Frege on indexicals

Philosophical Review

Volumn 115, Issue 4, 2006, Pages 487-516

  May, Robert ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

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EID: 77950024647     PISSN: 00318108     EISSN: 15581470     Source Type: Journal    
DOI: 10.1215/00318108-2006-011     Document Type: Article

References (49)

1. Most notably by Tyler Burge in "Sinning against Frege", Philosophical Review 88 (1979):398-432
2. John Perry in "Frege on Demonstratives", Philosophical Review 86 (1977):494-97, reprinted with appendix in John Perry, The Problem of the Essential Indexical and Other Essays (New York: Oxford University Press, 1993); citations are to the reprint.
3. When we say that sense uniquely deter mines reference, we mean that each sense determines one and only one reference; we do not mean to imply that each reference is determined by one and only one sense.
4. Of the indexicals Frege discusses, I will focus primarily on the pronominal, (that is, the personal pronouns), leaving aside for the most part temporal indexicals. Demonstratives will also be discussed; even though Frege does not explicitly mention them, much of what he says otherwise about indexicals holds for demonstratives too. In deference to this textual point, I will speak throughout of indexicals and demonstratives, meaning only to distinguish cases.
5. Burge, "Sinning against Frege, 405. Burge (and others) take the variability of sense to be general; sense may vary even if reference is held constant across contexts. On this view, the senses of proper names can be as variable as the senses of indexicals and demonstratives. But this is as unfaithful a reading of Frege on proper names as I will argue here it is for indexicals and demonstratives; see Robert May "The Invariance of Sense", Journal of Philosophy 102 (2006):111-44.
6. Gottlob Frege, "On Sense and Reference", in Translations from the Philosophical Writings of Gottlob Frege, ed. Peter Geach and Max Black (Oxford: Basil Blackwell, 1952), 57. 6. There is something of an analogy, although rather loose, to be drawn here with Russell's distinction of knowledge by acquaintance and knowledge by description: a reference would be present just in case we are acquainted with sense-data of it; otherwise, it would have to be presented, that is, described.
7. Note that for Frege there can be no "crisscrossed" languages in which there are proper names with demonstrative-like senses or demonstratives with name-like senses. This is because the type of an expression is defined by the type of its sense; if there are two types of senses, then there are two types of expressions corresponding to each sort of sense regardless of their particular outer linguistic form.
8. That is, "he" is standardly used to refer to a third party; note that its use is not precluded if the third party also happens to be the first or second party to a discussion. Well known are exotic cases in which, say, the addressee is referred to by "he" when additionally present, perhaps via picture or a reflection in a mirror, as a third party. Reference to the addressee would be indirect, and unless the speaker intends some sort of irony, would occur when the identity of the parties is unbeknownst to the speaker.
9. What we have said thus far is not dissimilar from the view developed by John Perry in "Frege on Demonstratives." In Perry's terminology, we have identified Fregean senses with his notion of role. Perry argues at length against a number of aspects of what he considers Frege's view of demonstratives, including that their senses are given by the senses of associated descriptions and that there are incommunicable senses. Perry's arguments are perfectly good against these positions; it is just that these are not positions that Frege held (see discussion in note 34). Perry does purport to give one argument against identifying roles with Fregean thought contents, but it is just to assert the argument we are presently discussing; that is, that role can remain constant while reference, and hence truth-value, can vary. What Perry does not recognize, I am arguing, is that this is not incompatible with Frege's view of senses as thought contents.
10. Gottlob Frege, The Basic Laws of Arithmetic [Grundgesetze der Arithmetik], trans. Montgomery Furth (Berkeley: University of California Press, 1967).
11. We must be careful in our usage here. Sentences containing indexicals or demonstratives only ever express complete thoughts. It is not as if there is some other entity, an incomplete thought, that exists prior to supplementation; it is just that we must take the supplementation into account in order to recognize what complete thought is expressed. We might hold, nevertheless, that there are incomplete thoughts, but these would be of a different character. They would be thoughts that contain senses that have modes of presentation but nonetheless fail to have a reference, and hence can be neither true nor false. Such thoughts are not judgeable thoughts; Frege labels them "mock" thoughts. In contrast, indexical and demonstrative thoughts are judgeable thoughts; they may be true or false since the senses of indexicals and demonstratives can be associated with references, via supplementation. The presence of indexical and demonstratives is in no way a "defect" of language in the sense that nonreferential terms are; the latter mark a fundamental breakdown in the relation of sense and reference that the former does not. Nevertheless, the presence of indexicals and demonstratives in a language does render it inappropriate for the codification of reasoning, that is, for logic, but for different reasons than empty names (or vague predicates, for yet even different reasons); see note 49.
