Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T16:28:35.541Z Has data issue: false hasContentIssue false
  • English
  • Français

What's Puzzling Gottlob Frege?

Published online by Cambridge University Press:  01 January 2020

Mike Thau  and
Ben Caplan
Mike Thau
Affiliation:
University of California, Los Angeles, Los Angeles, CA90095, USA
Ben Caplan
Affiliation:
University of California, Los Angeles, Los Angeles, CA90095, USA
Get access Rights & Permissions [Opens in a new window]

Extract

By any reasonable reckoning, Gottlob Frege's ‘On Sense and Reference’ is one of the more important philosophical papers of all time. Although Frege briefly discusses the sense-reference distinction in an earlier work (‘Function and Concept,’ in 1891), it is through ‘Sense and Reference’ that most philosophers have become familiar with it. And the distinction so thoroughly permeates contemporary philosophy of language and mind that it is almost impossible to imagine these subjects without it.

The distinction between the sense and the referent of a name is introduced in the second paragraph of ‘Sense and Reference.’

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 31 , Issue 2 , June 2001 , pp. 159 - 200
Copyright
Copyright © The Authors 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 For support in the form of a Doctoral Fellowship (#752-98-0363), thanks from the second author to the Social Sciences and Humanities Research Council (SSHRC) of Canada. For comments and discussion, thanks from both authors to the editors of, and anonymous referees for, the Canadian Journal of Philosophy and also to Kent Bach, Glenn Branch, Tyler Burge, Louis Derosset, David Kaplan, Sean Kelsey, Robert May, Scott Soames, and especially Mark Kalderon.

2 ‘Über Sinn und Bedeutung,’ Zeitschrift für Philosophie und philosophische Kritik 100 (1892) 25-50. The essay was translated by Black, Max as ‘On Sense and Meaning’ in Translations from the Philosophical Writings of Gottlob Frege, 3rd ed., Geach, Peter T. and Black, Max eds. (Oxford: Blackwell 1980) 56–78Google Scholar. It was reprinted as ‘On Sinn and Bedeutung’ in The Frege Reader, Beaney, Michael ed. (Oxford: Blackwell 1997) 151-71Google Scholar.

Black translates ‘Bedeutung’ as ‘meaning’ and ‘bedeuten’ as ‘mean’ (or sometimes as ‘designate’); Beaney translates ‘bedeuten’ as ‘stand for’ (or sometimes as ‘denote’). We emend their translations, of ‘Sense and Reference’ and other texts, so that ‘Bedeutung’ is translated as ‘reference’ or ‘referent,’ and ‘bedeuten’ is translated as ‘refer to,’ because we find this translation the most familiar and the easiest to understand. Other emendations to previous translations are indicated in the notes.

3 We use ‘name’ (or ‘sign’) as Frege does to include all singular terms. See ‘Sense and Reference,’ 27.

4 We translate ‘betreffen’ here as ‘touch’ (rather than ‘be concerned with’), as it is translated in section 8 of the Begriffsschrift; and we translate ‘Sache selbst’ there as ‘subject matter’ (rather than ‘matter’), as it is translated here. On our view, there is a close connection between these passages, so it is important to bring their translations in line.

5 Dunnett, Salmon, Sluga, and Weiner endorse the standard interpretation. See Dummett, Michael Frege: Philosophy of Language, 2nd ed. (Cambridge, MA: Harvard University Press 1981), 544Google Scholar; Salmon, Nathan Frege's Puzzle (Cambridge, MA: The MIT Press 1986), 51-4Google Scholar; Sluga, Hans Gottlob Frege (Boston: Routledge & Kegan Paul 1980), 149-61Google Scholar; and Weiner, Joan Frege (Oxford: Oxford University Press 1999), 91-2Google Scholar. Kaplan agrees that Frege rejects the name view, but he does not say that Frege accepts the object view instead. See Kaplan, David ‘Words,’ Supplement to the Aristotelian Society 64 (1990) 93–119, at 118.CrossRefGoogle Scholar

6 Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Halle: Nebert 1879). Preface and Part I trans. by Michael Beaney as ‘Begriffsschrift: A Formula Language of Pure Thought Modelled on that of Arithmetic’ in The Frege Reader, 47-78.

