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On Sense and Reference-frege

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2021-02-16 18:42
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2021年2月16日发(作者:favored)


On Sense and Reference



(Excerpt)


Gottlob Frege



1892


Equality gives rise to challenging questions which are not altogether easy to answer. Is it a


relation? A relation between objects, or between names or signs of objects? In my


Begriffsschriftz


I


assumed the latter. The reasons which seem to favour this are the following:


a


=


a


and


a


= b are


obviously statements of differing cognitive value;


a


=


a


holds a priori and, according to Kant, is to


be labelled analytic, while statements of the form


a


= b often contain very valuable extensions of our


knowledge and cannot always be established a priori. The discovery that the rising sun is not new


every morning, but always the same, was one of the most fertile astronomical discoveries. Even


today the identification of a small planet or a comet is not always a matter of course. Now if we were


to regard equality as a relation between that which the names


'a'


and '6' designate, it would seem that


a


= b could not differ from


a=a


(i-e., provided


a


= b is true). A relation would thereby be expressed


of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is


intended to be said by


a


= b seems to be that the signs or names


'a'


and 'by designate the same thing,


so


that


those


signs


themselves


would


be


under


discussion;


a


relation


between


them


would


be


asserted. But this relation would hold between the names or signs only in so far as they named or


designated something. It would be mediated by the connexion of each of the two signs with the same


designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible


event or object as a sign for something. In that case the sentence


a


= b would no longer refer to the


subject matter, but only to its mode of designation; we would express no proper knowledge by its


means. But in many cases this is just what we want to do. If the sign


'a'


is distinguished from the sign


'6'


only


as


object


(here,


by


means


of


its


shape),


not


as


sign


(i.e.


not


by


the


manner


in


which


it


designates


something),


the cognitive


value


of


a


=


a


becomes


essentially


equal


to


that


of


a


=


b,


provided


a


= b is true. A difference can arise only if the difference between the signs corresponds to


a


difference


in


the


mode


of


presentation


of


that


which


is


designated.


Let


a,


6,


c


be


the


lines


connecting


the


vertices


of


a


triangle


with


the


midpoints


of


the


opposite


sides.


The


point


of


intersection of


a


and b is then the same as the point of intersection of b and


c.


So we have different


designations


for


the


same


point,


and


these


names


('point


of


intersection


of


a


and


by,


'point


of


intersection


of


b


and


c


’)


likewise


indicate


the


mode


of


presentation;


and


hence


the


statement


contains actual knowledge.



It is natural, now, to think of there being connected with a sign (name, combination of words,


letter), besides that to which the sign refers, which may be called the reference of the sign, also what


I should like to call the


sense


of the sign, wherein the mode of presentation is contained. In our


example, accordingly, the reference of the expressions 'the point of intersection of


a


and b' and 'the


point of intersection of b and c' would be the same, but not their senses. The reference of 'evening


star' would be the same as that of 'morning star', but not the sense.



It is clear from the context that by 'sign' and 'name' I have here understood any designation


representing a proper name, which thus has as its reference a definite object (this word taken in the


widest range), but not a concept or a relation, which shall be discussed further in another article. The


designation of a single object can also consist of several words or other signs. For brevity, let every


such designation be called a proper name.



The


sense


of


a proper


name


is


grasped


by


everybody


who


is


sufficiently


familiar


with


the


language or totality of designations to which it belongs; but this serves to illuminate only a single


aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would


require us to be able to say immediately whether any given sense belongs to it. To such knowledge


we never attain.



The regular connexion between a sign, its sense, and its reference is of such a kind that to the


sign there corresponds a definite sense and to that in turn a definite reference, while to a given


reference


(an


object)


there


does


not


belong


only


a


single


sign.


The


same


sense


has


different


expressions


in


different


languages


or


even


in


the


same


language. To be


sure,


exceptions


to


this


regular behaviour occur. To every expression belonging to a complete totality of signs, there should


certainly correspond a definite sense; but natural languages often do not satisfy this condition, and


one must be content if the same word has the same sense in the same context. It may perhaps be


granted that every grammatically well-formed expression representing a proper name always has a


sense. But this is not to say that to the sense there also corresponds a reference. The words 'the


celestial body most distant from the Earth' have a sense, but it is very doubtful if they also have a


reference. The expression 'the least rapidly convergent series' has a sense; but it is known to have no


reference, since for every given convergent series, another convergent, but less rapidly convergent,


series can be found. In grasping a sense, one is not certainly assured of a reference.