12. Gottlob Frege, "Logic", in Posthumous Writings, ed. Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach (Chicago: University of Chicago Press, 1979), 135.
13. Gottlob Frege, "Introduction to Logic", in Posthumous Writings, 191. To emphasize: it is the object itself that is inessential to thought-content. This holds universally of thoughts; what does not is whether the thought-contents include modes of presentation, information sufficient in itself to obtain a reference.
14. Frege, "On Sense and Reference", 64.
15. Frege, "Introduction to Logic", 187.
16. Frege, "Logic", 135.
17. Presupposing a exists; see note 11.
18. Gottlob Frege, The Basic Laws of Arithmetic, 14. Frege makes the remarks quoted in this paragraph in the midst of an extended argument against the truth-relativism he perceived to be inherently embedded in psychologistic logic, for which he took the observation that sentences containing indexicals or demonstratives could vary in truth-value to be no argument. Rather, as noted, for Frege it is thoughts that have truth-values, and they do so invariantly. See May, "The Invariance of Sense."
19. It is this observation that lies at the heart of the dispute Frege had with Hilbert, at least from Frege's side; see the discussion in Aldo Antonelli and Robert May "Frege's New Science", Notre Dame Journal of Formal Logic 41 (2000):242-70.
20. Confusion on this is found notably in Perry's "Frege on Demonstratives." So, it is not "what Frege has in mind" that "to understand a demonstrative, is to be able to supply a sense for it on each occasion, which determines as reference the value the demonstrative has on that occasion" (15).
21. Gottlob Frege, Grundgesetze der Arithmetik, vol. 2, sec. 97, in The Frege Reader, ed. Michael Beaney (Oxford: Blackwell, 1997).
22. The distinction in perspective we are alluding to bears a resemblance to what Christopher Peacocke, in "Demonstrative Thought and Psychological Explanation", Synthese 49 (1981):187-217, appears to have in mind when he distinguishes between sense tokens and types, elaborating views of Gareth Evans in "Understanding Demonstratives", reprinted in Gareth Evans, Collected Papers (Oxford: Oxford University Press, 1985). There are, however, significant differences in our conceptions. According to Peacocke, it is only qua token that senses are invariably associated with references. "A token", Peacocke says, "can be regarded as obtained by indexing a type with an object" ("Demonstrative Thought and Psychological Explanation", 189), so that sense-tokens can be reckoned as pairings of sense-types and the objects those types are about. With an indexical or demonstrative, this pairing is given by specifying a reference in context for their unique, invariant sense, senses that place requirements on possible indexings. Every use of "I", for instance, may express a distinct sense-token in virtue of being associated with a distinct reference, but all of these tokens are of the same sense-type; there is only a difference in index. Token thoughts are compositions of token senses. It is token thoughts, on Peacocke's view, that people think when they think Fregean thoughts. But such token thoughts, containing as they do objectual content (the indexed object), might be thought suspect candidates for being Fregean thoughts. Perry, in The Problem of the Essential Indexical and Other Essays, 29, makes essentially this argument, directed specifically toward Evans, and he is right to do so. Peacocke is also not unaware of it; his defense is that his theory is Fregean de facto, if not de jure, since token thoughts, he argues, can play the roles-being simultaneously the objects of belief and the bearers of truth-that Frege requires of thoughts. An obvious way to get closer to a de jure theory would be to take the indexing not materially but as a formal annotation, indicating the existence of a relation between the sense and a reference. This would at least have the virtue of not effacing the sense/reference distinction since thoughts would contain no objectual content. But this would not make them any less suspect candidates for Fregean thoughts. If indices are formal marks, then there must be a formal way of representing senses, and hence thoughts. But this is something Frege denies. The only way, according to Frege, that we can represent thoughts is via the sentences that express them; otherwise, logic, which shows how true thoughts follow from other true thoughts, could be undertaken directly on the representation of thoughts rather than on their linguistic manifestations. (Not at issue here is whether senses can be named-they can be, for instance by "the sense of α", α schematic for expressions of the language-only whether they can be represent Ed.) To say that senses have indices, either material or formal, is to imbue them one way or the other with characteristics Frege denies they have.
