The invariance of sense

Journal of Philosophy

Volumn 103, Issue 3, 2006, Pages 111-144

[No Author Info available]

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60950178374     PISSN: 0022362X     EISSN: 19398549     Source Type: Journal    
DOI: 10.5840/jphil2006103336     Document Type: Article

References (32)

1. Burge, "Sinning against Frege, " The Philosophical Review, LXXXVIII (1979): 398-432, at p. 402.
2. Marcus, "Review of Leonard Linsky: Names and Descriptions, " The Philosophical Review, LXXXVII (1978): 497-504, at p. 503. This is not aninterpretation of Frege that Marcus herself endorses; see her remark citedbelow.
3. Noonan, Frege: A Critical Introduction (Cambridge, UK: Polity, 2001), p.179.
4. Forbes, "Indexicals and Intensionality: A Fregean Perspective, "The Philosophical Review, XCVI (1987): 3-31, at p. 5.
5. Perry, "Frege on Demonstratives, " The Philosophical Review, LXXXVI (1977): 474-97, at p. 485.
6. Kripke, "A Puzzle about Belief, " in Avishai Margalit, ed., Meaning and Use (Boston: Reidel, 1979), pp. 239-83 at p. 240.
7. Kripke also attributes this view to Russell. This attribution is closerto correct; Russell held that different speakers may take a given name toabbreviate different descriptions. In "Knowledge by Acquaintance and Knowledge by Description" (in Russell, Mysticism and Logic (New York:Norton, 1929), pp. 209-32), he remarks that "the thought in the mind of aperson using a proper name can generally only be expressed explicitly if wereplace the proper name by a description. Moreover, the description required toexpress the thought will vary for different people, or for the same person atdifferent times. The only thing constant (so long as the name is rightly used)is the object to which the name applies. But so long as this remains constant, the particular description involved usually makes no difference to the truth orfalsehood of the proposition in which the name appears" (p. 216). Russell'sview is rooted in his epistemology; the description by which a speakerabbreviates a proper name characterizes knowledge the speaker has of the objectdenoted. Part of my argument to follow is that it is incorrect to assimilate Frege's views to Russell's, in part because Frege's view of the relation ofsense and knowledge is not directly comparable to Russell's notion of knowledgeby description.
8. This view is most commonly associated with Michael Dummett; see chapterfive of Frege: Philosophy of Language (London: Duckworth, 1973); as he remarksthere "The notion of sense is thus of importance, no so much in giving anaccount of our linguistic practice, but as a means of systematizing it" (p.105).
9. I have in mind here the Chomsky-hierarchy that categorizes languages interms of their (weak) generative capacity. See Noam Chomsky, "Formal Properties of Grammars, " in R.D. Luce, R.R. Bush, and E. Galanter, eds., Handbook of Mathematical Psychology, Volume II (New York: Wiley, 1963), pp.323-418.
10. The remarks in the following paragraphs develop the discussion in Aldo Antonelli and Robert May, "Frege's New Science, " Notre Dame Journal of Formal Logic, XLI (2000): 242-70, in section 2.
11. Put in contemporary parlance, Fregean languages do not contain anynonlogical constants; there can be no schematization in Fregean languages, universality can only be expressed through generalization. This point is due to William Demopoulos in his "Frege, Hilbert, and the Conceptual Structure of Model Theory, " History and Philosophy of Logic, XV (1994): 211-25; see also Antonelli and May, and the discussion in footnote 11.
12. See in particular the discussion in "On Sense and Reference"(1892), translated by Max Black, in Peter Geach and Black, eds., Translationsfrom the Philosophical Writings of Gottlob Frege (Oxford: Blackwell, 1952), pp.62-63;
13. the terminology of "mock thoughts" is to be found in"Logic" (1897), translated by Peter Long and Roger White, in H.Hermes, F. Kambartel, and F. Kaulbach, eds., Posthumous Writings (Chicago:University Press, 1979), pp. 126-51, on p. 130. We turn to the significance ofsuch terms in section VII.
14. "On the Foundations of Geometry II" (1906), translated by Klugein Kluge, ed., On the Foundations of Geometry and Formal Theories of Arithmetic, pp. 49-112, on p. 82. In this passage I have altered the translationof the German zeichen, which Kluge translates as "sign, " to"symbol, " so that it accords with the usage we have established in theprevious section.
15. "The Thought" (1918), translated by Geach and R.H. Stoothof (as"Thoughts") in Geach, ed., Logical Investigations (Oxford: Blackwell, 1977), pp. 1-30, on p. 12. The German is as follows: Es muß alsoeigentlich gefordert werden, daß mit jedem Eigennamen eine einzige Weiseverknüpft sei, wie der, die oder das durch ihn Bezeichnete gegeben sei.Daß diese Forderung erfüllt werde, ist oft unerheblich, aber nichtimmer.
16. While in what follows translations are drawn from the Geach and Stoothofversion, their translation of the ellipsis in the cited passage, which reads"So we must really stipulate that, " does not capture as well Frege'sintention as A. and M. Quinton's translation in Mind, LXV (1956): 289-311, at p.298: "So it must really be demanded that...." The remainder of the Quinton's translation of this passage is however rather convoluted: "asingle way in which whatever is referred to is presented be associated withevery proper name."
