Now at the end we have: '"the" 4 is likewise the result of additively
combining
3 and 1'.
Gottlob-Frege-Posthumous-Writings
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. I do not believe that anything of value is to be learned by taking this route or that logicians will have any inclination to tread the same path. On the contrary, it seems far and away more appropriate to regard the replacement of the indefinite by the definite article as signifying the transition from a concept to an object falling under it, where the case holds that there is only one such object. So I do not go along with Kerry's saying that the object is like the concept in having as characteristic marks those of the concept; I say instead that the object has the characteristic marks of the concept as properties. And here we have the distinction. For the relation of a characteristic mark to a concept is different from that of property to an object (cf. Grund- lagen, ? 53).
Another consideration shows that the words 'the result of additively corn bining 3 and 1' designate an object. We have already seen that the first sentence of the passage from Kerry quoted above is to be construed as a definition and thus as a logical identity.
Now at the end we have: '"the" 4 is likewise the result of additively combining 3 and 1'. The author's view is that the role of
1 Vjschr. f wissensch. Philosophie 10 (1886) (ed. ).
? 104 On Concept and Object
[Footnote* top. 100 continued]
the grammatical subject is to desig- nate the concept-object and pre- sumably the definite article is enclosed in quotation marks to mark this object off from the concept. Obviously this last sentence has the sense of a logical identity too: "'the" 4 is nothing other than the result of additively combining 3 and 1'.
The view that this sentence is meant to express that an object falls under the concept result of etc. is immediately ruled out by the occur- rence of the definite article before 'result'. Otherwise the indefinite ar- ticle would have been used or the article would have to have been omitted. Now if the left-hand side of this identity is an object, the right- hand side must be an object too. Further, the right-hand side of the first identity is at the same time the right-hand side of the second: hence the two expressions to the left must designate the same thing: the num- ber 4 is nothing other than 'the' 4. I can see no significance in the use of quotation marks here. In my view the reason for the sorry state of affairs we find in Kerry, where the distinctions between concept and object, characteristic mark and pro- perty, are effaced is that logical and psychological questions and view- points are scrambled together, which greatly detracts from the value of his articles. He will speak now of a concept, then of the idea of a concept, now of an object, then of the idea of it, without its even being wholly clear whether it is the one or the other that is in question, whether we are engaged in a logical or psychological inquiry. Now it is no particular cause for wonder if we can find no way of distinguishing between the idea of a concept and
? ? can be the reference of a subject. It must here be remarked that the words 'all', 'any', 'no', 'some', are prefixed to concept-words. In uni- versal and particular affirmative and negative sentences, we are express- ing relations between concepts; we use these words to indicate the special kind of relation. They are thus, logically speaking, not to be more closely associated with the concept-words that follow them, but are to be related to the sentence as a whole. It is easy to see this in the case of negation. I f in the sentence
'all mammals are land-dwellers'
the phrase 'all mammals' expressed the logical subject of the predicate are land-dwellers, then in order to negate the whole sentence we should
On Concept and Object 105
that of an object. Perhaps they are often even difficult to hold apart. But here Kerry has simply succum- bed to a widespread sickness. In- deed would not Locke's empiricism and Berkeley's idealism, and so much that is tied up with these philosophies, have been impossible if people had distinguished adequately between thinking in the narrower sense and ideation, between the parts of a content (concepts, ob- jects, relations) and the ideas we have? Even if with us men thinking does not take place without ideas, still the content of a judgement is something objective, the same for everybody, and as far as it is con- cerned it is neither here nor there what ideas men have when they grasp it. In any case these are subjective and will differ from one person to another. What is here being said of the content as a whole applies also to the parts which we can distinguish within it.
? ? 106 On Concept and Object
have to negate the predicate: 'are not land-dwellers'. Instead, we must put the 'not' in front of 'all'; from which it follows that 'all' logically belongs with the predicate. On the other hand, we do negate the sen- tence 'The concept mammal is subordinate to the concept land- dweller' by negating the predicate: 'is not subordinate to the concept land-dweller'.
Ifwekeepitinmindthatinmy
way of speaking expressions like
'the concept F ' designate not con-
cepts but objects, most of [199]
Kerry's objections already collapse.
If he thinks (cf. p. 281) that I have
identified concept and extension of
concept, he is mistaken; I merely
expressed ny view that in the ex-
pression 'the number that applies to
the concept F is the extension of the
concept like-numbered to the
concept F' the words 'extension of words 'extension of the concept' the concept' could be replaced by
'concept'. Notice carefully that here
the word 'concept' is combined with
the definite article. Besides, this was
only an incidental remark; I did not
base anything upon it.
