FREGE Michael Beaney
9. Two problems about contexts
Fundamental to Frege’s application of function–argument analysis to language is the idea that the ‘value’ of a sentence is determined by the ‘value’ of its (logically significant) parts. In his early work, Frege called this value ‘content’. With content later split into sense and reference, however, this yields two principles of determination (sometimes also called principles of compositionality):
(PDS) The sense of a sentence is determined by the sense of its (logically signifi cant) parts.
(PDR) The reference of a sentence is determined by the reference of its (logically signifi cant) parts.
These principles have motivated a great deal of work in subsequent philosophy of language, but they are not unproblematic. In this final section we briefly consider two problems.34
The first concerns their application in so-called intensional contexts, that is, in contexts where there are attributions of propositional atti- tudes, such as saying of someone that they believe that p. Consider, for example, the following two sentences:
(GAA) Gottlob believes that Aristotle is Aristotle.
(GAP) Gottlob believes that Aristotle is the author of the Prior Analytics.
‘Aristotle’ and ‘the author of the Prior Analytics’ have the same refer- ence, so by the principle (PDR), (GAA) should have the same reference, that is, truth-value, as (GAP). But (GAA) can clearly be true without (GAP) being true. Frege recognized the problem here and argued that in these cases, the reference of the embedded sentence, that is, what fol- lows the ‘that’, is not its customary or direct reference but its indirect reference, where this is taken as its customary sense.35 In other words,
sense, that is, thought, that the sentence (normally) expresses. This is plausible in itself, for what determines whether (GAP), say, is true is the thought that Gottlob takes to be true (not the truth-value of the embed- ded sentence). The principles of determination can thus be preserved, albeit at the cost of complicating the account of sense and reference. There are further complications when we consider cases of multiply embedded sentences (such as ‘Bertrand hopes that Gottlob believes that Aristotle is Aristotle’); and the issue continues to be debated in philosophy of language today.36
There is a general message suggested here: that what counts as the sense and reference of an expression depends on the context. This mes- sage is reinforced when we consider the problem of indexicality. Indexi- cals are expressions such as ‘I’, ‘you’, ‘here’, ‘there’, ‘now’ and ‘then’, whose reference depends systematically on the context; and they pose a serious problem for Frege’s conception of sense. For if the reference changes, then so too must the sense. Consider the following:
(TS) Today is sunny.
Uttered today, this expresses a different thought from that that would be expressed if uttered tomorrow; so the sense of ‘today’ – as partly determining the thought, in accord with (PDS) – must differ on the two occasions. But then what is it?
Here is one suggestion as to how (TS) might be understood: (DS) Monday 8 November 2010 is sunny.
But it is clearly possible to hold (TS) as true but (DS) as false, and vice versa, in which case they cannot be taken to express the same thought; and the same will apply to any attempt to ‘cash out’ the indexical in terms of a definite description.37 The only response might seem to be
to take the sense of any indexical as used on a given occasion as primi- tive and irreducible. It is clear, however, that Frege allowed that the thought expressed by (TS) uttered today could be expressed on other occasions.38 To express tomorrow what I said today, I would have to
utter:
But how far can this go on? Next Monday, I might say:
(Y7S) The day before the day before the day before the day before the day before the day before yesterday was sunny.
Yet there is obviously a better sentence: (LMS) Last Monday was sunny.
This introduces the concept day of the week, so arguably goes beyond what is expressed in uttering (TS). And if we consider what I would say in a few years’ time, then it seems that I am going to end up using (DS) to express the thought, and we are back with the dilemma. In trying to capture the same thought through time, we seem to have been led to an arguably different thought.
Frege never provided a satisfactory solution to the problem of indexi- cality. As far as he was concerned, this was a problem that affected our use of ordinary language – and once again, was to be avoided in an ideal logical language (in which all indexicality is to be cashed out, as we might put it). Nevertheless, indexicality – and contextuality generally – is a pervasive feature of ordinary language, and the problems cannot be brushed aside if we want to apply Frege’s ideas.39 They do suggest that
the principles of determination and the account of sense and reference need, at the very least, to be qualified in important ways. This task was one of the many things that Frege bequeathed to his successors.