7 We do not draw any distinction between senses and modes of presentation. However, as stated above in the text, Frege claims in the second paragraph of ‘Sense and Reference’ that a sense contains a mode of presentation, which suggests that they are distinct. But the containment metaphor does not explain what, if anything, the distinction between senses and modes of presentation really amounts to. Moreover, after introducing the notion of a mode of presentation in ‘Sense and Reference,’ Frege gives examples of them; and, in each of his examples, a mode of presentation is given by a definite description: for example, by ‘the intersection of lines I and m.’ But, in a footnote to ‘Sense and Reference,’ Frege says: ‘In the case of an actual proper name such as “Aristotle” opinions as to the sense may differ.lt might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the great’ (27 n.B). So, in the footnote, Frege gives the sense (rather than the mode of presentation contained in the sense) of the name by a definite description This makes it very doubtful that the distinction between modes of presentation and senses that Frege seems to implicitly draw in the text represents something of importance to him. Indeed, we think the footnote (coupled with the fact that Frege says absolutely nothing about the distinction beyond the metaphor) makes it plausible that the apparent implication of the containment metaphor may be unintentional — that Frege doesn't mean to be suggesting that modes of presentation and senses are distinct. In any case, as far as we can tell, whatever distinction there might be between them has no bearing on our discussion.

8 We do not mean to take a stand here on whether Frege is a descriptivist: that is, whether he thinks that the sense of every name is given by a definite description. But it is clear (see note 7 above) that Frege thinks that the senses of at least some names are given by definite descriptions.

9 The notion of a directly referential expression is developed in Kaplan, David ‘Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals,’ Themes from Kaplan, Almog, Joseph Perry, John and Wettstein, Howard eds. (New York: Oxford University Press 1989) 481–563Google Scholar.

10 In the course of our research, we have come across various writers whose views, to various degrees, anticipate our own. See Stroll, Avrum ‘Identity,’ Encyclopedia of Philosophy vol. 4, Edwards, Paul ed. (New York: Macmillan 1967) 123-4Google Scholar; Dejnoža, Jan ‘Frege on Identity,’ International Studies in Philosophy 13.1 (1981) 31–41CrossRefGoogle Scholar, at 31-6, and The Ontology of the Analytic Tradition and its Origins: Realism and Identity in Frege, Russell, Wittgenstein, and Quine (Lanham, MD: Littlefield Adams 1996), 42-65; Currie, Gregory Frege: An Introduction to his Philosophy (Brighton: Harvester 1982), 98–100Google Scholar and 108-12; and Morris, Thomas V. Understanding Identity Statements (Aberdeen: Aberdeen University Press 1984), 27–34Google Scholar. But each falls short in some way. Discussing the details of Frege's texts is complicated enough; so, rather than explicitly signaling where we disagree with or go beyond other interpretations, we simply argue for our own.

11 ‘Über formale Theorien der Arithmetik, ’ Sitzungsberichte der Jenaischen Gesellschaft for Medizin und Naturwissenschaft 19 (Supplement 2, 1885) 94-104, at 101. Trans. by Kluge, Eike-Henner W. as ‘On Formal Theories of Arithmetic’ .in On the Foundations of Geometry and Formal Theories of Arithmetic (New Haven: Yale University Press 1971) 141-53.Google Scholar