Thus Kerry does not succeed in filling the gap between concept and object. Someone might attempt, however, to make use of my own statements in this sense. I have said that to assign a number involves an
Thus Kerry in his account does not succeed in filling the gap between concept and object. Someone might attempt, however, to make use of my own statements in this sense. For example, I have said (Grund?
? The question whether one should simply put 'the concept' for 'the extension of the concept' is in my view one of expediency.
So if we hold on to the fact that the words 'the concept F' designate not a concept but an object, most of Kerry's objections don't begin to stand up. If he thinks (p. 281) that I have identified concept and exten- sion of a concept, this is simply not the case. I merely expressed my view that in the expression 'the number belonging to the concept F is the extension of the concept like- numbered to the concept F', the
could be replaced by the word 'concept'. N. B. the word 'concept' is here combined with the definite article. Besides this was only an incidental remark; I based nothing on it in order not to have to grapple with the misgivings to which it might give rise. So Kerry's opposition to it has no bearing at all on the real core of my position. ?
? ? On Concept and Object 107
assertion about a concept;* I speak
of properties asserted of a concept,
and I allow that a concept may fall
under a higher one. ** I have called
existence a property of a concept. that a concept may fall under a
How I mean this is best made clear
by an example. In the sentence
'there is at least one square root of
4', we have an assertion, not about
(say) the definite number 2, nor
about -2, but about a concept,
square root of 4; viz. that it is not
empty. But if I express the same
thought thus: 'The concept square
root of 4 is realized', then the first viz. that it is not empty but is
realized. But if I express the same thought thus: 'The concept square root of 4 is realized', then the first six words form the proper name of an object. In general a content can be analysed in a number of ways and language seeks to provide for this by having at its disposal dif- ferent expressions for the same content. The distinction between the active and passive form, for exam- ple, enables us to present different parts of the content as the subject. This is why it is almost invariably a
six words form the proper name of
an object, and it is about this object
that something is asserted. But
notice carefully that what is asserted
here is not the same thing as was
asserted about the concept. This will
be surprising only to somebody who
fails to see that a thought can be
split up in many ways, so that now
one thing, now another, appears as
subject or predicate. The thought
itself does not yet determine what is
to be regarded as the subject. If we
say 'the subject of this judgement',
we do not designate anything mistake to put the definite article
definite unless at the same time we indicate a definite kind of analysis; as a rule, we do this in connexion with a definite wording. But we must never forget that different sentences may express the same thought. For example, the thought we are con- sidering could also be taken as an assertion about the number 4:
'The number 4 has the property that there is something of which it is the square. '
* Grund/agen, ? 46. ** Grundlagen, ? 53.
before the word 'subject' in such expressions as 'the subject of the judgement', 'the subject of the con- tent of a possible judgement'; for no part of the content can be picked out in advance as the subject. Even the expressions 'singular content of pos- sible judgement', 'particular content of possible judgement' are not quite accurate in that they ascribe to the content itself an attribute which, strictly speaking, belongs to it only under a certain form-a certain way
lagen, ? 46) that a statement of number contains an assertion about a concept; I speak of properties asserted of a concept, and I allow
higher one (Grundlagen, ? 53). I have called existence a property of a concept. How I mean this is best made clear by an example.
In the sentence 'There is at least one square root of 4', we have an assertion not about, say, the par- ticular number 2, nor about -2, but about a concept, square root of 4;
? ? ? 108 On Concept and Object
Language has means of present- of analysing it into subject and
ing now one, now another, part of the [200] thought as the subject; one of the most familiar is the distinction of active and passive forms. It is thus not impossible that one way of analysing a given thought should make it appear as a singular judge- ment; another, as a particular judge- ment; and a third, as a universal
judgement. It need not then surprise us that the same sentence may be conceived as an assertion about a concept and also as an assertion about an object; only we must observe that what is asserted is dif- ferent. In the sentence 'there is at least one square root of 4' it is impossible to replace the words 'square root of 4' by 'the concept square root of 4; i. e. the assertion that suits the concept does not suit the object. Although our sentence does not present the concept as a subject, it asserts something about it; it can be regarded as expressing the fact that a concept falls under a higher one. * But this does not in any way efface the distinction between object and concept. We see to begin with that in the sentence 'there is at least one square root of 4' the predicative nature of the concept is not belied; we could say 'there is something that has the property of giving the result 4 when multiplied by itself. ' Hence what is here asser- ted about a concept can never be asserted about an object; for a
* In my Grund/agen I called such a concept a second-order concept; in my work Function und Begriff I called it a second-level concept, as I shall do here.
predicate.