Further Reading
The Frege Reader (1997) contains the four key papers discussed in this chapter, as well as substantial selections from Frege’s three books and other works. For elaboration of the account offered in this chapter, see Beaney’s Frege: Making Sense (1996). The pioneering work on Frege was Dummett’s Frege: Philosophy of Language (1973; 2nd edn, 1981). Many of its claims are now seen as controversial, but the book did much to secure Frege’s place in modern philosophy of language. The four-volume collection of papers edited by Beaney and Reck (2005) contains the most influential papers, on all aspects of Frege’s philosophy, published between 1986 and 2005. Volume 4 is on Frege’s philosophy of thought and language. The recent (but long heralded) Cambridge
Companion to Frege (2010), edited by Potter and Ricketts, contains further papers. Textor’s Frege on Sense and Reference (2011) offers a useful book-length guide to many of the ideas covered in this chapter.
Notes
1 For a detailed chronology of Frege’s life, see Thiel and Beaney, 2005, where fur- ther references to biographical accounts can be found.
2 Although written 12 years after the completion of the Begriffsschrift, the clearest account of this can be found in Frege, 1891.
3 On this, see, for example, Frege’s letter to Marty of 1882, reprinted in Frege, 1997, p. 81.
4 Here, and in what follows, I use modern notation rather than Frege’s own two- dimensional Begriffsschrift. For an explanation of Frege’s symbolism, see App. 2 of Frege, 1997.
5 It should be noted that Frege does not himself use a separate symbol for the existential quantifier, relying on the equivalence, as we now write it, of ‘(x)Fx’ and ‘~(x)~Fx’ (cf. 1879, §12), nor for conjunction, which he defines in terms of conditionality and negation (1879, §7).
6 See, for example, Frege, 1882/1997, pp. 80–1; 1892b/1997, pp. 189–90. 7 See, for example, the papers in Beaney and Reck, 2005, IV, Part 12; Oliver, 2010;
Ricketts, 2010.
8 See esp. Frege, 1884, §§53, 57/1997, pp. 103, 106–7. For further discussion, see Beaney, 2005, §4.
9 Since Frege thinks that the relation between objects and first-level concepts (sub- sumption) is different from, though analogous to, the relation between first-level and second-level concepts, he talks of objects ‘falling under’ first-level concepts and first-level concepts ‘falling within’ second-level concepts; see Frege, 1892b/1997, p. 189. Both relations are different from subordination, which is a relation between concepts of the same level.
10 See, for example, Frege, 1882/1997, p. 82; 1884, §53/1997, p. 103.
11 I have called this ‘interpretive analysis’, which I see as characteristic of the Fregean strand in analytic philosophy. Cf. for example, Beaney, 2007b, 2007c.
12 Frege, 1879, §3/1997, pp. 53–4.
13 In his later work, Frege calls those aspects of meaning that lie outside this logical core ‘shading’ or ‘colouring’ (see, for example, 1892a, p. 31/1997, p. 155; 1892b, p. 196, fn./1997, p. 184, fn. G; cf. 1918, p. 63/1997, pp. 330–1; and esp. 1897, pp. 150–5/1997, pp. 239–44). These aspects have also been called ‘tone’. 14 See, for example, Frege, 1879, §§3, 9. Cf. Beaney, 2007d.
15 By Frege’s ‘early work’, I mean his work up to and including the Grundlagen of 1884, when the notion of conceptual content was operative. From 1891 onwards, this notion is split into the dual notions of sense and reference, as we will shortly see.
16 Frege, 1892a, pp. 25–6/1997, p. 152. Frege does not provide the diagram him- self, but it has been added here for illustration (as in The Frege Reader). 17 Frege, 1879, p. 14/1997, p. 64.