17. This and the following passages are drawn from Frege, "The Thought, " p. 12.
18. Frege discussion of this case anticipates aspects of the Paderewskipuzzle introduced by Kripke; see Robert Fiengo and May, De Lingua Belief(Cambridge: MIT, forthcoming), chapters 3 and 4, where the relation of thesecase is explicitly brought out.
19. All quotations from "Logic in Mathematics" (1914), translatedby Long and White, in Hermes, Kambartel, and Kaulbach, eds., Posthumous Writings, pp. 203-50, on p. 209.
20. An early reference in the English commentary on Frege in which this isobserved is Howard Jackson in his "Frege's Ontology, " The Philosophical Review, LXIX (1960): 394-95.
21. Frege, "On Sense and Reference, " p. 59. It is this claim that Russell takes exception to in the Gray's Elegy argument, in which he questionsthe coherence of the notion of reference being presupposed. Russell argument isthat the normal mechanisms of reference, by which it is senses that refer, doesnot work for referring to senses; rather, what we need for this is an abnormalmechanism, in which reference is explicated in some other way than that sensedetermines reference.
22. But what way this is "remains wholly mysterious" according to Russell, the explication "an inextricable tangle, " so much so that thedistinction of sense and reference has been "wrongly conceived" and"the point of view in question must be abandoned" - Russell, "OnDenoting, " Mind, XIV (1905): 479-93, at pp. 487-88.
23. "An Apparent Difficulty in Frege's Ontology, " The Philosophical Review, LXXI (1962): 462-75, at p. 464.
24. This would appear to imply that concept senses, as well as concepts, areunsaturated, and so cannot be objects. One way of understanding this would be totake concept senses as functions from object senses to thoughts, a viewsuggested by Geach in his "Critical Notice: Frege: Philosophy of Languageby Michael Dummett, " Mind, new series, LXXXV (1976): 436-49,
25. Note Frege's emphasis that it is the "only possible means." Oneoften hears it said that an identity criterion for senses can be specified suchthat senses are identical if and only if they can be substituted salvavertitate in oblique contexts. Since in such contexts the customary sense is theindirect reference, given Leibniz's Law, if substitutivity in such contextspreserves truth, then the substitutends have the same customary sense. Note, however, that this condition is not a logical condition; given the mention ofoblique contexts, the conditions cannot be stated within the vocabulary of(pure) logic. In this regard, as an identity criterion on senses it differsfrom, say, Hume's Principle, Frege's criterion for identity of numbers, whichcan be stated in this manner. (This is not to say that Hume's Principle is alogical principle, an issue that has been a matter of some considerable debate;cf. George Boolos, "Is Hume's Principle Analytic, " in Boolos, Logic, Logic, and Logic (Cambridge: Harvard, 1998), pp. 301-14,
26. and Crispin Wright, "Is Hume's Principle Analytic, " Notre Dame Journal of Formal Logic, XL (1999): 6-30. All I am saying is that given that Hume's Principle can be stated using only the resources of pure logic it is acandidate for being a logical principle, something in which a statement thatcannot be so given is not.) It is notable that the identity criterion that Fregehimself proposes does not explicitly give an identity criterion thatpresupposes a language with terms for propositional attitudes, and so, unlikethat based on substitution in oblique contexts, is a logical condition; if it issatisfied, then, Frege says, "what is capable of being judged true orfalse in the contents of A and B is identical, and this alone is of concern tologic, and this is what I call the thought expressed by both A and B."
27. Although Frege distinguishes abstract from concrete objects, both arenevertheless "ordinary" objects, in that they can be determined bymodes of presentation; thus, numerals express senses that have numbers as theirreferences. But what Frege leaves open about senses is whether they too areordinary objects, although perhaps it is just that his answer is overdetermined.If he were to abjure from senses, qua objects, having modes of presentation, then there could be no appeal to the semantics of sense and reference to explainhow we comprehend "the sense of the expression 'A'." But if thisexpression has no sense, and so no reference, then whence the support to startwith for the inference that senses are objects? Yet abjure we might, especiallywhen we consider senses in a more cognitive light. We may think of modes ofpresentation as the cognitive states we enter into upon grasp of a sense, thatcharacterize our cognitive perspectives on objects. But while we haveperspectives on things, we do not on our perspectives of those things; there isa certain absurdity to having perspectives on our perspectives. Observing this, Akeel Bilgrami and Carol Rovane, in their "Mind, Language and the Limits of Inquiry, " in James McGilvery, ed., The Cambridge Companion to Logic (New York: Cambridge, 2005), pp. 181-203, draw out as a corollary that modes ofpresentation are cognitively transparent; we know them, as it were, whole, nopart can be masked from us, (although it may be from our consciousness; cf.footnote 31). We can be short of knowledge of objects, for if we were not wecould not