It is conceivable that the same content should appear in one form as singular, in another as particular. It need not then surprise us that we can discern in the same content an assertion about a concept and also an assertion about an object. We must only take note that
what is asserted of the one is dif- ferent from what is asserted of the other. In the sentence 'There is at least one square root of 4' it is im- possible to replace the words 'square root of 4' by 'the concept square root of4'; i. e. the assertion that suits the concept does not suit the object. All the same something is asserted of a concept in our sentence. We can even say that our concept is presented as falling under a higher one*-one whose sole characteristic mark is is realized, understanding this word in the sense in which we are using it in the present context. But this does not in any way efface
the distinction between concept and object. We see to begin with that in the expression 'There is at least one square root of 4', 'square root of 4' is being used predicatively: 'there is something that is a square root of 4'. In place of this we could say 'there is something that has the property of giving the result 4 when multiplied by itself. Hence what is here asser-
* In my Grundlagen I called such a concept a second order concept; in my Funktion und Begriff I called it a second level concept, as I shall do here.
? proper name can never be a pre- dicative expression, though it can be partofone. Idonotwanttosayitis false to assert about an object what is here asserted about a concept; I want to say it is impossible, sense- less, to do so.
The sentence 'there is Julius Caesar' is neither true nor false but senseless; the sentence 'there is a man whose name is Julius Caesar' has a sense, but here again we have a concept, as the indefinite article shows. We get the same thing in the sentence 'there is only one Vienna'. We must not let ourselves be deceived because language often uses the same word now as a proper name, now as a concept-word; in our example, the numeral indicates that we have the latter; 'Vienna' is here a concept-word, like ? metropolis'. Using it in this sense, we may say: 'Trieste is no Vienna'. If, on the other hand, we substitute 1201] 'Julius Caesar' for the proper name formed by the first six words of the sentence 'the concept square root of 4 is realized', we get a sentence that has a sense but is false; for the assertion that some- thing is realized (as the word is being taken here) can be truly made only about a quite special kind of objects, viz. such as can be designated by proper names of the form 'the concept F'. Thus the words 'the concept square root of 4' have an
ted of a concept can never be asserted of an object. This is not to saythatitisfalsetodothis,butim- possible: a sentence which tried to express such a thing would be absolutely devoid of sense; for it has no sense to use the name of an object predicatively. We have seen that even where the form of a sentence makes it look as if this is being done, the truth is that the object forms only part of what is asserted, since 'nothing other than' has to be added in thought. A sentence such as 'There is at least Julius Caesar' is senseless, although the sentence 'There is at least one man whose name is "Julius Caesar"' has a sense; but here again we have a concept, as the 'one' shows.
On Concept and Object 109
If, on the other hand, we sub- stitute the proper name 'Julius Caesar' for the proper name formed by the first six words of the sentence 'The concept square root of 4 is realized', we get a sentence that has a sense but is false; for the assertion that something is realized, as the word is meant here, is one we can only truly make of such objects as stand in a quite special relation to a concept. Thus the words 'the con- cept square root of 4' have an essentially different behaviour, as
? 110 On Concept and Object
essentially different behaviour, as regards possible substitutions, from the words 'square root of 4' in our original sentence; i. e. the reference of the two phrases is essentially
different.
What has been shown here in one
example holds good generally; the behaviour of the concept is essen- tially predicative, even where some- thing is being asserted about it; consequently it can be replaced there only by another concept, never by an object. Thus the assertion that is made about a concept does not suit an object. Second-level con- cepts, which concepts fall under, are essentially different from first-level concepts, which objects fall under.
regards possible substitutions, from the words 'square root of 4' in our original sentence; i. e. the meanings of the two properties are different, thoughrelated.
What has been shown here in one example holds good generally: the behaviour of the concept is essen- tially predicative even when some- thing is being asserted of it; conse- quently it can be replaced there only by another concept, never by an object; i. e. the assertion that is made about a concept does not fit an object at all. Moreover a concept (of second level) under which a concept falls is essentially different from a concept (of first level) under which objects fall.
In the sentence 'There is at least one square root of 4' we assert that the first level concept square root of 4 falls under a concept of second level, whereas in the sentence 'The concept square root o f 4 is realized' we assert that the object the concept square root of4 falls under the first level concept concept that is realized. We do indeed have the same thought in the two concepts, [sic. ] but this, being analysed dif- ferently, is construed in a different way.
