Does our understanding of indexical expressions pose insuperable problems for Frege’s account of sense, reference and the relations between the two?

I. Introduction

In this essay I will consider whether our understanding of indexical terms such as ‘I’, ‘here’ and ‘now’ cause insuperable problems for Frege’s account of ‘sense’ (Sinn) and ‘reference’ (Bedeutung). I will begin by briefly outlining the key aspects of Frege’s account in order to show why indexicals are a problem for Frege, and what his own response to the problem was. This will be followed by a consideration of the constraints to which a genuinely Fregean response to the problem should adhere, and why these are not met by some of the alternative approaches. Finally, I will evaluate a proposal by Wolfgang Künne (1997) that purports to solve this problem in a manner closely matching Frege’s own approach, followed by some closing remarks by way of conclusion. For brevity, I shall restrict myself primarily to a consideration of the first-person pronoun, ‘I’, although much of what follows may also be applied, mutatis mutandis, to other indexicals such as ‘here’ and ‘now’.1

II. The Problem

In Frege’s later works, the notion of ‘conceptual content’ (Frege 1879: 49) gives way to those of Sinn and Bedeutung, or sense and reference, as they are commonly translated (Beaney 1997: 36–46). Under this account, the linguistic meaning of an expression is comprised of precisely two components: (i) an object that is being presented (its referent), and (ii) the mode or method by which the object is presented (its sense). The referent of an individual word or concept expression is typically some object or aspect of the world to which the term is said to ‘refer’. The referent of an entire sentence, or proposition, is its truth value. Frege thus concludes that every proposition refers to one of two objects, which he terms ‘the True’ and ‘the False’ (Frege 1906a: 297). The Fregean sense of a proposition is therefore a ‘mode of presentation’ (Frege 1892: 152) of its truth value, just as the sense of an individual word — a noun, for example — is the method by which the corresponding object is presented.2 Two different terms for the same object, e.g. ‘the person on the left’ and ‘the tall man’, will have the same referent (i.e. the object) but different senses (i.e. modes of presentation), as per a single location on a map that is picked out by two different routes (cf. ibid.). Moreover, Frege held that the sense of a sentence or proposition is determined by the senses of its constituent parts such that if these were replaced with other words possessing a different sense, the overall sense — and therefore the linguistic meaning — of the sentence would change, even if its truth value, i.e. its referent, did not (ibid: 155–7).3

Frege’s concern in developing the above linguistic apparatus was to render the meaning of words objective, as opposed to earlier ‘phenomenalist’ accounts of language which portrayed meaning as a primarily subjective phenomenon (Frege 1897). This has important consequences for Frege’s account of indexicals. Since the linguistic meaning of indexical propositions can vary — compare my utterance of ‘I am hungry’ with your utterance of the same sentence, for example — their sense cannot be determined by the form of words alone, but must be sensitive to some aspect of the context within which they are uttered, such as the identity of the speaker. Frege states that in order to express ‘the same thought’ today and tomorrow, where a ‘thought’ is the sense of some particular proposition, I would have to add a ‘time-specification’ (ibid.); e.g. the word ‘today’ or ‘yesterday’ or the date upon which the proposition was uttered (Frege 1919: 343–4). Consequently, ‘[o]nly a sentence [that is] complete in every respect, expresses a thought’ (ibid.). In his treatment of indexicals within the same essay, Frege states that ‘the knowledge of certain conditions accompanying the utterance […] is needed for us to grasp the thought correctly’ such that ‘[t]he same utterance containing the word “I” in the mouths of different men will express different thoughts’ (op. cit: 332). Thus, only once all of the indexicality has been fully cashed out with respect to time, place and identity can it be said that the following propositions express the same objective thought:

(1)  I am hungry [uttered by KW]

(2)  You are hungry [uttered by someone else about KW]

cf. Newen 1997: 111

Frege’s account of indexicals raises the following question: what exactly is the sense that these sentences express? (1) cannot have the same sense as

(3)  KW is hungry

where I, as a matter of fact, am KW, since I could conceivably that KW is hungry without believing that I am hungry — if I was suffering from amnesia, for example, and had forgotten who I am (cf. Lingens in Stalnaker 1981). As Perry (1979) points out, in order to explain my subsequent behaviour of going out to buy some food, for example, in addition to believing (3) I must also believe that

(4)  I am KW

However, it seems implausible that I do have to believe (4) in order to think that I am hungry since this (1) something I come to believe solely on the basis of my own feelings of hunger, and not through identifying with some particular individual ‘from the outside’, as it were (Newen op. cit.). Furthermore, (3) and (4) fail to offer a reductive analysis of the indexicality of (1), since (4) reintroduces the indexical ‘I’ into the explanans, and is therefore circular.

