Fregean Descriptivism

Authored by: Ian H. Dunbar , Stephen K. McLeod

The Routledge Handbook of Linguistic Reference

Print publication date:  December  2020
Online publication date:  December  2020

Print ISBN: 9780367629724
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By ‘Fregean descriptivism’, we mean the position attributed to Frege by Kripke (1980). It is a view about proper names that is frequently contrasted with that of John Stuart Mill. ‘Proper names’, writes Mill (1882, 40), ‘are not connotative: they denote the individuals who are called by them; but they do not indicate or imply any attributes as belonging to those individuals’.

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Fregean Descriptivism

1  Introduction

By ‘Fregean descriptivism’, we mean the position attributed to Frege by Kripke (1980). It is a view about proper names that is frequently contrasted with that of John Stuart Mill. ‘Proper names’, writes Mill (1882, 40), ‘are not connotative: they denote the individuals who are called by them; but they do not indicate or imply any attributes as belonging to those individuals’.

While it is debatable whether he holds, by contrast with Mill, that proper names are connotative, Frege (1892, 26–27) splits the notion of the meaning of a proper name into two components, which he calls ‘Sinn’ and ‘Bedeutung’. These terms are usually translated as ‘sense’ and ‘reference’. 1 On Frege’s account, the identity statements ‘The Morning Star is the Evening Star’ and ‘The Morning Star is the Morning Star’ differ in cognitive status. The first is a posteriori and informative; the second a priori and uninformative. Frege’s distinction between sense and reference serves, he thinks, to explain such differences. The names ‘the Morning Star’ and ‘the Evening Star’ have the same referent, but, Frege believes, different senses, containing different ‘modes of presentation’ of that referent.

Kripke (1980) argues against what he calls the ‘Frege-Russell view’ of proper names. While he acknowledges that the approaches of Frege and Russell were different, Kripke (1980, 27) sees them as converging on a denial of Mill’s account, and as holding that ‘a proper name, properly used, simply was a definite description abbreviated or disguised’. 2 Kripke (1980) attributes a form of meaning descriptivism to Frege: it holds that for any proper name, there is a definite description that (to use Kripke’s term, which we will shortly cash out) gives the name’s sense. The name then abbreviates or disguises the definite description, which is therefore synonymous with the name. 3 Let n be a proper name and let d be a definite description that is supposed to define it. Although synonymy is a symmetric matter, we take it that meaning descriptivism holds that d is cognitively prior (i.e., prior in the order of understanding) to n. By the lights of meaning descriptivism, one might understand d while never having encountered n, or before n entered the language, but to understand the sense of n (upon an occasion of proper use of n) that d gives (on that occasion) is, thereby, to understand (i.e., grasp the sense of) d (as, on that occasion, the sense of n). Meaning descriptivism, we take it, holds that to understand (i.e., grasp the sense of) n is just to grasp the sense of d (as the sense of n), and not vice versa. Hence, it is a reductionist view of the meanings of proper names, and, we suggest, was so regarded by Kripke.

Kripke (1980, 32–34, 53–60), distinguishes between meaning descriptivism and reference-fixing descriptivism, both of which he attributes to Frege, 4 and both of which he argues against. According to reference-fixing descriptivism, for any proper name, n, there is a definite description, d, such that n and d are co-referential and either d or d’s sense fixes n’s referent. 5 Kripke (1980, 57) is illustrative of the distinction between these two forms of descriptivism:

[S]‌uppose we say, ‘Aristotle is the greatest man who studied with Plato’. If we used that as a definition, the name ‘Aristotle’ is to mean [i.e., to be synonymous with] ‘the greatest man who studied with Plato’. Then of course in some other possible world that man might not have studied with Plato and some other man would have been Aristotle. If, on the other hand, we merely use the description to fix the referent then the man will be the referent of ‘Aristotle’ in all possible worlds. The only use of the description will have been to pick out to which man we mean to refer.

In section 2, we describe in more detail the descriptivist view that Kripke attributes to Frege. Within meaning descriptivism, we distinguish between two constituent theses. These are name descriptivism, which holds that proper names are abbreviations of definite descriptions, and sense descriptivism, which holds that the senses of proper names are given by (i.e., as we understand this piece of Kripkean terminology, reduce to the senses of) definite descriptions. In section 3, we argue that there is little evidence, other than the evidence of Frege’s supposed commitment to sense descriptivism, that Frege was a name descriptivist. In section 4, we question the good standing of Kripke’s depiction of Frege as a sense descriptivist. In section 5, we argue that Frege did not think that the reference of a proper name was fixed by a definite description or by the definite description’s sense.