12 Frege says ‘have the same content’ (‘denselben Inhalt haben’) rather than ‘refer to the same object.’ In 1885, Frege had yet to clearly distinguish sense and reference. He later came to think that sentences themselves are names and that his use of ‘the content (Inhalt) of a sentence’ in the Begriffsschrift was ambiguous between the sense of a sentence and its referent See his letter to Husserl, ‘Frege an Husserl 24.5.1891,’ Wissenschaftlicher Briefwechsel, Gabriel, Gottfried et al., eds. (Hamburg: Meiner 1976) 94-8, at 97Google Scholar; trans. by Kaal, Hans as ‘Frege to Husserl 24.5.1891’ in Philosophical and Mathematical Correspondence, McGuinness, Brian ed. (Oxford: Blackwell 1980) 61-4Google Scholar, and reprinted in part as ‘Letter to Husserl 24.5.1891’ in The Frege Reader 149-50. See also ‘Über Begriff und Gegenstand,’ Vierteljahrsschrift for wissenschaftliche Philosophie 16 (1892) 192-205, at 198; trans. by Black, Max as ‘On Concept and Object’ in Translations from the Philosophical Writings, 42–55Google Scholar, and reprinted in The Frege Reader, 181-93. And see Grundgesetze der Arithmetik: begriffsschriftlich abgeleitet [The Basic Laws of Arithmetic] vol. 1 (Jena: Pohle 1893), X and §5, 9 n.T; Preface, Introduction, and §§1-7, 26-9, and 32-3 trans. by Beaney, Michael in The Frege Reader, 194–223Google Scholar. But Frege makes no such claim about the content of names that are not sentences. And although in a number of places he uses ‘thecontentofaname(thatisnotasentence)’ for the referent of a name, nowhere does he use it for the sense of a name. For example, the statement of the name view in the Begriffsschrift (§8, 14) uses ‘content’ (‘Inhalt’) rather than ‘referent’ (‘Bedeutung’). Later in that same section, frege says of two names that refer to the same point: ‘The name B has therefore in this case the same content as the name A.’ And, in a passage from ‘Function and Concept’ quoted just below in the text, he uses ‘content’ and ‘referent’ interchangeably when speaking of names that are not sentences. See Function und Begriff: Vortag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medizin und Naturwissenschaft (Jena: Pohle 1891), 3; trans. by Geach, Peter T. as ‘Function and Concept’ in Translations from the Philosophical Writings, 21–41Google Scholar, and reprinted in The Frege Reader, 130-48.

13 Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung uber den Begriff der Zahl (Breslau: Koebner 1884); trans. by Austin, J.L. as The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, 2nd ed. (Evaston, IL: Northwestern University Press 1980)Google Scholar

14 We translate ‘die Bedeutung der rechtsstehenden Zeichenverbindung dieselbe sei wie die der linksstehenden’ as ‘the referent of the right-hand complex of signs is the same as that of the left-hand one’ rather than ‘the right-hand complex of signs has the same referent as the left-hand one.’

15 Grundgesetze der Arithmetik: begriffsschriftlich abgeleitet [The Basic Laws of Arithmetic] vol. 2 (Jena: Pohle 1903), §105, 113. §§56-67, 138-47 trans. by Beaney, Michael in The Frege Reader, 258-89Google Scholar. §§86-137 trans. by Black, Max as ‘Frege Against the Formalists’ in Translations from the Philosophical Writings, 162–213Google Scholar.

16 We translate ‘bedeuten’ as ‘refer to’ rather than ‘stand for’ (similarly for ‘bedeutet’). See note 2.

17 We translate ‘besagte’ here as ‘state’ (rather than ‘assert’), as ‘besagt’ is translated in ‘Formal Theories of Arithmetic’ (101).

18 Bernhardt, Stephen ‘Frege on Identity,’ Journal of Critical Analysis 8.4 (1980) 57-65, At 61-4CrossRefGoogle Scholar

19 We translate ‘meine’ and ‘meinen’ as ‘intend’ rather than ‘mean,’ since ‘bedeuten’ (which we translate as ‘refer to’) is sometimes translated as ‘mean.’ See note 1.

20 ‘Frege an Peano ohne Datum,’ Wissenschaftlicher Briefwechsel194-8, at 197; trans. by Kaal, Hans as ‘Frege to Peano undated,’ in Philosophical and Mathematical Correspondence, 125-9Google Scholar

21 On the name view, ⌈α = β⌉ expresses the thought that α and β co-refer. However, there is a closely related view—which we'll call the hybrid view—on which ⌈α = β⌉ expresses the thought that the referent of α = the referent of β. And, though the distinction is subtle, the thoughts

  1. (i)

    (i) that α and β co-refer

  2. (ii)