18 Frege, 1892a, p. 26/1997, p. 152. 19 Frege, 1879, p. 15/1997, p. 65.
20 The distinction is first drawn in Frege, 1891, but receives its fullest explanation in Frege, 1892a. The translation of ‘Bedeutung’ has generated enormous contro- versy. In The Frege Reader (Frege, 1997) I left it untranslated, for the reasons I give in §4 of my introduction. But I also say there that my own preference is for ‘reference’, and this is what I use in the present chapter.
21 Frege, 1892a, pp. 26–7/1997, p. 152.
22 It is common to see the indicative (declarative) mood as basic and other moods, such as the imperative and interrogative, as derivative. If so, then the sense of a non-indicative sentence can be taken as the sense of the corresponding indica- tive sentence. For recent discussion of the issues raised here, see, for example, Boisvert and Ludwig, 2006.
23 Cf. Frege, 1891, p. 13/1997, p. 137. Frege gives the example of the function x² = 1 and considers the four identity statements (equations) that result from taking −1, 0, 1 and 2 as arguments: −1 and 1 yield true identity statements, while 0 and 2 yield false identity statements.
24 Cf. ibid. I discuss Frege’s introduction of truth-values as objects in more detail in Beaney, 2007d.
25 A further possibility is to develop Frege’s earlier idea of the ‘circumstance’ or ‘state of affairs’ represented. It may be harder to think what this might be in the case of identity statements (which may be one reason why Frege offered a meta- linguistic construal of their ‘content’ in his early work), but it looks attractive in the case of simple sentences such as ‘Gottlob is human’, and is arguably what Frege needs to fill the gap that opens up between sense and reference. I discuss some of the issues raised here in Beaney, 1996, esp. §8.1.
26 Cf. Frege, 1891, p. 15/1997, p. 139.
27 See Frege, 1969, and in particular his ‘[Comments on Sinn and Bedeutung]’, trans. in Frege, 1997, pp. 172–80; and Frege, 1976, and in particular his letter to Husserl of 24 May 1891, partly trans. in Frege, 1997, pp. 149–50.
28 See Frege, 1976, pp. 96–7; trans. in Frege, 1997, p. 149. 29 Cf. for example, Frege, 1892a, pp. 28, 32–3/1997, pp. 153, 157. 30 See, for example, Frege, 1892a, p. 41/1997, p. 163.
31 Frege, 1892a, p. 27, fn./1997, p. 153, fn. B.
32 See, for example, Kripke, 1980, esp. Lecture 1. See the chapter on Kripke in this volume.
33 See the chapter on Russell in this volume.
34 For a fuller account of these problems, see my introduction to Frege, 1997, pp. 29–35, on which I draw here.
35 See Frege, 1892a, p. 37/1997, p. 160.
37 This has been called ‘the problem of the essential indexical’ (Perry, 1979). It is similar to the problem that arises if we identify the sense of a proper name with the sense of some corresponding definite description, as discussed in the previ- ous section.
38 Cf. Frege, 1918, p. 64/1997, p. 332.
39 For an introduction to these problems, see Beaney 1996, section 7.4, and Textor 2011, pp. 154–70.
Bibliography
Beaney, Michael (1996), Frege: Making Sense. London: Duckworth. —(1997), ‘Introduction’ to Frege, 1997, pp. 1–46.
—(2005), ‘Frege, Russell and Logicism’, in Beaney and Reck, 2005, vol. I, pp. 213–40. —(ed.) (2007a), The Analytic Turn: Analysis in Early Analytic Philosophy and Phenom-
enology. London: Routledge.
—(2007b), ‘Conceptions of Analysis in the Early Analytic and Phenomenological Tra- ditions: Some Comparisons and Relationships’, in Beaney, 2007a, pp. 196–216. —(2007c), ‘Analysis’, in The Stanford Encyclopedia of Philosophy, online at: plato.
stanford.edu/entries/analysis
—(2007d), ‘Frege’s Use of Function-Argument Analysis and his Introduction of Truth- Values as Objects’, in Dirk Greimann (ed.), Essays on Frege’s Conception of Truth, Grazer Philosophische Studien, 75, pp. 93–123.