2  Descriptivism in Kripke’s Frege

Kripke (1980) attributes various descriptivist theses to Frege.

Frege … thought … [that] really a proper name, properly used, simply was a definite description abbreviated or disguised. Frege specifically said that such a description gave the sense of the name.

Kripke 1980 , 27

Frege and Russell certainly seem to have the full blown theory according to which a proper name is not a rigid designator and is synonymous with the description which replaced it.

Kripke 1980 , 58 6

Frege should be criticized for using the term ‘sense’ in two senses. For he takes the sense of a designator to be its meaning; and he also takes it to be the way its reference is determined. Identifying the two, he supposes that both are given by definite descriptions. Ultimately, I will reject this second supposition too; but even were it right, I reject the first. A description may be used as synonymous with a designator, or it may be used to fix its reference. The two Fregean senses of ‘sense’ correspond to two senses of ‘definition’ in ordinary parlance. They should carefully be distinguished.

Kripke 1980 , 59

Alongside reference-fixing descriptivism, Kripke here attributes the following descriptivist theses to Frege.

Name descriptivism

for any proper name, it is an abbreviated or disguised definite description.

Sense descriptivism

names have senses and, for any proper name, and any sense that the name has, there is some definite description that gives that sense [see section 1 above].


for any proper name, there is a definite description with which it is synonymous.

Denial of rigidity

ordinary proper names are not rigid designators.

Name descriptivism and sense descriptivism are both elements of meaning descriptivism, but name descriptivism, which neither mentions nor alludes to the notion of sense, does not entail sense descriptivism. So, name descriptivism alone does not entail meaning descriptivism.

Sense descriptivism, as we have formulated it, leaves unsettled the question of whether, for any proper name, it has just one sense (be that on any given occasion of, or common to all occasions of, its proper use). Thus, it leaves open the question of whether a definite description gives the (rather than just a) sense of the name (on a given occasion of its proper use, or common to all such occasions).

3  Frege and Name Descriptivism

In section 1, we suggested, on Kripke’s behalf, that when one expression, d, gives the sense of another, n, this is to be understood as an asymmetrical and reductive relationship: one cannot understand n without understanding d but one can understand d without understanding n, and there is nothing more to understanding n but grasping the sense of d (as the sense of n). If giving sense means what we suggest Kripke takes it to mean, then sense descriptivism indeed entails name descriptivism. This interpretation of what Kripke intends by the notion of giving sense enables us to read Kripke as having provided a valid argument (in the quotation from Kripke (1980, 27) that opens section 2 above) for his interpretation of Frege as a name descriptivist.

There appears to be little evidence, other than the evidence that Frege was a sense descriptivist, for taking him to have been a name descriptivist. Kripke’s main piece of evidence for attributing a position that is logically stronger than name descriptivism, namely meaning descriptivism, to Frege appears to be the ‘Aristotle footnote’ in Frege’s ‘On Sense and Reference’ (which we quote later, at the beginning of section 4). In that footnote, Frege does not say that the name abbreviates or disguises any of the definite descriptions with which it is associated. If the footnote is a statement of descriptivism, then it is of sense descriptivism rather than explicitly one of name descriptivism. So, again, Kripke’s attribution of name descriptivism to Frege would seem to rest upon the view, accordant with our explanation of the content of sense descriptivism (and, more specifically, its notion of giving sense) that sense descriptivism entails name descriptivism.

The Aristotle footnote can, we suggest, support Kripke’s assertion that for Frege ‘a proper name, properly used, simply was a definite description abbreviated or disguised’ (1980, 27) only if the footnote supports sense descriptivism: for the footnote contains no more direct commitment on Frege’s part to name descriptivism. Let us proceed to the question of whether the footnote does support sense descriptivism.

4  Frege and Sense Descriptivism

In the Aristotle footnote, Frege (1892, 27) writes:

In the case of an actual proper name such as ‘Aristotle’ opinions as to the sense may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will attach another sense to the sentence ‘Aristotle was born in Stagira’ than will a man who takes as the sense of the name: the teacher of Alexander the Great who was born in Stagira. So long as the reference remains the same, such variations of sense may be tolerated, although they are to be avoided in the theoretical structure of a demonstrative science and ought not to occur in a perfect language.

