mark to the concept result of ad- ditive/y combining 3 and 1 than the existence, which is asserted in the sentence 'There is a God', is a characteristic mark of the concept God. What is here said of existence holds also for oneness. So we might well arrive at Kerry's view that the words 'the result of additively com- bining 3 and 1' mean the same concept as the words 'result o f additively combining 3 and 1'; for how else are concepts to be dis- tinguished if not by their charac- teristic marks or the way in which they are formed? The distinction between the two expressions would then be similar to that between 'Berlin' and 'the city of Berlin'. These both designate the same object. It is just that the latter happens in addition to remind us of certain properties. However it soon becomes clear that our two ex- pressions do not mean the same, as we should have to suppose they did if we wished to construe them as designations of concepts; unless one
wished to maintain that there was a further way of distinguishing con- cepts other than through their
? 102 On Concept and Object
[Footnote* top. 100 continued]
characteristic marks and mode of formation. When Kerry says 'By the number 4 we understand the result of additively combining 3 and 1', this is obviously meant to be a definition. A definition is always a logical identity. The sentence 'The number 4 is nothing other than the result of additively combining 3 and 1' would have the same sense. Thus this sentence does not claim to assert that the number 4 falls under the concept result o f additively combining 3 and 1, as does 'The number 4 is a result of additively combining 3 and 1'. This latter cannot be construed as a logical identity, as a definition, because it leaves it open whether there may not be something else which is also a result of this operation, and because it has a sense only if it has previously been established what the words 'the
number 4' designate. This can only be fixed by a logical identity to the effect that the same thing is to be understood by the words 'the num- ber 4', whose sense we know because the meanings of its parts and of the grammatical forms em- ployed are known to us. I t is, accordingly, clear that the definite article makes an essential con- tribution to the sense of our sentence and that the position here is conse- quently quite different from what it is in the case of 'The capital of the German Empire is the city of Ber- lin', where if you leave out 'the city of' you are only suppressing a quali- fication which is incidental to the sense. Thus I see no alternative but to deny that the words 'the result of additively combining 3 and 1' mean a concept, if one refuses to allow the possibility that concepts should be distinct from one another even through their characteristic marks
? ? On Concept and Object 103 [Footnote* top. 100 continued]
and mode of formation are the same. This alternative would be open to Kerry.
In fact Kerry seems to coun- tenance this possibility when he says on pp. 456 ff. 1 that the concept of a concept can contain the same characteristic marks as the concept itself. But there is no doubt that here again a property is being confused with a characteristic mark.