The relation of an object to a concept that it falls under is dif- ferent from the admittedly similar relation of a concept to a concept (of second level). From now on we shall give parallel expression to the similarity and the difference by saying than an object falls under a concept, and a concept falls within a concept (of second level); for, strictly speaking, we have been making a mistake in using the same
The relation of an object to a first-level concept that it falls under is different from the (admittedly similar) relation of a first-level to a second-level concept. (To do justice at once to the distinction and to the similarity, we might perhaps say: An object falls under a first-level concept; a concept falls within a second-level concept. ) The dis- tinction of concept and object thus still holds, with all its sharpness.
? With this there hangs together what I have said (Grund/agen, ? 53) about my usage of the words 'property' and 'mark'; Kerry's dis- cussion gives me occasion to revert once more to this.
The words serve to signify relations, in sentences like ? (/J is a property of T' and '(/J is a mark of il'. In my way of speaking a thing can at once be a property and a mark but not of the same
thing.
words to cover both cases. From this we can see that the distinction between object and concept still holds in all its sharpness.
Connected with this is another distinction, namely that between property and characteristic mark. I have already explained this in ? 53 of my Grundlagen and at the time I thought I had made it sufficiently clear. Since, however, Kerry makes no use of it and falls into error as a result, I can only assume, alas, that he has not understood me; this time I will try to be more successful.
The words 'property' and 'characteristic mark' serve to designate relations such that something can at the same time be a property of r and a characteristic mark of L1. We express ourselves more precisely if we use the words 'characteristic mark' only in the phrase 'characteristic mark of a concept'. If a thing is a property of an object, then it is a characteristic mark of a first level concept. We may also speak of properties of a first level concept, and these will then be characteristic marks of second level concepts. I will call the concepts under which an object falls its properties.
If the object r has the properties (/J, X and '1', I may combine them into n; so that it is the same thing if I say that r has the property n, or, that r has the property (/J and r has the property X and r has the property '1'. I then call (/J, X, and 'I' marks of the concept n, and, at the same time, properties of r. It is clear that the relations of (/J to r and to n are
I call the concepts under which an object falls its properties; thus 'to be (/J is a property of T' is just another way of saying: 'T falls under the concept of a (/J'. If the object r has the properties (/), X, and '1', I may combine them into n; so that it is the same thing if I say that r has the [202] property n, or, that r has the properties (/), X, and '1'. I then call (/J, X, and 'I' marks of the concept n, and, at the same time, properties of r. It is clear that the relations of (/J to r and to n are quite different, and that conse-
On Concept and Object Ill
? 112 On Concept and Object
quently different terms are required. quite different; r falls under the r falls under the concept f/J; but n, concept f/J; but n, which is itself a which is itself a concept, cannot fall concept, cannot fall under the first under the first-level concept f/J; only level concept f/J; only to a second to a second-level concept could it level concept could it stand in a
stand in a similar relation. n is, on the other hand, subordinate to f/J.
Let us consider an example. Instead of saying:
'2 is a positive number' and '2 is a whole number' and '2 is less than 10'.
we may also say
'2 is a positive whole number less than 10'.
Here
appear as properties of the object 2, and also as marks of the concept
positive whole number less than 10.
This is neither positive, nor a whole number, nor less than 10. It is indeed subordinate to the concept whole number , b u t d o e s n o t fall under it.
Let us now compare with this what Kerry says in his second article (p. 424). 'By the number 4 we understand the result of additively combining 3 and 1. The concept object here occurring is the numerical individual 4; a quite definite number in the natural number-series. This object obviously bears just the marks that are named in its concept, and no others besides-provided we refrain, as we
similar relation.
to be a positive number, to be a whole number, to be less than 10,
? ? surely must, from counting as propria of the object its infinitely numerous relations to all other individual numbers; "the" number 4 is likewise the result of additively combining 3 and 1. '
We see at once that my dis- tinction between property and mark is here quite slurred over. Kerry distinguishes here between the num- ber 4 and 'the' number 4. I must confess that this distinction is in- comprehensible to me. The number 4 is to be a concept; 'the' number 4 is to be a concept-object, and none other than the numerical individual 4. It needs no proof that what we have here [203] is not my distinction between concept and object. I t almost looks as though what was floating (though very obscurely) before Kerry's mind were my dis- tinction between the sense and the reference of the words 'the number 4'. * But it is only of the reference of the words that we can say: this is the result of additively combining 3 and 1.
Again, how are we to take the word 'is' in the sentences 'the num- ber 4 is the result of additively combining 3 and I' and '"the" number 4 is the result of additively combining 3 and I'? Is it a mere copula, or does it help to express a logical equation? In the first case, 'the' would have to be left out before 'result', and the sentences would go like this:
'The number 4 is a result of addi- tively combining 3 and I';
* Cf. my essay 'On Sense and Reference' (cited above).