From around this point in his career onwards, Frege is normally fastidious in observing his distinction between expressions and their senses. Here, however, Frege does not carefully distinguish between definite descriptions themselves and their senses. The differing opinions are apt to be construed, we suggest, not as about which definite description is the sense of the name, but about which gives it. (On this point, we think, Kripke interprets Frege charitably.)

The Aristotle footnote raises two separate questions about what Frege is saying about the senses of proper names. Does Frege support sense descriptivism: i.e., the thesis that these senses are given by definite descriptions? Does Frege believe that a proper name can have multiple senses? Before we return to the main issue of whether Frege was a sense descriptivist, let us briefly consider the second question. We cannot attempt decisively to answer it here; instead, we merely offer some relevant considerations. 7

May (2006, 126–131) argues that despite the appearance of two definite descriptions in the footnote, Frege believed that a proper name can only have one sense. For Frege, May argues, the definite descriptions that feature in the footnote do not give different senses of ‘Aristotle’, but rather, as Frege writes in the footnote’s first sentence, varying (presumably false) opinions as to what the sense of ‘Aristotle’ is. It is true that Frege then talks about that which can be tolerated in natural languages as ‘variations of sense’. May’s interpretation would require that phrase to be replaced by ‘variations of opinions about sense’: accordingly, it would be these that Frege would hold to be debarred when the language involved is a logically perfect language. 8

The main text, both in the sentence to which the footnote attaches and later, suggests that Frege indeed believes that any given proper name has but one sense:

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.

Frege 1892 , 27

[O]‌ne 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 [translator’s italics], whereas in the case of an idea one must, strictly speaking, add whom it belongs to 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 connection. They are not prevented from grasping the same sense; but they cannot have the same idea.

Frege 1892 , 29–30

In the second quotation, Frege is entertaining for the purposes of argument, rather than endorsing, the suggestion that different users of a name associate distinct senses with it. His point is that even if that suggestion is true, senses are public in that any sense that belongs to a proper name is graspable by any two users of the name. In the first quotation, to which the Aristotle footnote is appended, Frege is saying that rather than a word’s sense merely being graspable in this way, it is actually grasped by everyone who is sufficiently au fait with the language. 9

To return to the main business, does the Aristotle footnote really show, as Kripke interprets it, that Frege was a sense descriptivist? Maunu (2015, 110–111) criticizes as ‘uncharitable’ the use of the footnote as decisive evidence that Frege was a descriptivist, and he quotes two passages that appear to sit ill with the attribution of sense descriptivism to Frege:

The sentence ‘Mont Blanc is over 4000 m high’ does not express the same thought as the sentence ‘The highest mountain in Europe is over 4000 m high’, although the proper name ‘Mont Blanc’ designates the same mountain as the expression ‘the highest mountain in Europe’.

Frege 1906 , 208 [192]

‘Copernicus’ and ‘the author of the heliocentric view of the planetary system’ designate the same man, but have different senses; for the sentence[s]‌ ‘Copernicus is Copernicus’ and ‘Copernicus is the author of the heliocentric view of the planetary system’ do not express the same thought.

Frege 1914 , 243 [225]

In each example a proper name and a co-referential definite description are given, and sameness of sense is denied, for those specific examples. These examples do not rule out the possibility that Frege might think that there can be, or even that there must be, for each example, another definite description that does give the sense of the proper name. Nevertheless, Frege never gives us a clear indication that he does think this. Indeed, judging by these later works, this looks very unlikely to have been his considered view, whatever his view was in 1892.

The upshot of this incursion into the history of Frege’s discussion of specific proper name/definite description co-referential pairings is as follows. Frege (1892) provides the main evidence that Frege was a sense descriptivist and even there it is in a footnote the credentials of which, as a genuine endorsement of this kind of descriptivism, are dubious. In other works Frege makes remarks that, even if not strictly inconsistent with sense descriptivism, make it look very unlikely that Frege was a sense descriptivist. So, even if, in the footnote, Frege did, whether inadvertently or otherwise, endorse this kind of descriptivism, there appears to be quite a strong case for taking this to have been a temporary lapse. 10

In order to assess whether Frege was a sense descriptivist, it is pertinent to look not only at Frege’s discussions of specific co-referential proper name/definite description pairings, but also at general statements he makes about names and their senses. Frege writes:

It may perhaps be granted that every grammatically well-formed expression figuring as a proper name always has a sense. But this is not to say that to the sense there also corresponds a reference.