In order to avoid the above problems, Frege held that ‘everyone is presented to himself in a special and primitive way, in which he is presented to no one else’ (Frege op. cit: 333). This makes the Fregean sense of each first-person indexical expression private and unique to each individual, and therefore inaccessible to anyone else (Perry op. cit: 14–15), thus presenting a quite different problem. On the Fregean view, communication takes place when two or more individuals ‘grasp’ the objective sense of a proposition. However, if the sense of an indexical proposition containing the word ‘I’, e.g. (1), is inaccessible, then how can anyone else possibly understand it? At best, the listener might grasp a different proposition that is sufficiently similar to the original thought to enable them to respond appropriately — (3) perhaps, or ‘the person who said “I am hungry” is hungry’. However, they can no longer be said to have grasped the same thought since, as has already been shown, (1) and (3) have different senses. Moreover, if we (pace Frege) take a similar position concerning temporal indexicals such as ‘now’, ‘today’ and ‘yesterday’, it would be impossible to express one and the same temporally-indexed thought at different times, since each time would have a unique mode of presentation that is inaccessible from within the context of another time (Beaney op. cit: 32). This would lead to a profusion of senses and, since the truth of most propositions is in some respect sensitive to time, an almost total lack of communicability, thus undermining the objectivity of language that Frege sought to establish.

III. Towards a Solution

Despite the above difficulties, it seems that we are able to understand one another’s use of indexicals and express the same thought across time. If Frege’s account of sense and reference is to hold, a more detailed account of the meaning or sense of indexical propositions must therefore be given. Such an account should explain both (a) the way in which the senses of (1), (2) and (3) are similar enough to convey what can be recognised by different individuals as ‘the same thought’, and (b) how (1) differs from (3) such that it explains KW’s behaviour in a way that (3) cannot. Furthermore, if the account is to be a Fregean one then it must some satisfy some additional constraints arising from Frege’s account of sense and reference as follows:

1. 1.Such an account should explain precisely what the sense of indexical terms (‘I’, ‘now’, and so on) is, since according to Frege, only the senses of words and not objects can contribute to the sense of a proposition (Frege 1969: 203f in Künne op. cit: 54).4 This rules out treating indexicals as devices of ‘pure reference’ that introduce an object into the truth conditions of a sentence but do not have any sense in their own right (e.g. Wettstein 1979 and Marti 1995). Such accounts cannot properly be classed as Fregean since they reject the applicability of Frege’s notion of sense to indexical expressions, but rather are representative of the so-called New Theory of Reference in the style of Kripke and J. S. Mill’s accounts of proper names (ibid.).
   

2. 2.The sense of any indexical expression should be objective such that it (or some appropriately derived aspect of it) can be grasped by others in order that genuine communication may take place. This is arguably true of John Perry’s (op. cit.) account in which different individuals are said to hold the same belief in different ways, by virtue of being in different ‘belief states’ (ibid.); e.g. in the indexical and non-indexical cases (1) and (3). However, the definition and individuation of such states is itself problematic and lacks independent justification in the philosophy of mind, making this an unattractive solution.
   

3. 3.In order to meet the tests that Frege lays down for sameness of sense (Frege 1906b: 299; Beaney 2005: 35), any reductive analysis of indexical terms should be intersubstitutable for the original salva veritate5 such that it would be immediately apparent to any competent language user who understood both that they have the same truth value.6 In possible worlds based accounts, such as Stalnaker (1981), the content of an indexical proposition such as ‘It is now 5 o’clock’ may differ between speakers who already know which possible world they are in (i.e. they know what time it is) and those who don’t, since only the latter — Stalnaker’s ‘diagonal proposition’ (ibid: 138–9) — will range across possible worlds (Newen op. cit: 110). It is therefore unclear whether the truth of one proposition can be determined from the other as is required in order for them to have the same sense. However, even if this were to be the case, Stalnaker’s account also suffers from the difficulty that it requires first-person propositions like (1) to range across all possible referents, picking out the particular possible world in which KW is hungry. As described above, this is implausible since I do not have to believe that I am any particular person in order to believe (1), let alone to doubt which possible world I inhabit (ibid: 111).
   

As has already been established, indexical expressions are unusual in that their linguistic meaning varies systematically with the context of utterance. Their Fregean sense — if indeed they have any — must therefore incorporate some salient aspect of this context whilst retaining an underlying structure or form that can be understood and ‘tracked’ (through time, for example) by substituting the appropriate token-reflexive terms (‘today’, ‘yesterday’, etc.). Any attempt to simply replacing the indexical element with some proper name or definite description will fail on the basis that there are circumstance in which the name or description can misidentify the referent (ibid: 113; Künne, op. cit: 54); e.g. Perry’s (op. cit.) supermarket example, or the amnesiac Lingens in Stalnaker (op. cit.). Even the definite description ‘the thinker of this thought’ has a plausible if somewhat surprising counterexample in Newen’s (op. cit: 115) case of the schizophrenic whose thoughts are not always presented to her as her own.7 Nevertheless, the unique relation between the way in which a first-person thoughts is presented  (its sense) and the thinker (its object) forms the basis for the Fregean account of the indexical ‘I’ by Wolfgang Künne (op. cit.) that I shall be considering throughout the remainder of this essay.