* 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. I do not believe that anything of value is to be learned by taking this route or that logicians will have any inclination to tread the same path. On the contrary, it seems far and away more appropriate to regard the replacement of the indefinite by the definite article as signifying the transition from a concept to an object falling under it, where the case holds that there is only one such object. So I do not go along with Kerry's saying that the object is like the concept in having as characteristic marks those of the concept; I say instead that the object has the characteristic marks of the concept as properties. And here we have the distinction. For the relation of a characteristic mark to a concept is different from that of property to an object (cf. Grund- lagen, ? 53).
Another consideration shows that the words 'the result of additively corn bining 3 and 1' designate an object. We have already seen that the first sentence of the passage from Kerry quoted above is to be construed as a definition and thus as a logical identity.
Now at the end we have: '"the" 4 is likewise the result of additively combining 3 and 1'. The author's view is that the role of
1 Vjschr. f wissensch. Philosophie 10 (1886) (ed. ).
? 104 On Concept and Object
[Footnote* top. 100 continued]
the grammatical subject is to desig- nate the concept-object and pre- sumably the definite article is enclosed in quotation marks to mark this object off from the concept. Obviously this last sentence has the sense of a logical identity too: "'the" 4 is nothing other than the result of additively combining 3 and 1'.
The view that this sentence is meant to express that an object falls under the concept result of etc. is immediately ruled out by the occur- rence of the definite article before 'result'. Otherwise the indefinite ar- ticle would have been used or the article would have to have been omitted. Now if the left-hand side of this identity is an object, the right- hand side must be an object too. Further, the right-hand side of the first identity is at the same time the right-hand side of the second: hence the two expressions to the left must designate the same thing: the num- ber 4 is nothing other than 'the' 4. I can see no significance in the use of quotation marks here. In my view the reason for the sorry state of affairs we find in Kerry, where the distinctions between concept and object, characteristic mark and pro- perty, are effaced is that logical and psychological questions and view- points are scrambled together, which greatly detracts from the value of his articles. He will speak now of a concept, then of the idea of a concept, now of an object, then of the idea of it, without its even being wholly clear whether it is the one or the other that is in question, whether we are engaged in a logical or psychological inquiry. Now it is no particular cause for wonder if we can find no way of distinguishing between the idea of a concept and
? ? can be the reference of a subject. It must here be remarked that the words 'all', 'any', 'no', 'some', are prefixed to concept-words. In uni- versal and particular affirmative and negative sentences, we are express- ing relations between concepts; we use these words to indicate the special kind of relation. They are thus, logically speaking, not to be more closely associated with the concept-words that follow them, but are to be related to the sentence as a whole. It is easy to see this in the case of negation. I f in the sentence
'all mammals are land-dwellers'
the phrase 'all mammals' expressed the logical subject of the predicate are land-dwellers, then in order to negate the whole sentence we should
On Concept and Object 105
that of an object. Perhaps they are often even difficult to hold apart. But here Kerry has simply succum- bed to a widespread sickness. In- deed would not Locke's empiricism and Berkeley's idealism, and so much that is tied up with these philosophies, have been impossible if people had distinguished adequately between thinking in the narrower sense and ideation, between the parts of a content (concepts, ob- jects, relations) and the ideas we have? Even if with us men thinking does not take place without ideas, still the content of a judgement is something objective, the same for everybody, and as far as it is con- cerned it is neither here nor there what ideas men have when they grasp it. In any case these are subjective and will differ from one person to another. What is here being said of the content as a whole applies also to the parts which we can distinguish within it.
? ? 106 On Concept and Object
have to negate the predicate: 'are not land-dwellers'. Instead, we must put the 'not' in front of 'all'; from which it follows that 'all' logically belongs with the predicate. On the other hand, we do negate the sen- tence 'The concept mammal is subordinate to the concept land- dweller' by negating the predicate: 'is not subordinate to the concept land-dweller'.
Ifwekeepitinmindthatinmy
way of speaking expressions like
'the concept F ' designate not con-
cepts but objects, most of [199]
Kerry's objections already collapse.
If he thinks (cf. p. 281) that I have
identified concept and extension of
concept, he is mistaken; I merely
expressed ny view that in the ex-
pression 'the number that applies to
the concept F is the extension of the
concept like-numbered to the
concept F' the words 'extension of words 'extension of the concept' the concept' could be replaced by
'concept'. Notice carefully that here
the word 'concept' is combined with
the definite article. Besides, this was
only an incidental remark; I did not
base anything upon it.