be unaware of identity, that, for instance, that Hesperus is Phosphorus. But how could senses ever be presented to us in such a way that wewould not know immediately of their identity, whether the sense of "A"is the same as the sense of "B"? But if we have no identity puzzlesfor senses because modes of presentation are transparent to us - "The senseof 'A' is the same as the sense of 'B'" would be analytic - then it willalso be the case that someone who believes that Cicero is a Roman, but that Tully is not, is in no way uninformed about her beliefs; it cannot be that shehas contradictory beliefs but just does not realize it. What she is un-(or mis-)informed about is something about the world, not her beliefs. If we are toconclude from these considerations that senses are not objects, or at least notordinary objects, it cannot be, however, at the expense of the objectivity andaccessibility of senses, or at least of the sort of information that senses areintended to carry; we do not want to give up on the reasons that drew Frege toclaim that senses are objects. Arguably, Bilgrami and Rovane maintain, we havethe epistemological wherewithall to make good on this, even if Frege did not.
28. Frege, "Logic, " p. 131.
29. For an illuminating discussion of the role of abstracta in Frege'sthrought see Teri Merrick, "Frege's Distinction between Concepts and Objects: A Descendant of Kant's Distinction between Concepts and Intuitions" (Doctoral dissertation, University of California, Irvine).Merrick makes the point that Frege's commitment is not to abstract objects perse, but rather reflects deeper commitments to scientific theories thatincorporate such objects as aspects of their conceptual and empirical structure.Frege's embrace of abstracta is thus relative to the role they play inscientific explanation.
30. The argument just surveyed adapts an argument presented by Michael Kremerin his "Sense and Meaning: The Origins and Development of the Distinction" (ms., University of Chicago); cf. Section IX. Kremer developshis argument starting with an observation initially due to Dummett, in his paper"Truth" (reprinted in Truth and Other Enigmas (Cambridge: Harvard, 1978), pp. 1-24). Frege maintains that a truth predicate is eliminable becausethe statements "'p' is true" and "The thought that p istrue" express nothing more than what is expressed by "p" itself.This is not so, however, if "p" contains a term whose sense does notdetermine a reference, since then "p", "'p' is true" and"The thought that p is true" do not express the same thought;"p" in this circumstance is neither true nor false, but both "p'is true" and "The thought that p is true" are false. Insofar asthis is an issue about inference, Frege has a ready dodge, in that logicallyperfect languages contain no terms without reference. Kremer, however, sees adifferent problem looming; in languages in which truth is ineliminable as aproperty of thoughts, Frege's conception of judgment, based on a relationbetween thoughts and a designated object, will be jeopardized. (There is much tobe said about this claim, which we leave for another occasion.) Kremer'sresponse, as per the argument in the text, is that terms without reference arealso terms without sense; on this assumption all three of the statements abovereturn to being on par, as being neither true nor false. Kremer then draws outthe consequences that modes of presentation, necessary in order to link thoughtsto what they are about, and hence to facilitate their judgment, are inherently"private, subjective, and can vary from speaker to speaker, " thuscommitting Frege to a psychologism of senses. Frege's remarks on the variance ofsense are to be understood as indicating Frege's acceptance of thischaracteristic of senses. This creates, according to Kremer, a fundamentalunderlying tension in Frege's conception of senses with his claims that they areobjective and omni-accessible: "The idea of a "common store ofthoughts" is threatened when the sense of our words is reduced to theinterpretation placed on them by each individual speaker." Kremer iscorrect in pointing out that this is the consequence of the view he describes;where I think Kremer errs is in holding that Frege held that senses, includingtheir modes of presentation, ever have the characteristic subjective privacy ofideas. There is no tension in Frege's views precisely because of his care indistinguishing senses from ideas.
31. While senses cannot be defined, they can be references (of terms thatoccur in oblique contexts), and this is sufficient, in Fregean terms, toestablish their objectual status. (For discussion of the relation of objectivityand reference, see May, "Frege on Indexicals, " and Wright, Frege's Conception of Numbers as Objects (Aberdeen: University Press, 1983), chapter 1.)Lack of definability, however, may be a bar to a logic of senses; so, for Frege, it is the definability of numbers, qua abstract objects, that brings themwithin the purview of logic. Note that by indefinability we mean lack ofexplicit definition, the only sort of definition that Frege countenances.Although we might be able to give identity criteria for senses, (see section vand footnote 39), this would not be sufficient as a definition, given Frege'srejection in Grundlagen of identity criteria as contextual definitions in theface of the Caesar problem.
32. "On Sense and Reference, " p. 58.