23. Gottlob Frege, "Thoughts", in Logical Investigations, ed. P. T. Geach (Oxford: Basil Blackwell, 1977), 1-30. Frege's other explicit discussion of indexicals and demonstratives is found in Frege, "Logic", 134-35. As in "The Thought", his overall point is to establish the objectivity of thoughts, even of the thoughts expressed by indexicals and demonstratives, in opposition to the subjectivity of ideas. This fragment, dated to 1897, presages much of what Frege discusses in "The Thought", at times in almost the same wording.
24. My thoughts in this section have been strongly influenced by Daniel Vest's excellent, insightful discussion of the Lauben argument in his "Who's Gustav Lauben? Frege on Singular Terms and Private Reference" (unpublished manuscript, University of California, Irvine, 2003).
25. Frege, "The Thought", 11.
26. Note that Perry's example in "Frege on Demonstratives" of Heimson and Hume is an elaboration of this aspect of the Lauben argument in terms of two parties rather than three.
27. Languages for Frege consist of signs, bi-unique pairings of senses and linguistic forms; consequently, no language can contain homonyms. There can be some slack allowed on this requirement, however, just so long as the language is not called upon to serve as the métier for reasoning, in which case it must be strictly enforced. This is because for Frege a proof shows that a particular true thought follows from other true thoughts by rule-governed manipulations of the linguistic forms inhabited by the thoughts. This procedure would not be reliable, however, if there were more than one thought lurking in any given form, for how would we know which thought it is that has been proven? See Aldo Antonelli and Robert May, "Frege's New Science", Notre Dame Journal of Formal Logic 41 (2000):242-70, especially sec. 2, for discussion of Frege's conception of language.
28. Frege, "The Thought", 12.
29. Ibid., 17.
30. This observation is due to Vest, "Who's Gustav Lauben?"
31. Frege, "The Thought", 13.
32. Frege ends the Lauben argument with a footnote in which he acknowledges that there is no nondemonstrative description that properly reveals the sense of "I." Frege puts it that there is no way to "put a thought in the hands of my readers with the request that they should examine it from all sides" other than "wrapped up in a perceptible linguistic form." But, the way language describes, its "pictorial aspect", Frege calls it, is improper for the task; senses are not linguistically describable- essentially so, if you will-and so one "fights against language", in the hope of making clear, or elucidating, thoughts. Frege's elucidation in the case of the first-person pronoun is just a way of describing the context-independent invariances, yet allowing for variation in reference with use of the pronoun by different speakers.
33. As opposed to ideas.
34. Note that I am taking exception to a commonly held interpretation of this passage on which Frege is read as endorsing private senses for the first-person pronoun when used in thinking about oneself, but holding that because of the exigencies of communication it is necessary to take the sense in spoken language as that of a closely associated definite description. Perry, in "Frege on Demonstratives", is well known for taking this position. On Perry's view, Frege holds this position as a partial patch for "the failure to find a suitable description for the value of the demonstrative, whose sense would complete the sense of the sentence in just the right way. If the sense we are looking for is private and incommunicable, it is no wonder the search was in vain" (19). Perry argues, however, that there can be no senses like this; the reason is that others can take me in the same way as I take myself personally, and so have the same sense of me as I have of myself. My personal, private way of being aware of myself, my mode of presentation, may be as tall, dark, and handsome; certainly others could take me this way as well, even if I was unaware they were doing so. The alternative is that I am presented to myself, as it were, by direct conscious awareness of myself-I present myself simply as me, unmediated by any presentation of me, so that in my private thoughts I would directly refer to myself. But although essentially private, this would be in effect to deny that there are modes of presentation, at least in any sense with which Frege would be familiar. What is queer, however, about Perry's dialectic as an argument against Frege's view is that he gives an argument that Frege would wholeheartedly endorse against a position that is hardly Frege's to begin with. Frege would have agreed with Perry in rejecting that there are private, incommunicable senses "which would be the natural sense to associate with 'I' if it happen to be used, not merely to communicate with others, but think about oneself" (18).