Beaney, Michael and Reck, Erich H. (eds) (2005), Gottlob Frege: Critical Assessments, 4 vols. London: Routledge.
Boisvert, Daniel and Ludwig, Kirk (2006), ‘Semantics for Nondeclaratives’, in Ernest Lepore and Barry C. Smith (eds), The Oxford Handbook of Philosophy of Lan- guage. Oxford: Oxford University Press, pp. 864–92.
Dummett, Michael (1973), Frege: Philosophy of Language. London: Duckworth; 2nd edn. 1981.
Frege, Gottlob (1879), Begriffsschrift. Halle: L. Nebert; Preface and most of part I (§§1–12) trans. in Frege, 1997, pp. 47–78.
—(1882), ‘Letter to Marty, 29.8.1882’, trans. in Frege, 1997, pp. 79–83.
—(1884), Die Grundlagen der Arithmetik. Breslau: W. Koebner; selections trans. in Frege, 1997, pp. 84–129.
—(1891), ‘Funktion und Begriff’, Jena: H. Pohle; trans. as ‘Function and Concept’ in Frege, 1997, pp. 130–48.
—(1892a), ‘Über Sinn und Bedeutung’. Zeitschrift für Philosophie und philosophische Kritik, 100, 25–50; trans. as ‘On Sinn and Bedeutung’ in Frege, 1997, pp. 151–71. —(1892b), ‘Über Begriff und Gegenstand’. Vierteljahrsschrift für wissenschaftliche
Philosophie, 16, 192–205; trans. as ‘On Concept and Object’ in Frege, 1997, pp. 181–93.
—(1893/1903), Grundgesetze der Arithmetik (vol. I 1893, vol. II 1903). Jena: H. Pohle. Selections trans. in Frege, 1997, pp. 194–223, 258–89.
—(1918), ‘Der Gedanke’. Beiträge zur Philosophie des deutschen Idealismus, 1, 58–77; trans. as ‘Thought’ in Frege, 1997, pp. 325–45.
—(1969), Nachgelassene Schriften, ed. H. Hermes, F. Kambartel and F. Kaulbach. Hamburg: Felix Meiner; trans. as Frege, 1979.
—(1976), Wissenschaftlicher Briefwechsel, ed. G. Gabriel, H. Hermes, F. Kambartel, C. Thiel and A. Veraart. Hamburg: Felix Meiner; abridged and trans. as Frege, 1980.
—(1979), Posthumous Writings (translation of Frege, 1969 by P. Long and R. White). Oxford: Blackwell.
—(1980), Philosophical and Mathematical Correspondence (translation of Frege, 1976, ed. B. McGuinness, trans. H. Kaal). Oxford: Blackwell.
—(1997), The Frege Reader, ed. and with an introduction by M. Beaney. Oxford: Blackwell.
Kripke, Saul (1980), Naming and Necessity. Oxford: Blackwell.
Oliver, Alex (2010), ‘What is a predicate?’ in Potter and Ricketts, 2010, pp. 118–48. Perry, John (1979), ‘The Problem of the Essential Indexical’. Noûs, 13, 3–21. Potter, Michael and Ricketts, Tom (eds) (2010), The Cambridge Companion to Frege.
Cambridge: Cambridge University Press.
Ricketts, Thomas (2010), ‘Concepts, Objects and the Context Principle’, in Potter and Ricketts, 2010, pp. 149–219.
Textor, Mark (2011), Frege on Sense and Reference. London: Routledge.
Thiel, Christian and Beaney, Michael (2005), ‘Frege’s Life and Work: Chronology and Bibliography’, in Beaney and Reck, 2005, vol. I, pp. 23–39.