Thus Kerry does not succeed in filling the gap between concept and object. Someone might attempt, however, to make use of my own statements in this sense. I have said that to assign a number involves an
Thus Kerry in his account does not succeed in filling the gap between concept and object. Someone might attempt, however, to make use of my own statements in this sense. For example, I have said (Grund?
? The question whether one should simply put 'the concept' for 'the extension of the concept' is in my view one of expediency.
So if we hold on to the fact that the words 'the concept F' designate not a concept but an object, most of Kerry's objections don't begin to stand up. If he thinks (p. 281) that I have identified concept and exten- sion of a concept, this is simply not the case. I merely expressed my view that in the expression 'the number belonging to the concept F is the extension of the concept like- numbered to the concept F', the
could be replaced by the word 'concept'. N. B. the word 'concept' is here combined with the definite article. Besides this was only an incidental remark; I based nothing on it in order not to have to grapple with the misgivings to which it might give rise. So Kerry's opposition to it has no bearing at all on the real core of my position. ?
? ? On Concept and Object 107
assertion about a concept;* I speak
of properties asserted of a concept,
and I allow that a concept may fall
under a higher one. ** I have called
existence a property of a concept. that a concept may fall under a
How I mean this is best made clear
by an example. In the sentence
'there is at least one square root of
4', we have an assertion, not about
(say) the definite number 2, nor
about -2, but about a concept,
square root of 4; viz. that it is not
empty. But if I express the same
thought thus: 'The concept square
root of 4 is realized', then the first viz. that it is not empty but is
realized. But if I express the same thought thus: 'The concept square root of 4 is realized', then the first six words form the proper name of an object. In general a content can be analysed in a number of ways and language seeks to provide for this by having at its disposal dif- ferent expressions for the same content. The distinction between the active and passive form, for exam- ple, enables us to present different parts of the content as the subject. This is why it is almost invariably a
six words form the proper name of
an object, and it is about this object
that something is asserted. But
notice carefully that what is asserted
here is not the same thing as was
asserted about the concept. This will
be surprising only to somebody who
fails to see that a thought can be
split up in many ways, so that now
one thing, now another, appears as
subject or predicate. The thought
itself does not yet determine what is
to be regarded as the subject. If we
say 'the subject of this judgement',
we do not designate anything mistake to put the definite article
definite unless at the same time we indicate a definite kind of analysis; as a rule, we do this in connexion with a definite wording. But we must never forget that different sentences may express the same thought. For example, the thought we are con- sidering could also be taken as an assertion about the number 4:
'The number 4 has the property that there is something of which it is the square. '
* Grund/agen, ? 46. ** Grundlagen, ? 53.
before the word 'subject' in such expressions as 'the subject of the judgement', 'the subject of the con- tent of a possible judgement'; for no part of the content can be picked out in advance as the subject. Even the expressions 'singular content of pos- sible judgement', 'particular content of possible judgement' are not quite accurate in that they ascribe to the content itself an attribute which, strictly speaking, belongs to it only under a certain form-a certain way
lagen, ? 46) that a statement of number contains an assertion about a concept; I speak of properties asserted of a concept, and I allow
higher one (Grundlagen, ? 53). I have called existence a property of a concept. How I mean this is best made clear by an example.
In the sentence 'There is at least one square root of 4', we have an assertion not about, say, the par- ticular number 2, nor about -2, but about a concept, square root of 4;
? ? ? 108 On Concept and Object
Language has means of present- of analysing it into subject and
ing now one, now another, part of the [200] thought as the subject; one of the most familiar is the distinction of active and passive forms. It is thus not impossible that one way of analysing a given thought should make it appear as a singular judge- ment; another, as a particular judge- ment; and a third, as a universal
judgement. It need not then surprise us that the same sentence may be conceived as an assertion about a concept and also as an assertion about an object; only we must observe that what is asserted is dif- ferent. In the sentence 'there is at least one square root of 4' it is impossible to replace the words 'square root of 4' by 'the concept square root of 4; i. e. the assertion that suits the concept does not suit the object. Although our sentence does not present the concept as a subject, it asserts something about it; it can be regarded as expressing the fact that a concept falls under a higher one. * But this does not in any way efface the distinction between object and concept. We see to begin with that in the sentence 'there is at least one square root of 4' the predicative nature of the concept is not belied; we could say 'there is something that has the property of giving the result 4 when multiplied by itself. ' Hence what is here asser- ted about a concept can never be asserted about an object; for a
* In my Grund/agen I called such a concept a second-order concept; in my work Function und Begriff I called it a second-level concept, as I shall do here.
predicate.