Frege 1892 , 28

The examples that Frege then gives are of a probably empty and a certainly empty definite description: respectively, ‘the celestial body most distant from the earth’ and ‘the least rapidly convergent series’. It seems that by ‘grammatically well-formed expression’, Frege did not intend to include proper names, like ‘Paris’, ‘New York’, or ‘Robert Louis Stevenson’, that (even when they are composed from more than one word, and are thus syntactic compounds) are not compound expressions in the sense, for which we now reserve the term, that they possess a function-argument structure. For Frege, compound names have senses that derive from the senses of their constituent expressions. By contrast, the sense of a simple name has to be conferred upon it (e.g., by baptism or by definition).

Frege (1892, 31) sets out some of the terminology pertinent to his distinction between sense and reference:

A proper name (Eigenname) (word, sign, sign combination, expression) expresses its sense, stands for (bedeutet) or designates its reference. By employing a sign we express its sense and designate its reference.

For Frege it is of secondary importance whether an Eigenname is (in his sense) simple, like ‘Paris’ and ‘Robert Louis Stevenson’, or compound, like ‘the capital of France’. What really matters is that both sorts of expression designate objects (e.g., Frege 1892, 40–44). While Frege includes definite descriptions among the different sorts of syntactic units that can be Eigennamen, he does not privilege definite descriptions over simple names. He is content to think that Eigennamen exhibit this syntactic diversity, without ever suggesting that simple names are always abbreviations of, or disguised, compound names.

Frege (1892, 41) remarks:

A logically perfect language (Begriffsschrift) should satisfy the conditions, that every expression grammatically well constructed as a proper name out of signs already introduced shall in fact designate an object, and that no new sign shall be introduced as a proper name without being secured a reference.

Those proper names that are ‘constructed … out of signs already introduced’ are compound names. As we already mentioned, these inherit their senses from those of the expressions from which they are composed. What about the case of those proper names that are neither compound nor empty? We suggest that, for Frege, there are two ways in which their senses are acquired. The first way is by functioning as an abbreviation for a compound name the sense of which derives from that of its constituent expressions. Accordingly, a simple name that is an abbreviation for a compound name is synonymous with, and also derives its sense from the constituent expressions of, the compound name. The second way is simply by being introduced to refer to an object, without functioning as a form of shorthand for a compound name. Any symbol that is used, in this way, to refer thereby has a sense, simply in virtue of that use. It becomes an expression that neither admits of a definition nor is synonymous with a definite description. For Frege, we suggest, the two ways in which proper names in logically perfect languages come to designate, and thus to have their senses, are the same two ways in which non-empty proper names in natural languages come to designate, and thus to have their senses.

Some of Frege’s remarks about definitions in mathematics might help to clarify his views about how proper names acquire senses.

We have … to distinguish two quite different cases:

  1. We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a ‘constructive definition’, but we prefer to call it a ‘definition’ tout court.
  2. We have a simple sign with a long established use. We believe that we can give a logical analysis of its sense, obtaining a complex expression which in our opinion has the same sense. We can only allow something as a constituent of a complex expression if it has a sense we recognise. The sense of the complex expression must be yielded by the way in which it is put together. That it agrees with the sense of the long established simple sign is not a matter for arbitrary stipulation, but can only be recognised by an immediate insight. No doubt we speak of a definition in this case too. It might be called an ‘analytic definition’ to distinguish it from the first case. But it is better to eschew the word ‘definition’ altogether in this case, because what we should here like to call a definition is really to be regarded as an axiom. In this second case there remains no room for an arbitrary stipulation, because the simple sign already has a sense. Only a sign which as yet has no sense can have a sense arbitrarily assigned to it. So we shall stick to our original way of speaking and call only a constructive definition a definition. According to that a definition is an arbitrary stipulation which confers a sense on a simple sign which previously had none. This sense has, of course, to be expressed by a complex sign whose sense results from the way it is put together.

Frege 1914 , 227 [210]

While the passage concerns the use of definitions in mathematics, it might indicate what Frege thought about how compound names, including definite descriptions, can give the senses of some simple names. A proper name is a special case of a ‘simple sign’ (einfaches Zeichen) and a definite description is a special case of a ‘complex expression’ (zusammengesetzer Ausdruck).

When the relationship between a simple proper name and an associated definite description is one of case (1), then we have a restricted, but full-blown, version of meaning descriptivism. The simple name is an abbreviation for the definite description. The simple name’s sense is the same as that which, by virtue of the latter’s composition, the definite description expresses. Moreover, the definite description gives the sense of the simple name.