IV. Ego-Modes of Presentation

Central to Künne’s account is his notion of an ego-mode of presentation. This is a Fregean sense, symbolised by α, that is both ‘simple’, i.e. not analysable in terms of other, more primitive senses, and which meets the following condition for a given subject, y:

(EMP)   ⃞(∀x)(∀y)(x is presented to y by α → x = y)

Künne, op. cit: 55

In other words, an ego-mode of presentation is a primitive mode of presentation whose object (its referent) is necessarily the same as its subject (i.e. the individual thinker or speaker). Thus, the sense of the word ‘I’ for subject y is defined as the ego-mode of presentation in which the referent of the indexical is necessarily identical to y herself, and so private and unique to that individual as per Frege’s specification. This forms the basis for Künne’s account of indexical belief, according to which the situation outlined in proposition (1) may be restated from a third-person perspective as:

(1*)    (∃α)(KW = the object presented by α &
α is an ego-mode of presentation &
‘α is hungry’ is the content of one of KW’s beliefs)

cf. ibid: 61

This may be differentiated from the more straightforward logical form of (3) on the basis that it involves a distinct mode of presentation, or sense, denoted by α. This sense is none other than the ego-mode of presentation that is contributed by the indexical ‘I’ and by which KW and KW alone can refer to himself, as defined above. Moreover, since the propositional content of the belief ascribed to KW (‘α is hungry’) neither names nor describes any particular individual, it is immune to counterexamples arising from misidentification, since the identity of the subject and object is built right into the definition of an ego-mode of presentation. Furthermore, by defining the indexical ‘I’ in terms of the ‘special and primitive’ mode of presentation by which an individual is presented to himself and no other, it is no longer necessary that the subject believe that he is in fact KW in order to explain the behaviour that results from his belief.8 This addresses Perry’s point concerning the explanatory inadequacy of (3) as an analysis of (1), as well as accounting for the difference between (1) and (3) in terms of the content of the beliefs in question.

Having establishing what is common to all ‘I’ beliefs, namely that they involve an ego-mode of presentation (ibid: 57), Künne’s account must also explain how thoughts like (1) can be communicated, since the relevant mode of presentation is ‘logically private’ to each individual (ibid.) and so cannot be grasped or expressed by a third party. According to Künne, indexical thoughts such as (1) are ‘propositionally opaque’ (ibid: 59) in that they do not fully reveal their propositional content and are thus, in the strict sense, of the word, inaccessible. However, the fact that the thought expressed by (1) employs an ego-mode of presentation can be grasped by a third party by virtue of its containing the first-person pronoun, ‘I’. Similarly, the predicate, ‘… is hungry’ may be grasped from the overall form of the sentence. All that remains, therefore, in order to yield an understanding of all three conjuncts of (1*) is the fact that KW is the object being presented, as is revealed by the context of utterance, since it is KW who is expressing his belief.9 Thus, it is true that the thought grasped by the listener, (1*), is different to the sense of the original utterance, (1), by virtue of its having a different logical form. However, since (1*) varies enables all of the important content of (1) — namely the object of presentation (KW), the type of mode of presentation (the ego-mode), the predicate (being hungry) and a belief ascription — this does not necessarily stand in the way of communication. On the contrary, in understanding the indexical proposition, (1), the listener is effectively able to ‘collapse’ the indexicality, revealing the sense of the corresponding third-person statement, (3). Moreover, the listener is able to identify which first-person proposition was being uttered, which is arguably all that is required for successful communication (Künne, op. cit: 63–4).