It is conceivable that the same content should appear in one form as singular, in another as particular. It need not then surprise us that we can discern in the same content an assertion about a concept and also an assertion about an object. We must only take note that
what is asserted of the one is dif- ferent from what is asserted of the other. In the sentence 'There is at least one square root of 4' it is im- possible to replace the words 'square root of 4' by 'the concept square root of4'; i. e. the assertion that suits the concept does not suit the object. All the same something is asserted of a concept in our sentence. We can even say that our concept is presented as falling under a higher one*-one whose sole characteristic mark is is realized, understanding this word in the sense in which we are using it in the present context. But this does not in any way efface
the distinction between concept and object. We see to begin with that in the expression 'There is at least one square root of 4', 'square root of 4' is being used predicatively: 'there is something that is a square root of 4'. In place of this we could say 'there is something that has the property of giving the result 4 when multiplied by itself. Hence what is here asser-
* In my Grundlagen I called such a concept a second order concept; in my Funktion und Begriff I called it a second level concept, as I shall do here.
? proper name can never be a pre- dicative expression, though it can be partofone. Idonotwanttosayitis false to assert about an object what is here asserted about a concept; I want to say it is impossible, sense- less, to do so.
The sentence 'there is Julius Caesar' is neither true nor false but senseless; the sentence 'there is a man whose name is Julius Caesar' has a sense, but here again we have a concept, as the indefinite article shows. We get the same thing in the sentence 'there is only one Vienna'. We must not let ourselves be deceived because language often uses the same word now as a proper name, now as a concept-word; in our example, the numeral indicates that we have the latter; 'Vienna' is here a concept-word, like ? metropolis'. Using it in this sense, we may say: 'Trieste is no Vienna'. If, on the other hand, we substitute 1201] 'Julius Caesar' for the proper name formed by the first six words of the sentence 'the concept square root of 4 is realized', we get a sentence that has a sense but is false; for the assertion that some- thing is realized (as the word is being taken here) can be truly made only about a quite special kind of objects, viz. such as can be designated by proper names of the form 'the concept F'. Thus the words 'the concept square root of 4' have an
ted of a concept can never be asserted of an object. This is not to saythatitisfalsetodothis,butim- possible: a sentence which tried to express such a thing would be absolutely devoid of sense; for it has no sense to use the name of an object predicatively. We have seen that even where the form of a sentence makes it look as if this is being done, the truth is that the object forms only part of what is asserted, since 'nothing other than' has to be added in thought. A sentence such as 'There is at least Julius Caesar' is senseless, although the sentence 'There is at least one man whose name is "Julius Caesar"' has a sense; but here again we have a concept, as the 'one' shows.
On Concept and Object 109
If, on the other hand, we sub- stitute the proper name 'Julius Caesar' for the proper name formed by the first six words of the sentence 'The concept square root of 4 is realized', we get a sentence that has a sense but is false; for the assertion that something is realized, as the word is meant here, is one we can only truly make of such objects as stand in a quite special relation to a concept. Thus the words 'the con- cept square root of 4' have an essentially different behaviour, as
? 110 On Concept and Object
essentially different behaviour, as regards possible substitutions, from the words 'square root of 4' in our original sentence; i. e. the reference of the two phrases is essentially
different.
What has been shown here in one
example holds good generally; the behaviour of the concept is essen- tially predicative, even where some- thing is being asserted about it; consequently it can be replaced there only by another concept, never by an object. Thus the assertion that is made about a concept does not suit an object. Second-level con- cepts, which concepts fall under, are essentially different from first-level concepts, which objects fall under.
regards possible substitutions, from the words 'square root of 4' in our original sentence; i. e. the meanings of the two properties are different, thoughrelated.
What has been shown here in one example holds good generally: the behaviour of the concept is essen- tially predicative even when some- thing is being asserted of it; conse- quently it can be replaced there only by another concept, never by an object; i. e. the assertion that is made about a concept does not fit an object at all. Moreover a concept (of second level) under which a concept falls is essentially different from a concept (of first level) under which objects fall.
In the sentence 'There is at least one square root of 4' we assert that the first level concept square root of 4 falls under a concept of second level, whereas in the sentence 'The concept square root o f 4 is realized' we assert that the object the concept square root of4 falls under the first level concept concept that is realized. We do indeed have the same thought in the two concepts, [sic. ] but this, being analysed dif- ferently, is construed in a different way.