    (ii) that the referent of α = the referent of β

are in fact distinct. The thought (t) contains modes of presentation that determine the names α and β, whereas the thought (it) contains modes of presentation (given by ⌈the referent of α⌉ and ⌈the referent of β⌉) that determine the objects a and b. So, like the object view, the hybrid view implies that identity is strictly speaking a relation between objects; however, it's important not to let this area of agreement obscure the fact that the views differ radically about the thoughts expressed by identity statements. For example, on the object view, ‘Hesperus= Phosphorus’ expresses the thought that Hesperus is Phosphorus; whereas, on the hybrid view, ‘Hesperus= Phosphorus’ expresses the metalinguistic thought (of type (it)) that the referent of ‘Hesperus’ =the referent of ‘Phosphorus.’ In this respect, the hybrid view is much closer to the name view, on which ‘Hesperus = Phosphorus’ expresses the metalinguistic thought (of type (i)) that ‘Hesperus’ and ‘Phosphorus’ co-refer. Indeed, these metalinguistic thoughts are so closely related that Frege appears not to distinguish them. In three of the six passages cited in this section (ie., the first, fourth, and sixth passages), what he says suggests that identity statements express thoughts of type (t), whereas in the other three passages (ie., the second, third, and fifth ones) what he says suggests that identity statements express thoughts of type (ii) (given that, as he says in a footnote to ‘Sense and Reference’ (25 n.A), he is using ‘coincides with’ (‘fallen zusammen’) and ‘=’ interchangeably). We interpret Frege as holding the name view rather than the hybrid view because it fits better with the central texts: in Section 8 of the Begriffsschrift, Frege says that an identity statement expresses that the names ‘have the same content’ (‘denselben Inhalt haben’) and thus identity is a relation between names, (§8, 14); and, in the opening paragraph of ‘Sense and Reference,’ Frege (26) says that, on his view from the Begriffsschrift, an identity statement expresses that the names ‘refer to the same thing’ (‘dasselbe bedeuten’) and that ‘a relation between them [the names] would be asserted’ (26). (On the interpretation of ‘have the same content’ (‘denselben Inhalt haben’), see note 12 above.) But there might be other reasons to attribute the hybrid view rather than the name view to Frege. Given how subtle the distinction between the two views is, it would take another paper to settle the issue. However, whether Frege holds the name view or the hybrid view, the standard interpretation wrongly supposes that, in ‘Sense and Reference,’ Frege rejects his earlier view that identity statements express metalinguistic thoughts.

22 There is one aspect of the name view that Frege mentions in the Begriffsschrift that is not mentioned in ‘Sense and Reference’: namely, that when a name flanks the identity sign it does not refer to the object it customarily refers to; rather, it refers to itself (§8, 13-14). This raises the question of why Frege does not mention this aspect of the view in ‘Sense and Reference.’ One answer is that, as we will see in Section VIII, Frege is not particularly concerned with identity in ‘Sense and Reference.’ But another answer is that, even in the Begriffsschrift, Frege is not so concerned with this aspect of the name view. He mentions it only in two, consecutive sentences; and, in the very first sentence where he mentions it, he proceeds to ignore it. For in that sentence he goes on to say that an identity statement expresses that the names refer to the same object; and they obviously don't refer to the same object if they refer to themselves (and aren't the same name).

As we will see in this section, although Frege does have an inchoate version of the sense-reference distinction in the Begriffsschrift, it is worth noting that, once the role of the sense-reference distinction is more fully worked out, the distinction seems to justify Frege's claim in the Begriffsschrift that a name that flanks the identity sign doesn't have its customary referent. After all, given the compositionality of reference, the referent of an expression is what's relevant to determining the truth-value (i.e., the referent) of a sentence it occurs in; and, on the name view, what's relevant to the truth-value of an identity statement are the names that flank the identity sign, since, on that view, an identity statement expresses the thought that those names co-refer.

23 The only other reason for thinking that there would be no need for the identity sign on the name view is that, instead of saying ⌈α = β⌉ one could always say that α and β co-refer. However, this can't be what Frege is thinking, because there is no way around this objection. Any analysis of identity in terms of something else will make the identity sign superfluous in this sense.

24 We translate ‘bedeutet’ as ‘refers to’ rather than ‘denotes.’ See note 2.

25 On the translation of ‘Sache selbst’ as ‘subject matter’ (rather than ‘matter’), see note 4 above.

26 We use ‘mode of determination’ and ‘mode of presentation’ interchangeably. As far as we can tell, there is no reason to think that the change of terminology amounts to anything.