In case (2), however, the simple name is not given its sense by the definite description, for the simple name already had its sense, and that sense was grasped by competent users of the name, before the simple name came to be related, in cognition, to the definite description. The simple name’s sense had already been conferred upon it in some way, independently of the use of the definite description. The definite description, then, does not give, but merely articulates, that sense. We deploy the compound name as a means of analysing what that pre-existing sense is. We do this, thinks Frege (1914, 226 [209]), so that we can produce proofs that were not possible while the sense of the name was not explicitly articulated. The correctness of such an analysis ‘can only be recognised by immediate insight’ (Frege 1914, 227 [210]), rather than proved, because the analysis is precisely what is needed if we want to carry out proofs. The sense of the simple name is grasped, because the name has already been in proper use, prior to the attempt having been made to articulate that sense by appeal to the sense of the definite description. In judging the value of this attempt at articulation, we must exercise our prior, unarticulated grasp of the simple name’s sense.

Frege has here identified two types of proper name (as special cases of simple expressions). There are those that start off without a sense and are given one by stipulation, using a compound name that inherits its sense from its components. For these proper names, both name descriptivism and sense descriptivism are true. A proper name that is of the other variety already has a sense, and descriptions are used only when we try to articulate what this sense might be.

In describing this second type, Frege does, however, assume that our grasp of the prior, tacit, sense is accurate enough for us to know when we have achieved an accurate analysis. When we succeed in giving the prior sense a post hoc definition, we obtain the result that the definite description expresses the sense of, and is therefore synonymous with, the original name. The asymmetry that characterizes sense descriptivism, however, is not present.

In distinguishing between two forms of ‘definition’ in mathematics, Frege does not intend to suggest, either for mathematical or for more general language, that, for each simple expression, it is pertinent to one of the two cases. On Frege’s view there are simple signs that are indefinable. Indeed, we suggest that Frege takes those simple names that are ordinary proper names in natural languages, and concerning which we think he has been mischaracterized as a meaning descriptivist, to be indefinable. We have already encountered some of his discussion of the following examples: ‘Aristotle’, ‘Mont Blanc’, ‘Copernicus’ and ‘Columbus’. In the last three cases, he produces ‘famous deeds’-style definite descriptions that he states do not give the senses of the corresponding names. In the Aristotle footnote he gives two definite descriptions that reflect what he calls differing opinions as to the sense of the name. Frege then says in the footnote that this might be good enough in normal circumstances, but that it would be better if it could be avoided. 11

Frege wrote relatively little about the senses of those names that feature in everyday discourse. What he does write about this topic mostly concerns the question of whether each proper name does, or should, have only one sense. There is only meagre and indecisive evidence that he thought that the sense of each such proper name is given, or ought to be given, by a definite description.

5  Frege and Reference-Fixing Descriptivism

Kripke (1980) attributes to Frege the view that the referent of any given proper name is fixed by its sense and that the sense, in turn, is given by a definite description. We will shortly argue that it is because Kripke attributes sense descriptivism, along with the view that sense fixes reference, to Frege that Kripke thinks that Frege is a descriptivist about reference fixing. Our remaining purpose in this section, other than to give the aforementioned argument, is to clarify, in so far as it bears on Frege, the dialectical territory in which Kripke’s arguments against reference-fixing descriptivism work.

The slogan ‘sense determines reference’ is now, apparently thanks to Dummett’s coinage and influence, part of orthodox Frege exegesis. Dummett (1981b, 249; 1991, 87) distinguishes between ‘weak’ and ‘strong’ interpretations of it. 12 Weakly interpreted, it just means that, for any two referring expressions, sameness of sense entails sameness of reference. Thus interpreted, it is logically independent of sense descriptivism: i.e., neither entails the other.

The weak interpretation can be distinguished from the strong one via the thesis that an expression’s sense is a way in which its referent is determined. 13 While the strong interpretation entails this thesis, the weak interpretation does not.

On the strong interpretation, the sense of an expression constitutes a manner in which something is determined as being its referent, or, to put it in terms of our understanding of the expression, that is, of what is involved in grasping its sense, to grasp the sense is to apprehend the condition for something to be its referent.

Dummett 1981b , 249

This quotation is ambiguous: it does not make it clear whether it is the question of how an expression comes to refer that is of concern, or rather that of how it comes to have the referent that it has. Despite this, and that the quotation leaves it quite obscure as to what it is to determine something as being an expression’s referent, we take it that it at least illustrates the crux of the difference between the weak and the strong interpretations.

