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Informative Identities in the Begriffsschrift and ‘On Sense and Reference’

Published online by Cambridge University Press:  01 January 2020

Imogen Dickie
Imogen Dickie*
Affiliation:
University of Toronto, TorontoONM5S 1A2, Canada
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Extract

This paper is about the relationship between Frege's discussions of informative identity statements in the Begriffsschrift and ‘On Sense and Reference’. The question of how these discussions relate to one another has a more-or-less standard answer that goes like this. In the Begriffsschrift Frege proposes a metalinguistic solution to the puzzle about how an identity statement can be informative. He says that what you find out when you discover that, for example, Hesperus is identical with Phosphorus, is that the two names ‘Hesperus’ and ‘Phosphorus’ are names for the same thing. In ‘On Sense and Reference’ Frege rejects this solution on the ground that it treats identity statements as statements about names rather than statements about objects. His new solution is that if ‘a = b’ is potentially informative for co-referring ‘a’ and ‘b’ this is because ‘a’ and ‘b’, though they refer to the same object, are associated with different ways of being presented with the object: finding out that a = b is finding out that the objects presented in these ways are the same.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 38 , Issue 2 , June 2008 , pp. 269 - 287
Copyright
Copyright © The Authors 2008

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References

1 See, for example, Dummett, Michael Frege: Philosophy of Language (London: Duckworth 1973)Google Scholar (hereafter ‘FPL’), 279. In Thau, Michael and Caplan, Ben ‘What's Puzzling Gottlob Frege’ Canadian Journal of Philosophy 31 (2001) 159–200,CrossRefGoogle Scholar Thau and Caplan argue that Frege never abandoned the Begriffsschrift view. I take Heck's response to their paper (Richard Heck ‘Frege on Identity and Identity Statements: A Reply to Thau and Caplan’ Canadian Journal of Philosophy 33 (2003) 83-102) (hereafter ‘Heck “Frege on Identity”’) to provide a decisive refution of their interpretation. See Heck 83, 101 for re-statements of the standard view. This paper is intended as a continuation of the Thau/Caplan-Heck discussion in that it sets out and addresses a problem for the standard interpretation that Heck's paper leaves unconsidered.

2 Frege, Gottlob ‘On Sense and Meaning,’ trans. Max Black in Translations from the Philosophical Writings of Gottlob Frege, ed. Black, Max and Geach, Peter (Oxford: Blackwell 1952) (hereafter ‘Sense and Reference’), 56.Google Scholar

3 Frege says ‘… a = a holds a priori and, according to Kant, is to be labeled analytic….’ For grounds for reading the second of these conditions as ‘is incapable of extending our knowledge’ see Frege, Gottlob The Foundations of Arithmetic, trans. Austin, J.L.. (Oxford: Blackwell 1980)Google Scholar (hereafter ‘Grundlagen’), §88.

4 Gottlob Frege, Begriffsschrift, trans. Bauer-Mengelberg, Stefan in From Frege to Godel: A Source Book in Mathematical Logic ed. Heijenoort, Jean van (Lincoln, NE: Universe. com 2000)Google Scholar (hereafter ‘Begriffsschrift’).

5 Here and throughout I follow Frege in assuming that tokens of the same name occurring in a single context share their content. Compare ‘Sense and Reference’ 58.

6 Kaplan, David ‘Words,’ Proceedings of the Aristotelian Society Supplementary Volume LXIV (1990), 118;Google Scholar May, Robert ‘Frege on Identity Statements’ in Semantic Interfaces: Reference, Anaphora and Aspect, ed. Cecchetto, C. Chierchia, G. and Guasti, M. T. (Stanford: CSLI Publications 2001), 55;Google Scholar Heck ‘Frege on Identity’ 98-100. Heck extends the standard reading, suggesting that Frege's abandonment of the Begriffsschrift view is motivated at least partly by problems associated with whether the view can cope with sentences in which one of the argument places flanking the identity sign is occupied by a variable (87), and partly by the realization that the puzzle about the difference in cognitive value between ‘a = a’ and ‘a = b’ general izes to ‘Fa’ and ‘Fb’ combined with reluctance to extend the metalinguistic view to all cases where substitution of a co-referring term does not preserve cognitive value (100).