27 On the standard interpretation there is another place where Frege appears to be oddly silent about a change in his view. As we pointed out in Section II, in the second volume of The Basic Laws, eleven years after ‘Sense and Reference,’ Frege agrees with Dedekind that the name view is the correct account of the identity sign. But immediately after expressing his agreement with Dedekind, Frege responds to an objection of Thomae's concerning identity by citing the sense-reference distinction. Hence, if the standard interpretation is correct, Frege must again have changed his mind about which view the distinction makes defensible and again failed to make any note of the change. With this said, there are difficulties in interpreting Frege's criticism of Thomae. Thomae's objection in Elementary Function Theory from 1898 is that ‘if equality or the equality sign = were only to stand for identity, then we would be left with trivial knowledge, or if one prefers, the conceptual necessity a is a (a = a)’ (quoted in The Basic Laws vol. 2, §138, 140). So Thomae's objection seems to be the objection to the object view: namely, that if ⌈α = β⌉ expresses that a and b are the same object, then it would seem to express the same thing as ⌈α = β⌉. Since Frege replies to Thomae by citing the distinction between sense and reference, it might seem that Frege is using that distinction to defend the object view. But Frege asserts neither the object view nor the name view in his reply to Thomae. Frege says that senses determine cognitive value and that the senses of the two identity statements can differ, but he does not say how they differ. More importantly, as we pointed out at the beginning of this note, the quotation from Thomae and Frege's reply occur immediately after, and continue the discussion started in, the citation from Dedekind and Frege's claim that Dedekind's view ‘exactly agrees with our own.’ It is because of these interpretive difficulties that we have not discussed the criticism of Thomae in the text. But however these difficulties are resolved, it is clear that Frege appeals to senses (or modes of presentation) to reply to an objection to a view about identity; and it is clear that Frege is at the same time assuming that the name view is true. 28 Notice that, like the name view and the object view, the mode of determination view has consequences for what the referent of a name that flanks the identity sign is. The object view implies that the referent of a name that flanks the identity sign is its customary referent and, as pointed out in note 22, the name view implies that the referent of a name that flanks the identity sign is the name itself. On the mode of determination view, the referent of a name that flanks the identity sign will be the name's customary mode of determination; for, according to the mode of determination view, an identity statement expresses the thought that the modes of determination associated with the names determine the same object.

29 ‘│—’ is the assertion sign. And, as Frege makes clear in the first volume of The Basic Laws, he eventually replaces ‘≡’ with‘=’ (IX). The reader might be tempted to make something of Frege's use of ‘conceptual content’ rather than ‘content’; however, in the preface to the Begriffsschrift, Frege makes it clear that the conceptual content of a name is just its referent. He says: ‘I have called, in §3, that which solely mattered to me conceptual content’ (IV; original emphases). And, with regard to names, the content that matters to Frege in the Begriffsschrift is the name's referent.

30 Frege assumes a related version of this claim in ‘Sense and Reference.’ He says: ‘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’ rather than saying that the sense is grasped by anyone who merely understands the name itself (27).

31 In ‘Sense and Reference,’ Frege uses ‘a,’ ‘b,’ and ‘c’ as the names of the lines. Since he also uses ‘a= b’ as an identity statement, we've changed the names of the lines to avoid confusion.

32 In the second sentence, Frege does say that a difference can arise only if the two names are associated with distinct modes of presentation. And it might be claimed that his talk of a difference rather than an interesting or substantive difference suggests that he's offering a defense of the object view. But the second sentence appears to be nothing more than a contrapositive of the first sentence; hence, given that he talks of essential sameness in the first sentence, it is natural to read ‘a difference’ in the second sentence as referring to a difference that wouldn't make the cognitive values essentially the same.