Interpreted weakly, ‘sense determines reference’ is, we think, a misleading phrase: for, unlike on the strong interpretation, it is not an allusion to the questions of how it is that a referring expression comes to refer, or comes to have the referent that it has. Interpreted weakly, the slogan is a truism about Frege’s philosophy. When interpreted strongly (as putative Frege exegesis) it suffers, in our opinion, from the flaw that there is little in Frege’s works to suggest that he had a general interest in these questions.

In the quotation from Kripke (1980, 59) near the start of section 2 above, Kripke uses ‘fix its reference’ in a way that suggests that he intends talk of sense determining reference and talk of sense fixing reference to be two ways of saying the same thing. If the sense is, as Kripke understands reference fixing, to fix the reference then, presumably, the sense must, in accordance with the strong interpretation of ‘sense determines references’, be identical to, or perform the role of being, a way in which the reference is determined.

Kripke (1980, 53–60) takes reference-fixing descriptivism to be distinct from, consistent with and weaker than meaning descriptivism. Kripke (1980, 57) characterizes reference-fixing descriptions in the following terms. A reference-fixing description serves to pick out the object to which a speaker intends, via the speaker’s use of a particular proper name, to refer. This relates reference fixing specifically to our referential intentions, rather than to the enterprise of linguistic understanding. In so doing, it accords with Dummett’s first characterization of the strong interpretation, which appeals to reference determination without appealing to understanding, but not with Dummett’s (apparently inequivalent, but see Dummett (1981b, 549)) second characterization, which does the reverse. Indeed, in order to understand a referring expression, rather than to introduce it anew into the language, the expression’s reference must already have been fixed (independently of speakers’ subsequent referential intentions).

In order to assist with the understanding of some of the material that follows, we mark out, further, the following four theses as distinct.

Reference fixing

for any proper name, something other than a speaker’s mere use of it plays the role of picking out the object to which the speaker intends, in using the name, to refer.

Sense fixes reference

for any proper name, its sense plays the reference-fixing role.

Reference-fixing descriptivism

for any proper name, either an associated definite description or the sense of that definite description plays the reference-fixing role.

Reference-fixing pure descriptivism

for any proper name, it is an associated definite description itself (rather than that description’s sense) that plays the reference-fixing role.

Reference-fixing sense descriptivism

reference fixing, sense fixes reference and sense descriptivism all hold; for any proper name, the sense of an associated definite description gives the name’s sense and plays the reference-fixing role.

Reference-fixing sense descriptivism and reference-fixing pure descriptivism are contrary views. The form of reference-fixing descriptivism that Kripke (1980, 59) attributes to Frege specifically involves the notion of sense, and it consists of the following two theses (i) the reference of a proper name is fixed by its sense; (ii) the sense is given by a definite description (i.e., sense descriptivism). These two theses together entail, but are not entailed by, reference-fixing descriptivism as we have formulated that thesis (largely to the letter of Kripke’s account). According to Kripke’s Frege, it is thanks to a definite description with which a proper name is co-referential that we are able, on an occasion of use of that proper name, thereby to pick out the object that is the name’s referent. This is because the definite description gives the name’s sense and the sense is that which fixes the name’s reference. It is not because the definite description itself, rather than its sense, plays the reference-fixing role.

In relation to reference fixing, descriptivism and Frege, the dialectic of Kripke (1980) can, we suggest, charitably be reconstructed as follows. Frege was a reference-fixing sense descriptivist and a meaning descriptivist. Meaning descriptivism falls to the following objection (Kripke 1980, 3–15, 48–49, 74–76). While any given ordinary proper name is a rigid designator, referring to the same individual under all counterfactual suppositions, this is not true of any co-referential definite description that is associated with the name. Accordingly, substitution, in a sentence, of the name by a co-referential definite description can result in a sentence with a different modal status to that of the original sentence. Since this could not happen if the name and the description were genuinely synonymous, meaning descriptivism is false. That concludes the objection. Now in holding that senses are both the meanings of, and fix the references of, proper names, Frege attributed to senses, construed as being given by definite descriptions, two roles between which a sharp distinction must be observed. Decoupling reference-fixing descriptivism from meaning descriptivism enables the independent evaluation of reference-fixing descriptivism. So as to observe the distinction that is violated by Frege’s notion of sense, let us now not think of Fregean senses, construed as the elements of linguistic meaning that explain synonymy and the lack thereof, as the putative reference fixers. Rather, let us take the definite descriptions (semantically, rather than merely syntactically, individuated) that Frege thinks give those senses as themselves being the putative reference fixers. That is, let us consider the thesis, which does not invoke Frege’s notion of sense, that for any proper name, an associated definite description itself plays the reference-fixing role. For various reasons, even this thesis must be rejected (Kripke 1980, Lecture II). These reasons include that a speaker who associates a definite description that is false of the name’s bearer can still succeed, when using the name, in referring to the name’s bearer (Kripke 1980, 82–89).