To return to the constraints that I laid down in section III, Künne’s account grants indexical expressions as having a Fregean sense involving, in the case of ‘I’, an ego-mode of presentation described by (EMP). It also makes the content of such propositions sufficiently objective that they can — in part, at least — be grasped by any third person whilst at the same time retaining Frege’s notion of a ‘special and primitive’ mode of presentation that is particular to each speaker. Whether the proposition that is communicated, e.g. (1*), has the same sense as the original, i.e. (1), however, is questionable since the first-person indexical, ‘I’, cannot be presented in precisely the same manner (i.e. as an ego-mode of presentation) to the listener as was expressed by the original speaker, even though they may be able grasp its logical form, or type. However, far from being a disadvantage, this is exactly what we would expect from an account of the first-person indexical. What a listener would understand in hearing (1) is not the same as what they themselves express by the words ‘I am hungry’, but rather that ‘KW is hungry’ (or perhaps ‘KW believes that he is hungry’), and so in a strictly formal sense they do understand a different proposition to the one originally uttered. Indeed, Frege himself admits as much in his discussion of the word ‘I’ (Frege 1919: 332), but this is now backed up with a detailed account of the sensitivity of first-person propositions to their context in terms of ego-modes of presentation and the logical structure of (1*). So, whilst (1*) and (3) are not intersubstitutable salva vertitate, neither should we expect them to be. It is sufficient that any competent speaker who understands both (1) and (1*), including the indexical nature of the ego-mode of presentation, is able to immediately infer the truth of one from the truth of the other, and vice-versa, and so cannot hold one to be true and the other false without contradiction. Künne’s analysis of the sense of the indexical ‘I’ therefore meets Frege’s crucial test for sameness of sense.

One possible problem for Künne’s account is the fact that, according to (EMP), the Fregean sense of a first-person proposition uttered by subject s is conditional on the existence of s (Künne, op. cit: 55). This might be thought to undermine the objectivity of such senses, since the resulting thoughts would literally not exist in the absence of the thinker. However, as Künne (ibid.) himself points out, Frege’s account only requires that the sense of a proposition can be grasped by a thinker independently of their thinking it; i.e. that it is not a subjective ‘idea’ in the mind of the agent. The fact that the sense of an indexical proposition cannot exist in the absence of the individual whose ego-modes of presentation it involves does not show that it is subjective, but rather emphasises the point that the sense of a proposition depends upon the existence the objects to which it refers, just as with any other non-indexical expression.

V. Conclusion

Künne’s account shows how indexical terms such as ‘I’, ‘now’, here’, etc. can have both an objective sense and a determinate reference in a given context whilst also contributing to the sense of the sentences that contain them in a systematic and communicable fashion.10 The plausibility of his account hangs on whether it is possible to make sense of Frege’s notion of a ‘special and primitive’ mode of presentation by which each of us is presented to ourselves and no-one else in a way that does not simply beg the question. Nevertheless, if we grant the existence of such ‘ego-modes’ of presentation, and are willing to let go of the assumption that communication requires both speaker and listener to grasp precisely the same proposition (ibid: 63), then our understanding of indexicals need not present any insurmountable problems for Frege’s account of sense and reference.

——————

Bibliography

Beaney, Michael (ed.) 1997: The Frege Reader. Malden, MA: Blackwell Publishing.

Frege, Gottlob 1879: ‘Begriffsschrift’. In The Frege Reader, M. Beaney (ed.), pp. 47–78.

—————  1892: ‘On Sinn and Bedeutung’. In The Frege Reader, M. Beaney (ed.), pp. 151–71.

—————  1897: ‘Logic’. In The Frege Reader, M. Beaney (ed.), pp. 227–50.

—————  1906a: ‘Introduction to Logic’. In The Frege Reader, M. Beaney (ed.),
pp. 293–8.

—————  1906b: ‘A Brief Survey of My Logical Doctrines’. In The Frege Reader, M. Beaney (ed.), pp. 299–300.

—————  1906c: ‘Letters to Husserl, 1906’. In The Frege Reader, M. Beaney (ed.), pp. 301–7.

—————  1919: ‘Thought’ (Der Gedanke). In The Frege Reader, M. Beaney (ed.), pp. 325–45.

—————  1969: Nachgelassene Schriften. In Frege: Posthumous Writings, B. McGuinness (ed.). Oxford: Basil Blackwell.

Künne, Wolfgang 1997: ‘First Person Propositions: A Fregean Account’. In Direct Reference, Indexicality, and Propositional Attitudes. W. Künne, A. Newen, M. Anduschus (eds.), Stanford: CSLI Publications, pp. 49–67.

Marti, Genoveva 1995: ‘The Essence of Genuine Reference’. Journal of Philosophical Logic, 24, pp. 275–89.

Newen, Albert 1997: ‘The Logic of Indexical Thoughts and the Metaphysics of the “Self”’. In Direct Reference, Indexicality, and Propositional Attitudes. W. Künne, A. Newen, M. Anduschus (eds.), Stanford: CSLI Publications, pp. 105–31.

Perry, John 1979: ‘The Problem of the Essential Indexical’. Noûs, 13, pp. 3–21.

Stalnaker, Robert C. 1981: ‘Indexical Belief’’. Synthese, 49, pp. 129–51.

Wettstein, Howard K. 1979: ‘Indexical Reference and Propositional Content’. Philosophical Studies, 36, pp. 91–100.