The relation of an object to a concept that it falls under is dif- ferent from the admittedly similar relation of a concept to a concept (of second level). From now on we shall give parallel expression to the similarity and the difference by saying than an object falls under a concept, and a concept falls within a concept (of second level); for, strictly speaking, we have been making a mistake in using the same
The relation of an object to a first-level concept that it falls under is different from the (admittedly similar) relation of a first-level to a second-level concept. (To do justice at once to the distinction and to the similarity, we might perhaps say: An object falls under a first-level concept; a concept falls within a second-level concept. ) The dis- tinction of concept and object thus still holds, with all its sharpness.
? With this there hangs together what I have said (Grund/agen, ? 53) about my usage of the words 'property' and 'mark'; Kerry's dis- cussion gives me occasion to revert once more to this.
The words serve to signify relations, in sentences like ? (/J is a property of T' and '(/J is a mark of il'. In my way of speaking a thing can at once be a property and a mark but not of the same
thing.
words to cover both cases. From this we can see that the distinction between object and concept still holds in all its sharpness.
Connected with this is another distinction, namely that between property and characteristic mark. I have already explained this in ? 53 of my Grundlagen and at the time I thought I had made it sufficiently clear. Since, however, Kerry makes no use of it and falls into error as a result, I can only assume, alas, that he has not understood me; this time I will try to be more successful.
The words 'property' and 'characteristic mark' serve to designate relations such that something can at the same time be a property of r and a characteristic mark of L1. We express ourselves more precisely if we use the words 'characteristic mark' only in the phrase 'characteristic mark of a concept'. If a thing is a property of an object, then it is a characteristic mark of a first level concept. We may also speak of properties of a first level concept, and these will then be characteristic marks of second level concepts. I will call the concepts under which an object falls its properties.
If the object r has the properties (/J, X and '1', I may combine them into n; so that it is the same thing if I say that r has the property n, or, that r has the property (/J and r has the property X and r has the property '1'. I then call (/J, X, and 'I' marks of the concept n, and, at the same time, properties of r. It is clear that the relations of (/J to r and to n are
I call the concepts under which an object falls its properties; thus 'to be (/J is a property of T' is just another way of saying: 'T falls under the concept of a (/J'. If the object r has the properties (/), X, and '1', I may combine them into n; so that it is the same thing if I say that r has the [202] property n, or, that r has the properties (/), X, and '1'. I then call (/J, X, and 'I' marks of the concept n, and, at the same time, properties of r. It is clear that the relations of (/J to r and to n are quite different, and that conse-
On Concept and Object Ill
? 112 On Concept and Object
quently different terms are required. quite different; r falls under the r falls under the concept f/J; but n, concept f/J; but n, which is itself a which is itself a concept, cannot fall concept, cannot fall under the first under the first-level concept f/J; only level concept f/J; only to a second to a second-level concept could it level concept could it stand in a
stand in a similar relation. n is, on the other hand, subordinate to f/J.
Let us consider an example. Instead of saying:
'2 is a positive number' and '2 is a whole number' and '2 is less than 10'.
we may also say
'2 is a positive whole number less than 10'.
Here
appear as properties of the object 2, and also as marks of the concept
positive whole number less than 10.
This is neither positive, nor a whole number, nor less than 10. It is indeed subordinate to the concept whole number , b u t d o e s n o t fall under it.
Let us now compare with this what Kerry says in his second article (p. 424). 'By the number 4 we understand the result of additively combining 3 and 1. The concept object here occurring is the numerical individual 4; a quite definite number in the natural number-series. This object obviously bears just the marks that are named in its concept, and no others besides-provided we refrain, as we
similar relation.
to be a positive number, to be a whole number, to be less than 10,
? ? surely must, from counting as propria of the object its infinitely numerous relations to all other individual numbers; "the" number 4 is likewise the result of additively combining 3 and 1. '
We see at once that my dis- tinction between property and mark is here quite slurred over. Kerry distinguishes here between the num- ber 4 and 'the' number 4. I must confess that this distinction is in- comprehensible to me. The number 4 is to be a concept; 'the' number 4 is to be a concept-object, and none other than the numerical individual 4. It needs no proof that what we have here [203] is not my distinction between concept and object. I t almost looks as though what was floating (though very obscurely) before Kerry's mind were my dis- tinction between the sense and the reference of the words 'the number 4'. * But it is only of the reference of the words that we can say: this is the result of additively combining 3 and 1.
Again, how are we to take the word 'is' in the sentences 'the num- ber 4 is the result of additively combining 3 and I' and '"the" number 4 is the result of additively combining 3 and I'? Is it a mere copula, or does it help to express a logical equation? In the first case, 'the' would have to be left out before 'result', and the sentences would go like this:
'The number 4 is a result of addi- tively combining 3 and I';
* Cf. my essay 'On Sense and Reference' (cited above).