35. Bertrand Russell, in Human Knowledge: Its Scope and Limits (London: George Allen and Unwin, 1948), groups indexicals and demonstratives under the moniker "egocentric" terms. About such terms, Russell observes that they denote "a different object on each occasion of use: what is constant is not the object denoted, but its relation to the particular use of the word. Whenever the word is used, the person using it is attending to something, and the word indicates this something" (107).
36. It is inadvertent shifts of this nature without the possibility of such knowledge that gives rise to "phone-booth"-puzzles of the sort brought to light by Mark Richard in "Direct Reference and Ascriptions of Belief", Journal of Philosophical Logic 12 (1983):425-52. See discussion in Robert Fiengo and Robert May, Indices and Identity (Cambridge, MA: MIT Press, 1994), sec. 1.2.
37. Notice that the general effect we are considering obtains in all linguistic contexts, indirect as well as direct; compare "Leo Peter believes I am smart", uttered by Lauben and "Leo Peter believes he is smart", uttered by Lingens. This is not surprising, given that such beliefs are de re, as discussed below, so here too sense can shift so long as reference is known to remain the same. In general, if the Lauben "test" is passed/failed by pairs of expressions in direct contexts, it will be passed/failed regardless of the linguistic context in which they occur.
38. For discussion of the sense invariance of proper names, see May, "The Invariance of Sense."
39. Perry's case in "Frege on Demonstratives" (12-13) of the aircraft carrier Enterprise, demonstrated first with only its bow observable and then again with only its stern on view, is another case of the same sort.
40. Robert May, "Frege on Identity Statements", in Semantic Interfaces: Reference, Anaphora, and Aspect, ed. Carlo Cecchetto, Gennaro Chierchia, and Maria Teresa Guasti (Stanford: CSLI Publications, 2001), 1-50.
41. Thus, knowing that a reference is a present reference does not depend upon anyone being able to supply a description of the way in which the reference is present; accordingly, there is no reason to think that speakers have to be able to declare why they think things look the same or different.
42. An up shot of this discussion is that present reference is not to be identified with the demonstratum. There may be any number of present references corresponding to a single demonstratum, and it is additional knowledge to know that various present references are the same object. Herein lies the difference between a Fregean theory of demonstratives and a direct reference theory, a point emphasized by Richard Heck in his excellent "Do Demonstratives Have Senses?" Philosophers' Imprint 2 (2002):1-33. Heck presents a view of demonstratives similar to that developed here, although he is more reticent about whether what we have identified as the senses of indexicals and demonstratives, what he calls their standing meaning, deserves that status since the work sense does with proper names is accomplished otherwise. Roughly, Heck's view is that knowing the thought expressed by a sentence is tantamount to understanding that sentence; but knowing the standing meaning without the supplementation of what we have called the present reference is not sufficient for understanding, and so cannot be the sense expressed. Although I find the view of understanding and communication on which Heck bases his view independently attractive (see the discussion in Robert Fiengo and Robert May, De Lingua Belief [Cambridge, MA: MIT Press, 2006]), for the reasons presented in the text, I see the implications of indexicals and demonstratives for the doctrine of sense and reference somewhat differently than Heck.
43. I take it that the notion of present reference is what James Higginbotham has in mind in his "Competence with Demonstratives", Philosophical Perspectives 16 (2002):1-16, when he speaks of "Fregean elements" of indexicals and demonstratives that "are not senses; however, they may involve objects intrinsically, and they may be perceptual rather than linguistic" (13).