If words are used in the ordinary way, what one intends to speak of is their reference. It can also


happen, however, that one wishes to talk about the words themselves or their sense. This happens,


for instance, when the words of another are quoted. One's own words then first designate words of


the other speaker, and only the latter have their usual reference. We then have signs of signs. In


writing,


the


words


are


in


this


case


enclosed


in


quotation


marks.


Accordingly,


a


word


standing


between quotation marks must not be taken as having its ordinary reference.



In order to speak of the sense of an expression 'A' one may simply use the phrase 'the sense of


the expression


is quite clear that in this way of speaking words do not have their customary reference but designate


what is usually their sense. In order to have a short expression, we will say: In reported speech,


words are used


indirectly


or have their


indirect


reference. We distinguish accordingly the


customary


from the


indirect


reference of a word; and its


customary


sense from its


indirect


sense. The indirect


reference of a word is accordingly its customary sense. Such exceptions must always be borne in


mind


if


the


mode


of


connexion


between


sign,


sense,


and


reference


in


particular


cases


is


to


be


correctly understood.



The


reference


and


sense


of


a


sign


are


to


be


distinguished


from


the


associated


idea.


If


the


reference of a sign is an object perceivable by the senses, my idea of it is an internal image, arising


from memories of sense impressions which I have had and acts, both internal and external, which I


have performed. Such an idea is often saturated with feeling; the clarity of its separate parts varies


and oscillates. The same sense is not always connected, even in the same man, with the same idea.


The idea is subjective: one man's idea is not that of another. There result, as a matter of course, a


variety of differences in the ideas associated with the same sense. A painter, a horseman, and a


zoologist


will


probably


connect


different


ideas


with


the


name


'Bucephalus'.


This


constitutes


an


essential distinction between the idea and the sign's sense, which may be the common property of


many and therefore is not a part of a mode of the individual mind. For one can hardly deny that


mankind has a common store of thoughts which is transmitted from one generation to another.



In the light of this, one need have no scruples in speaking simply of


the


sense, whereas in the


case


of an


idea


one


must,


strictly


speaking,


add


to


whom


it


belongs


and at


what


time.


It


might


perhaps be said: Just as one man connects this idea, and another that idea, with the same word, so


also one man can associate this sense and another that sense. But there still remains a difference in


the mode of connexion. They are not prevented from grasping the same sense; but they cannot have


the same idea. Si


duo idem faciunt, non est idem.


If two persons picture the same thing, each still has


his own idea. It is indeed sometimes possible to establish differences in the ideas, or even in the


sensations, of different men; but an exact comparison is not possible, because we cannot have both


ideas together in the same consciousness.



The reference of a proper name is the object itself which we designate by its means; the idea,


which we have in that case, is wholly subjective; in between lies the sense, which is indeed no


longer subjective like the idea, but is yet not the object itself. The following analogy will perhaps


clarify these relationships. Somebody observes the Moon through a telescope. I compare the Moon


itself to the reference; it is the object of the observation, mediated by the real image projected by the


object glass in the interior of the telescope, and by the retinal image of the observer. The former I


compare to the sense, the latter is like the idea or experience. The optical image in the telescope is


indeed


one- sided


and


dependent


upon


the


standpoint


of


observation;


but


it


is


still


objective,


inasmuch as it can be used by several observers. At any rate it could be arranged for several to use it


simultaneously. But each one would have his own retinal Image. On account of the diverse shapes of


the


observers'


eyes,


even


a


geometrical


congruence


could


hardly


be


achieved,


and


an


actual


coincidence


would


be


out


of


the


question.


This


analogy


might


be


developed


still


further,


by


assuming A's retinal image made visible to B; or A might also see his own retinal image in a mirror.


In this way we might perhaps show how an idea can itself be taken as an object, but as such is not for


the observer what it directly is for the person having the idea. But to pursue this would take us too


far afield.



We


can


now


recognize


three


levels


of


difference


between


words,


expressions,


or


whole


sentences. The difference may concern at most the ideas, or the sense but not the reference, or,


finally, the reference as well. With respect to the first level, it is to be noted that, on account of the


uncertain connexion of ideas with words, a difference may hold for one person, which another does


not find. The difference between a translation and the original text should properly not overstep the


first


level.


To


the


possible differences


here


belong


also


the


colouring


and


shading which


poetic

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