Abstract
This essay offers a detailed philosophical criticism of Frege’s popular thesis that identity is a relation of names. I consider Frege’s position as articulated both in ‘On Sense and Reference’, and in the Grundgesetze, where he appears to take an objectual view of identity, arguing that in both cases Frege is clearly committed to the proposition that identity is a relation holding between names, on the grounds that two different things can never be identical. A counterexample to Frege’s thesis is considered, and a positive thesis is developed according to which, in contradistinction to the Fregean position, identity is a reflexive, symmetric, and transitive relation holding only between a thing and itself which can be expressed as a relation between names.
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Notes
Gottlob Frege, ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und philosophische Kritik, 100, 1892, p. 25, translated as ‘On Sense and Reference’, in P.T. Geach and Max Black, Translations from the Philosophical Writings of Gottlob Frege (Oxford: Basil Blackwell, 1970), p. 56 (all references to ‘On Sense and Reference’ to this edition and translation).
Ibid. See Frege, Begriffsschrift, Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens [1879], in Begriffsschrift und andere Aufsätze, second edition, edited by Ignacio Angelelli (Hildesheim: Georg Olms Verlagsbuchhandlung, 1964), §§8, 20–21. Compare §8, p. 15; translation by Terrell Ward Bynum in Frege, Conceptual Notation and Related Articles (Oxford: Clarendon Press, 1972), p. 126: ‘Now, let ⊢ (A ≡ B) mean: the symbol A and the symbol B have the same conceptual content, so that we can always replace A by B and vice versa.’
Frege, ‘On Sense and Reference’, p. 78.
Frege, Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet, Band I (Jena: Verlag Hermann Pohle, 1893) §7; in Gottlob Frege, The Basic Laws of Arithmetic: Exposition of the System, translated and edited with an introduction by Montgomery Furth (Berkeley and Los Angeles: University of California Press, 1967), p. 40.
Wittgenstein (1922): “That identity is not a relation between objects is obvious.” 5.5303: “Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing.”
Frege, “On Sense and Reference”, p. 59. Also p. 58: “If words are used in the ordinary way, what one intends to speak of is their reference. It can also happen, however, that one wishes to talk about the words themselves or their senses. This happens, for instance, when the words of another are quoted. One’s own words then first designate the words of the other speaker, and only the latter have their usual reference. We then have signs of signs.”
Ibid., p. 58 note *. See White (1977–78): “…by and large the fragmentary hints we find in Frege do not so much point in the direction of a coherent and sustained reflection on the notion of sense, as much as suggesting that Frege, having established the existence of senses in order to overcome the problems in a theory of meaning he would otherwise be unable to resolve, was content to allude to sense so as to put it to one side for the sake of his main concerns which as far as his reflections on meaning were concerned were almost all bound up with his other notion, the notion of reference.”
Russell (1905). Russell, beginning in 1905, departs significantly from Frege in understanding the meaning of proper names in several respects, including distancing himself finally from the concept of a Fregean Sinn in understanding the meaning of a logically proper name.
Mill (1973): “Proper names are not connotative: they denote the individuals who are called by them; but they do not indicate or imply any attributes as belonging to those individuals. When we name a child by the name of Paul, or a dog by the name Caesar, these names are simply marks used to enable those individuals to be made the subjects of discourse. It may be said, indeed, that we must have had some reason for giving them those names rather than any others; and this is true; but the name, once given, is independent of the reason. A man may have been named John, because that was the name of his father; a town may have been named Dartmouth, because it is situated at the mouth of the Dart. But it is no part of the signification of the word John, that the father of the person so-called bore the same name; nor even of the word Dartmouth, to be situate at the mouth of the Dart. If sand should choke up the mouth of the river, or an earthquake change its course, and remove it to a distance from the town, the name of the town would not necessarily be changed…Proper names are attached to the objects themselves, and are not dependent on the continuance of any attribute of the object.”
Frege, “On Sense and Reference,” p. 58.
Ibid., p. 57: “Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names (“point of intersection of a and b,” “point of intersection of b and c”) likewise indicate the mode of presentation; and hence the statement contains actual knowledge…In our example, accordingly, the reference of the expression “the point of intersection of a and b” and “the point of intersection of b and c” would be the same, but not their senses. The reference of “evening star” would be the same as that of “morning star”, but not the sense”.
The model for these diagrams derives from Frege’s famous explication of his parallel treatment of the meaning of proper names and sentences in his Letter to Edmund Husserl, 1891, in Frege, Philosophical and Mathematical Correspondence, edited by Brian McGuinness, translated by Hans Kaal (Oxford: Basil Blackwell, 1979), p. 96.
Quine (1961). Also Quine, Word and Object (Cambridge: The MIT Press, 1960), especially pp. 144–151; 271–276.
Frege, “On Sense and Reference”, p. 64. Frege quotes the original Latin, “Eadem sunt, quae sibi mutuo substituti possunt, salva veritate”. Frege does not give his source for Leibniz’s famous statement of the identity of indiscernibles and indiscernibility of identicals. The passage appears in Gottfried Wilhelm Leibniz, Mathematische Schriften, edited by C.J. Gerhardt [1850–63] (Hildesheim: Georg Olms Verlag, 1971), 7, p. 372. See also Dummett (1981).
Frege, “On Sense and Reference”, p. 58, note *. See supra note 8.
Frege, “Über Begriff und Gegenstand”, Vierteljahrschrift für wissenschaftliche Philosophie, 16, 1892, pp. 1979–198; translated as, “On Concept and Object,” in Geach and Black, Translations from the Philosophical Writings of Gottlob Frege, pp. 46–47.
The term “‘Fido’-Fido theory of reference” originates with Ryle (1949). I use the expression not merely to designate any theory that reduces meaning to reference, but more specifically to purely formal disquotational referential meaning. As in Ryle, “‘Fido’-Fido” has continued also to be used to characterize a strictly referential theory of belief.
An excellent discussion of the topic appears in Makin (2001), especially pp. 117–126. Makin writes, p. 117: “The slogan ‘sense determines reference’ is by now established as a fundamental and unchallenged truth which most writers on Frege would subscribe to—and I am no exception. But its precise meaning, as I will show, is controversial and in need of careful delineation.” See Dummett, Frege: Philosophy of Language, pp. 93–97, 104–105, 227–229, 241–243, 589–590, 679–680. Also Dummett, The Interpretation of Frege’s Philosophy, especially pp. 95, 157, 245–246, 248–253, 362, 369–370, 441, 447, 461, 480, 549.
Frege, “On Sense and Reference,” pp. 60–61.
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Jacquette, D. Frege on Identity as a Relation of Names. Int Ontology Metaphysics 12, 51–72 (2011). https://doi.org/10.1007/s12133-011-0077-3
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DOI: https://doi.org/10.1007/s12133-011-0077-3