Thus interpreted, Kripke moves from arguing against a position that we think Frege did not hold (namely meaning descriptivism) to one that Kripke rightly thinks that Frege did not hold (namely reference-fixing pure descriptivism). Whether Frege held that sense fixes reference, at least as understood by Kripke, is another question and one that we do not have room to address. We end merely with a reminder that Kripke’s interpretation of Frege on this point aligns with Dummett’s reading of Frege as a supporter of ‘sense determines reference’, strongly interpreted.

6  Conclusion

We have taken Fregean descriptivism to be a view, attributed to Frege by Kripke, that incorporates both meaning descriptivism and reference-fixing descriptivism. For each of these views, in turn, we have broken it down into constituent theses between which Kripke himself did not clearly distinguish. In the case of meaning descriptivism, among its constituent theses are name descriptivism, according to which, for any proper name, it is an abbreviated or disguised form of a definite description, and sense descriptivism, according to which the senses of names are given by definite descriptions.

In Frege’s writings, the Aristotle footnote is the main evidence that Frege was a sense descriptivist. If one supposes that the footnote commits Frege to sense descriptivism, then one must take it that Frege denies that a proper name is synonymous with any definite description that gives its sense, for the footnote is meant to suggest that one name can (presumably correctly) have associated with it many definite descriptions that differ in sense. Alternatively, one might follow May (2006) in holding that the Aristotle footnote is not about sense itself, but rather about opinions about sense. Elsewhere Frege appears to express the belief that each name has but one sense. Frege (1914), in discussing definitions, distinguishes between cases where a compound name assigns a sense to a proper name that had no prior sense (which is sense descriptivism for a limited class of expressions), and those where the name already (somehow) had a sense, and definite descriptions are used in attempts to articulate what that sense is. In these latter cases, Frege leaves it open as to how this original sense was established.

We have argued that Kripke’s interpretation of Frege as a reference-fixing descriptivist stems from his ascription of two other views, each logically weaker than reference-fixing descriptivism itself, to Frege. These are sense descriptivism and the view that sense fixes reference. The meaning descriptivism and the reference-fixing descriptivism of Kripke’s Frege have sense descriptivism as their common, logically weaker, core. Since we do not concur with Kripke’s view that Frege was a sense descriptivist, we do not share his reasons for thinking that Frege was a reference-fixing descriptivist.


We thank Michael Hauskeller, Daniel Hill and the editors for their comments.


We follow this convention, including in quoted passages from Frege’s works. For works published in Frege’s lifetime, references are to the pages of the original publications. For posthumously published works, references are to the German edition followed, in square brackets, by the English edition.

Kripke uses ‘proper name’ in a manner intended to exclude definite descriptions themselves. Frege’s ‘Eigenname’ (‘proper name’), on the other hand, includes them.

What Kripke (1980, 31) calls ‘the cluster concept theory’ involves a version of meaning descriptivism that requires a formulation different to that, upon which we will shortly expand, just given.

Kripke does not name these two types of descriptivism. We adopt shortened forms of the names used by Macià (1998, 447).

We take it, and we think that we are following Kripke in this, that reference-fixing descriptivism does not necessarily involve the notion of sense. It is one thing to claim that a definite description fixes a name’s reference, another to say that it is the sense of the definite description that does so, and yet another to say that it is the name’s sense that does so. In section 5, we explain the relevance of these nuances.

Kripke (1980, 48–49) introduces the notion of rigid designation and the view that proper names are rigid designators.

To pursue the matter in greater depth, see May (2006) and the works cited therein.

Logically perfect languages are artificial, and they are to be constructed so that each symbol within them has a clear and determinate sense and so that there are no cases in which two token symbols (individuated purely syntactically) of the same type symbol are token expressions (i.e., symbols with senses) of different expression types (in that their senses differ).

On May’s exegesis, Frege holds that this is so even when two competent users of a name have differing opinions as to what the name’s sense is. See May (2006, 128). May therefore sees Frege as having held that one might grasp a sense without being able properly to articulate, or to specify, exactly what it is that one has grasped.