7 For illustrative passages see Begriffsschrift, preface 5-6; Grundlagen introduction p. IX, 102-3 (§§90-91); Gottlob Frege, Grundgesetze der Arithmetik vol. 1, excerpted in Black and Geach (1952) (hereafter ‘Grundgesetze’), 118-19, 128.

8 Grundlagen §3, 3

9 Grundlagen §17, 23

10 See Grundlagen §93, 102 for the distinction between ‘logical’ and ‘intuitive’ self-evidence, and see Grundlagen §16, 23, §80, 93 for the same distinction put in different terms.

11 Compare Begriffsschrift, 12: ‘…the contents of two judgments may differ in two ways: either the consequences derivable from the first, when it is combined with certain other judgments, always follow also from the second, when it is combined with these same judgments, and conversely, or this is not the case….Now I call that part of the content that is the same in both the conceptual content’ [Frege's italics].

12 The stipulation that ‘b’ does not occur in γ1, …, γn is required to set aside cases like the transformation of ‘Fa, Gb, therefore ∃x(Fx & Gx)’ into ‘Fb, Gb, therefore ∃x(Fx & Gx)’ and ‘˜Fa, Fb, therefore p’ into ‘˜Fb, Fb, therefore p’.

13 This is the first sentence of the quotation from ‘Sense and Reference’ given on p. 272.

14 The secondary roles are to be the oblique referent of an expression occurring in a ‘that’ context (‘Sense and Reference’, 58-9, 65) and to be what is passed from speaker to hearer in successful communication (‘Sense and Reference’, 59).

15 See Grundgesetze vol. 1 §5 for explicit statement of the claim that steps in a proof are steps between thoughts.

16 Thau and Caplan base their claim that Frege never rejected the Begriffsschrift view partly on this problem: ‘What's Puzzling Gottlob Frege’, 177-8.

17 This formulation is derived from Evans's ‘intuitive criterion of difference’ for the senses of sentences — see Gareth Evans The Varieties of Reference (Oxford: Oxford University Press 1982), 19-20. See Heck, Richard ‘Do Demonstratives have Senses?’ Philosophers’ Imprint 2 (2002), 11,Google Scholar 21 for an example of this kind of criterion at work.

18 See for example Soames, Scott Beyond Rigidity (Oxford: Oxford University Press 2002)CrossRefGoogle Scholar especially ch. 2 and pp. 63-64. Soames is expanding on the arguments against description theories of names in Kripke, Saul Naming and Necessity (Oxford: Blackwell 1972)CrossRefGoogle Scholar, Lecture 2.

19 See his comment on the analogous definition for ‘the number of F's’ at the start of §69: ‘That this definition is correct will perhaps be hardly evident at first.‘

20 See note 14.

21 For a canonical statement of the anti-Fregean side of this debate see Perry, John ‘Frege on Demonstratives’ The Philosophical Review 86 (1977) 474-97.CrossRefGoogle Scholar For a Fregean reply see Evans, Gareth ‘Understanding Demonstratives’ reprinted in Evans's Collected Papers (Oxford: Oxford University Press 1985), 291–321.Google Scholar For a more recent discussion see Heck, Richard,‘The Sense of Communication’ Mind 104 (1995), 79–106.CrossRefGoogle Scholar

22 Compare Grundlagen §3, 3.

23 Thanks to Kevan Edwards, Gurpreet Rattan, David Velleman, and two anonymous referees for this journal for comments on drafts of this paper. Thanks also to audiences at the 2006 congress of the Canadian Philosophical Association, Oxford University, and the University of Canterbury, New Zealand.