33 We have interpreted Frege as saying that sameness of mode of presentation type is both necessary and sufficient for sameness of sign type. This implies that any two exact synonyms are of the same sign type; but it is certainly implausible that, for example, ‘doctor’ and ‘physician’ count as the same sign. Hence it might be thought that a more charitable interpretation would have Frege saying that the individuation conditions of signs include those of objects—that sameness of mode of presentation type and sameness of object type are both required for sameness of sign type. Now in the end nothing that we say depends upon accepting the interpretation in the text over this alternative. But we have interpreted Frege as we do for two reasons. First, he talks of distinguishing ‘a’ from ‘b’ as an object and ‘not as a sign,’ and this suggests that the individuation conditions of objects are not included in those of signs. And second, he talks of individuating ‘a’ from ‘b’ ‘not as a sign (i.e., not by the manner in which it designates something)’; and his use of ‘i.e.’ suggests that to not individuate names as signs just is to not individuate them by their modes of presentation. Of course, neither reason is conclusive; but notice that the alternative interpretation suggested above is not really more charitable to Frege. Granted, if Frege holds that sameness of sign type requires sameness of mode of presentation type as well as sameness of object type, then ‘doctor’ and ‘physician’ turn out to be different signs on his view. But, implausibly, ‘color’ and ‘colour’ also turn out to be different signs; and, if we individuate spoken signs in part by their sounds, dialectical differences in spoken language (for example, the British and American pronunciations of ‘schedule’) will also imply that the relevant signs are different. The alternative interpretation simply trades one set of counterintuitive consequences for another and, hence, we stick with the one that we think best fits the text.

It should also be noted that Frege says: ‘In the case of an actual proper name such as “Aristotle” opinions as to the sense may differ’ (27 n.B); and this might suggest that he thinks that two token names can be of the same sign type even if they are associated with distinct modes of presentation. But it is plausible that, when Frege says that there can be differences in opinion as to the sense attached to a name, he is individuating names as objects rather than as signs. Recall that names can be individuated as objects. Moreover, at the end of the footnote, Frege says that ‘such variations of sense may be tolerated,’ but that they ‘ought not to occur in a perfect language’ (27 n.B). So, even if Frege is individuating ‘Aristotle’ as a name, it's very plausible that his claims about the way signs are individuated qua signs are meant to apply only to a perfect language and that what makes a language in which there are such variations imperfect is (at least in part) that the relevant signs in such a language aren't individuated correctly qua signs.

Finally, since any identity statement occurs in a single language, there is no reason to think that Frege is committed to the implausible claim that two token signs from distinct languages are of the same sign type if they are associated with the same mode of presentation. So the claim about sign individuation should probably be qualified so that it applies only to signs from the same language. For simplicity's sake, we ignore this complication in the text.

34 We do not mean to claim that Frege explicitly held this view when he wrote the Begriffsschrift. Although it is possible that he did explicitly hold it, his conflation of names with the modes of determination associated with them is explained if he was in some way merely implicitly inclined to think that linguistic items are individuated entirely by their semantic properties. Although this seems to be the only way to explain his conflation, the explanation doesn't require that his explicit thoughts on the subject were very clear.

35 Of course, in the case of a name, it might be impossible for everyone to be ignorant of the mode of presentation associated with it. For, if everyone were ignorant of the connection, it might be hard to see how that mode of presentation came to be associated with that name in the first place. But surely it's possible for someone to be ignorant of the connection.

36 In note 33 above, we discussed the possibility that Frege's ‘Sense and Reference’ reply involves the claim that sameness of mode of presentation type as well as sameness of object type is required for sameness of name type, rather than (as we interpret him in the text) the claim that sameness of mode of presentation type is necessary and sufficient for sameness of name type. In the note we gave reasons that favor the interpretation in the text, but we also said that in the end it doesn't matter to our discussion if the alternative interpretation turns out to be correct. If the alternative interpretation is correct, then obviously we will need to retract our claim that, for Frege, sameness of mode of presentation simply amounts to sameness of name. However, even on the alternative interpretation - and, indeed, on any reasonable interpretation- Frege is positing a very close metaphysical connection between which type a name token belongs to and the mode of presentation associated with it. Hence it's still plausible that this led him to think that knowledge of a name token's type (i.e., knowing which name the relevant sign is) implies knowledge of which mode of presentation is associated with it.