We agree with Dummett (1981a, 97–98, 110–111) that Frege’s sense theory does not entail sense descriptivism. Beyond his brief comments on specific co-referential name/definite description pairings, Frege frequently invokes the notion of sense, including when he writes that empty names have senses. Such passages do not show, and we do not think that they strongly suggest, that he was a sense descriptivist.

There is a related discussion, controversial among Frege scholars, about Dr Gustav Lauben and expressions that refer to him, in Frege (1918, 65–66). See May (2006, 121–126).

If Dummett was indeed the slogan’s originator then it is odd that he distinguishes between two interpretations of it. From Dummett (1967, 105) onwards the slogan repeatedly arises in Dummett’s writings. (In 1967, Dummett uses ‘meaning’, rather than ‘reference’, where Frege would use ‘Bedeutung’.) ‘Sense, Frege says, determines reference’ writes Dummett (1991, 87). Dummett thereby attributes to Frege a slogan that, thus formulated, Frege never enunciates and an ambiguity that Frege himself does not bequeath to us. The slogan also occurs in numerous other sources (that we do not have space to cite) that have appeared since the 1970s.

The chances of the strong interpretation’s being a truism about Frege’s philosophy would be greater were it to be Frege’s view that the senses of non-empty proper names are modes of presentation of their referents. In fact, Frege (1892, 26–27) writes, albeit more obscurely, that these senses contain (‘enthalten’) modes of presentation of their referents. May (2006, 131) makes play of this distinction.


Dummett, M. A. E. (1967) ‘Frege, Gottlob’ in P. Edwards (ed.), Encyclopedia of Philosophy, vol. III, pp. 225–237 (New York: Macmillan), repr. (as ‘Frege’s Philosophy’) in M. A. E. Dummett , Truth and Other Enigmas (London: Duckworth, 1978), pp. 87–115. Page references are to the latter.
Dummett, M. A. E. (1981a) Frege: Philosophy of Language (2nd ed., London: Duckworth).
Dummett, M. A. E. (1981b) The Interpretation of Frege’s Philosophy (London: Duckworth).
Dummett, M. A. E. (1991) Frege and Other Philosophers (Oxford: Oxford University Press).
Frege, G . (1892) ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und philosophische Kritik 100: 25–50, trans. M. Black as ‘On Sense and Reference’ in P. T. Geach and M. Black (eds), Translations from the Philosophical Writings of Gottlob Frege (3rd ed., Oxford: Blackwell, 1980), pp. 56–78.
Frege, G. (1906) ‘Einleitung in die Logik’, unpublished; reproduced in H. Hermes , F. Kambartel and F. Kaulbach (eds), Nachgelassene Schriften (Hamburg: Felix Meiner, 1969), pp. 201–212, trans. P. Long and R. White as ‘Introduction to Logic’ in H. Hermes , F. Kambartel and F. Kaulbach (eds.), Posthumous Writings (Chicago, IL: University of Chicago Press, 1979), pp. 185–196.
Frege, G. (1914) ‘Logik in der Mathematik’, unpublished; reproduced in H. Hermes , F. Kambartel and F. Kaulbach (eds.), Nachgelassene Schriften (Hamburg: Felix Meiner, 1969), pp. 219–270, trans. P. Long and R. White as ‘Logic in Mathematics’ in H. Hermes , F. Kambartel and F. Kaulbach (eds.), Posthumous Writings (Chicago, IL: University of Chicago Press, 1979), pp. 203–250.
Frege, G. (1918) ‘Der Gedanke. Eine logische Untersuchung’, Beiträge zur Philosophie des deutschen Idealismus I (1918–1919): 58–77, trans. A. Quinton and M. Quinton as ‘The Thought: A Logical Inquiry’ in E. D. Klemke (ed.), Essays on Frege (Urbana, IL: University of Illinois Press, 1968), pp. 507–535.
Kripke, S. A. (1980) Naming and Necessity (Oxford: Blackwell).
Macià, J . (1998) ‘Does Naming and Necessity Refute Descriptivism?’, Theoria (Spain) 13: 445–476.
Maunu, A. (2015) ‘Frege and the Description Theory: An Attempt at Rehabilitation’, Grazer Philosophische Studien 92: 109–116.
May, R . (2006) ‘The Invariance of Sense’, Journal of Philosophy 103: 111–144.
Mill, J. S. (1882) A System of Logic (8th ed., New York: Harper and Brothers). Project Gutenberg eBook 27942 (2009).
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