44. At this point, Frege's view, as we are recounting it, can be contrasted with Peacocke's in "Demonstrative Thought"; the differences are particularly clear with the first person. On Peacocke's reconstruction, Frege held that there are first-person thoughts that contain private, incommunicable senses as constituents, but, and here is Peacocke's innovation, when the exigencies of communication impose themselves, rather than employing such senses, which we do when thinking of ourselves, we refer to them, just as we refer to an expression's customary sense in an oblique context. When we do so, given Peacocke's notion of token senses, reference is to an object, the speaker, under a way of thinking about that object, "that type of way of thinking of something under which any person can think only of himself, and under which no one else can think of him" (190), a sense "which can be a constituent of [his], and no one else's thoughts" (191). We have already voiced our hesitancy to claiming Frege's advocacy of private thoughts, as well as to his advocacy of thoughts with objectual content, Peacocke's token thoughts. To this we can add a further hesitancy. On Peacocke's view, the mode of presentation is internal to the sense, so that all token senses of "I" present their references in the same particular way, as the holder of a private sense. But the point is just the opposite-the mode of presentation, the way the reference is present-is external to sense. Consequently, though the mode of presentation may be private, it is not required to be so; it is not even required to be the same for the speaker and hearer, as we have seen. Unlike Peacocke, on our view, the references of indexicals and demonstratives are never senses of anything.
45. Although I have been brief, bear in mind that these sorts of considerations are not anything peculiar to Frege's or to Fregean theories per se; an account of the circumstances under which an object can be recognized as a reference or demonstratum of an indexical or demonstrative, and so be present or salient in the context of utterance, will be applicable to any theory of indexicals and demonstratives.
46. On Frege's theory, a belief attribution is true only if an agent believes a particular thought; "Max believes Sirius twinkles at night" is true only if Max believes the thought expressed by "Sirius twinkles at night" that contains the sense of "Sirius." But suppose that Max doesn't believe this thought-perhaps he has not grasped the sense of "Sirius" and does not have this proper name in his vocabulary-but yet is willing to assert "That star twinkles at night", with the demonstrative referring to Sirius. The attribution nevertheless still seems appropriate, as do others, such as "Max believes my favorite star twinkles at night", where it is contextually obvious that Sirius is the speaker's favorite star. (See David Kaplan's notion of pseudo-de re attributions.) It is not entirely clear what Frege would say about this circumstance, although he would most likely trace the source of the difficulty to a mismatch in the languages of the speaker and agent. As with other linguistic mismatches, a weaker criterion could be employed, one that only requires that the speaker and the agent have thoughts about the same thing, that is, the criterion that would apply if the attribution had been "Max believes that star twinkles at night."
47. Our remarks here are completely general; if there is cognitive access to reference in a direct context, then there is access at any degree of indirection-cognitive access to reference is an hereditary property of the infinite sequence of senses. Suppose that a speaker has grasped a sense of degree n ≥ 1; its reference will be an indirect sense of degree n-1. This is determined by linguistic rule. But this indirect sense will itself have been grasped by the speaker, for it will be the sense expressed at one degree less embedding. A finite number of iterations of this procedure, for any given indirect sense, will ultimately lead back sequentially to the corresponding customary sense, that is, the sense of degree 0, a sense whose reference is not fixed by linguistic rule. Thus, if we grant that a speaker can grasp an indirect sense of any degree (and how could we not?), then it follows that for an indirect sense of any degree, there will be a path back to the customary sense. (Of course, this is moot if there is not an infinite hierarchy of senses, as suggested by Michael Dummett in Frege: Philosophy of Language, 2nd ed. [Cambridge, MA: Harvard University Press, 1981], and Terence Parsons in "Frege's Hierarchies of Indirect Sense and the Paradox of Analysis", in Midwest Studies in Philosophy, vol. 6 of The Foundations of Analytic Philosophy, ed. Peter A. French, Theodore Edward Uehling Jr., and Howard K. Wettstein [Minneapolis: University of Minnesota Press, 1981], 37-57.)
48. On Higginbotham's view in "Competence with Demonstratives", language use is divided into a setting-up phase and a saying-things phase. Setting up involves establishing a perspective for reference, where this may be set either by meaning, for proper names, or by a rule of use, for indexicals and demonstratives. Higginbotham's distinctions roughly correlate with the Fregean distinctions of thought grasped/judgment and constraining/presenting senses.
49. A language of pure logic, in fact, could not contain indexicals and demonstratives. If they did, the problem would arise as to how we could know that "it" refers to a number in "It is greater than seven" rather than Julius Caesar. Within the confines of logic itself there would be no way to state this restriction-it is nothing about logic (or arithmetic) that would limit the reference of indexicals and demonstratives. Because of this, languages with such terms would not be compatible with logicism.