37 Many philosophers take the problems about identity raised at the beginning of ‘Sense and Reference’ to be at bottom problems about substitution failures: how can it be that co-referring names aren't always substitutable salva veritate or salva significatione? (See, for example, Salmon, Frege's Puzzle, 11-12 and 79-80.) It is true that, for Frege, the problem that he is raising in ‘Function and Concept’ is about the substitution of co-referring names; but that results from his idiosyncratic view that sentences are names that refer to truth-values, so for him two sentences that have the same truth-value just are co-referring names. And, insofar as Frege is concerned with the problem of substituting co-referring names that aren't sentences, it is because he is concerned with the problem about sentences and wants to show that the relevant sentences have the same truth-value. (See ‘Function and Concept,’ 13-14 and ‘Sense and Reference,’ 50, which are discussed in the text.)

38 For a detailed discussion of Frege's view, in ‘Sense and Reference’ and elsewhere, that sentences refer to truth-values, see Burge, Tyler ‘Frege on Truth,’ in Frege Synthesized: Essays on the Philosophical and Foundational Work of Gottlob Frege, Haaparanta, Leila and Hintikka, Jaakko eds. (Dordrecht: Reidel 1986) 97–154, at 97-123CrossRefGoogle Scholar.

39 We translate ‘für der Erkenntniswert’ as ‘for the cognitive value’ rather than ‘for the purpose of acquiring knowledge.’

40 The final paragraph of ‘Sense and Reference’ is not the only place in which Frege purports to discuss a worry particularly about identity but actually winds up discussing the more general worry from ‘Function and Concept.’ As mentioned in note 27, in the second volume of The Basic Laws, immediately after agreeing with Dedekind that the name view of identity statements is correct, Frege cites Thomae's objection to the object view: namely, that it implies that ⌈α = β⌉ expresses the same triviality as ⌈α = β⌉. However, although Frege has just asserted the name view of identity statements, his reply is not (as one would expect) that the name view avoids the objection that Thomae has raised against the object view so long as names are individuated by their modes of presentation. He does say that the explanation of why Thomae is mistaken is that the names can have different senses, but he goes on to say ‘and that it is precisely the sense of the sentence-besides its referent, its truth-value -that determines its cognitive value’ (§138, 140). Hence Frege clearly uses the fact that the names α and β can have different senses to conclude that the sentences ⌈α = α⌉ and ⌈α = β⌉ can have different senses, despite the fact that their truth-values are the same. So, just as in the final paragraph of ‘Sense and Reference,’ Frege begins by discussing the problems peculiar to the identity sign, but winds up discussing an entirely more general problem: namely, the worry from ‘Function and Concept’ about how two sentences with the same truth-value can differ in cognitive value.

41 The fact that much of ‘Sense and Reference’ is concerned with cases in which an expression fails to have its customary referent might seem to present a problem for our interpretation of the text. After all, as we pointed out in note 22, in the Begriffsschrift Frege says that on the name view a name that flanks the identity sign refers to itself and, hence, doesn't have its customary referent. But if Frege is concerned in ‘Sense and Reference’ with cases in which an expression fails to have its customary referent, and if he still holds the name view there, then why doesn't he discuss the reference of names in identity statements? The answer is that, although Frege does spend much of ‘Sense and Reference’ discussing cases in which an expression fails to have its customary referent, such cases are not his main concern. As stated in the text, his concern is to defend his claim that the referent of a sentence is its truth-value; and he discusses cases in which he thinks an expression fails to have its customary referent only because they constitute potential counterexamples to his claim that the referent of a sentence is its truth-value. In each case, Frege claims that the relevant expression fails to have its customary referent, because this allows him rebut the potential counterexample. That is to say, his claims in ‘Sense and Reference’ about expressions that fail to have their customary referents are made in order to defend his claim about the reference of a sentence. The alleged fact that a name that flanks the identity sign doesn't have its customary referent is a consequence of the name view; but it doesn't serve any purpose in rebutting counterexamples to his claims about the referents of sentences, nor does it present any potential counterexamples to these claims.

42 Thanks to Mark Kalderon for directing our gaze to the forest.

43 In the preface, Frege says: ‘It is my intention, in the near future, as I have indicated elsewhere, to explain how I express the fundamental definitions of arithmetic in my Begriffsschrift, and how I construct proofs from these solely by means of my symbols. For this purpose it will be useful to be able to refer to this lecture so as not to be drawn then into discussions which many might condemn as not directly relevant, but which others might welcome’ (i).