meaning, with the dictionary translation, where “Bedeutung” is given as signification, meaning, standing for, and so on, and (I believe) with Frege’s intention. The passages from Frege’s comments on Schroeder are barely intelligible otherwise.
12. Frege clearly presumes that if a sentence is meaningful, then it is meaningful whether true or false. But if the sentence asserts of any of its components that the component is meaningful, and if the meaning of the sentence depends on its components, the sentence would not be meaningful if false.
13. Geach, Logic Matters, 52.
14. Ibid., 59.
15. Frege, G. (1895) “A critical elucidation of some points in E. Schroeder’s Vorlesungen Über Die Algebra der Logik,” Archiv fur systematische Philosophie, 1895, 433–56, trans. Geach in Geach & Black, 86–106, p. 454, my emphasis. See also “On concept and object,” G&B, 42 ff. “A concept . . . is predicative. On the other hand, a name of an object, a proper name, is quite incapable of being used as a grammatical predicate” (p. 43). We can, of course, say that someone is Alexander the Great. But this involves a different use of the word “is,” that is, the “is” of predication versus the “is” of identity, which I will discuss later.
16. The term is Brandom’s (Brandom, Making it Explicit, 301).
17. There is a dispute about whether Frege’s account of reference implies the standard theory, but I am not concerned here with matters of Fregean exegesis. Evans, The Varieties of Reference chapter 1 is the locus classicus.
18. Aristotle, On Interpretation, 17b1.
19. Aptus natus est praedicari de uno solo. Quine (Word and Object, 96, my emphasis) says “a singular term is one that purports to refer to just one object.”
20. Kretzmann, William of Sherwood’s Introduction to Logic, 110.
21. In Aristotelian semantics, a proposition is a type of sentence which, unlike a question or a command, is capable of truth or falsity. In Fregean semantics, the sentence expresses a proposition, an extra-mental Platonic truthbearer.
22. Traditionally, the proposition is the bearer of truth and falsity. Aristotle distinguishes (On Interpretation 17 a4) a sentence (λόγος, oratio) from a proposition (ἀπόφανσις, propositio) or declarative sentence (λόγος ἀποφαντικός, oratio enuntiativa), for only the proposition is capable of truth and falsity. Thus, a prayer is not a proposition (nor is a question or a command). He dismisses all other types of sentence in order to focus on the proposition, saying that other types of sentence are the domain of rhetoric or poetry. Contemporary philosophers take a different view of the proposition, regarding it not as a type of sentence, but rather as the meaning or thought or “Russellian proposition” expressed by the sentence. Some regard it as a wholly extralinguistic item, which includes as a component the object that the proposition is about, although Russell himself did not seem to have endorsed this. Whenever I use the word, I shall mean an assertoric or declarative sentence, a form of words in which something is propounded, put forward for consideration, and which is thus capable of being true or false, rather than a thought or a meaning. People who don’t like “proposition” can replace it mentally with “statement.”
23. Significare sequitur intelligere.
24. Frege himself acknowledged the problem: “that part of the thought which corresponds to the name ‘Etna’ cannot be Mount Etna itself. . . . For each piece of frozen, solidified lava which is part of Mount Etna would then also be part of the thought that Etna is higher than Vesuvius. But it seems to me absurd that pieces of lava, even pieces of which I had no knowledge, should be parts of my thought” (Frege, “Letter to Jourdain” in Moore, 43). See also Frege’s letter to Russell, Jena 13 November 1904, in Frege, Philosophical and Mathematical Correspondence, 169, where the examplar is Mont Blanc “with its snowfields.”
25. Mill, An Examination of Sir William Hamilton’s Philosophy, 323.
26. This thesis bears a superficial resemblance to the one worked out in Brandom (Making it Explicit, 305–327) and passim. Brandom argues that a reference statement like “The term ‘Leibniz’ refers to Leibniz” can be interpreted as “The one referred to by the term ‘Leibniz’ = Leibniz,” where the indirect description “The one referred to etc.” is anaphorically dependent on some previously occurring token of “Leibniz.” The resemblance is only superficial, in my view. For example, Brandom quotes with apparent approval Chastain’s claim that indefinite descriptions can be straightforwardly referential. See my discussion of this point in chapter 3.
27. This is an old argument. Quine (Methods of Logic, 199) argues that “Parthenon” names the Parthenon and only the Parthenon, whereas “the Parthenon-idea” names the Parthenon-idea. Frege (“On sense and reference,” 31) says that the sentence “The Moon is smaller than the Earth” is not about the idea of the Moon. “If this is what the speaker wanted, he would use the phrase ‘my idea of the Moon’” Earlier than that, Mill (A System of Logic, I.v.i) notes that “fire causes heat” does not mean that my idea of fire causes my idea of heat. “When I mean to assert any thing respecting the ideas, I give them their proper name, I call them ideas: as when I say, that a child’s idea of a battle is unlike the reality, or that the ideas entertained of the Deity have a great effect on the characters of mankind.” In the late thirteenth century, Duns Scotus argued that if “stone” referred to the idea of a stone, then Aristotle’s claim in De anima III “A stone is not in the soul, but the idea of a stone” would be contradictory, because “being in the soul” is first removed from the idea of a stone, which is signified by the name “stone” by the first part of the proposition, “a stone is not in the soul,” and yet in the second part, the same predicate would be attributed to the “same subject” (Duns Scotus On Time and Existence, 31, I have changed the translation from “species” to “idea”).
28. Locke, An Essay Concerning Human Understanding, III. iii. 3.
29. Reid, The Works of Thomas Reid, 389.
30. Sainsbury, “Fregean sense,” 136.
31. It may be objected that in English, as well as in Greek and Latin, a relative may anticipate a pronoun in such a way that the pronoun refers to a preceding or succeeding relative or vice versa. I deal with this objection in chapter 3.
32. Strawson, Individuals, 21.
My first thesis is that co-reference is signified or guaranteed when it is clear from the meaning of two terms that if they have a referent at all, they have a single referent, that is, that if one is true of a thing, the other, if true, is true of the same thing also. Consider pronouns: if the (definite) antecedent refers, the pronoun refers to the same thing. Since we understand this even when the antecedent term is empty (“As soon as the demon smells the odour, it will flee”), it follows that the co-reference is signified without any semantic connection between the terms and some external object. The connection is internal or intralinguistic, and must be determined by some rule of use. There can be co-reference without a co-referent.
I shall argue that the same must be true of proper names and definite descriptions
