1 Geach, P. T.Reference and Generality (Cornell University Press, Ithaca, 1962), p. 112.
2 For a record of the change in definition see first Reference and Generality, pp. 124ft., then ‘Referring Expressions Again', in Logic Matters (Blackwell, Oxford, 1972), pp. 97–8, then ‘Back-Reference', Philosophia5 (1975), p. 194. The change turns out to be important.
3 Klima, E. ‘Negation in English', in Fodor, J. and Katz, J. (eds.) The Structure of Language (Prentice Hall, Englewood Cliffs, 1964), p. 297.
4 Tarski, A. ‘The Concept of Truth in Formalized Languages', in Logic, Semantics and Metamathematics (Clarendon, Oxford, 1956).
5 My attribution of this theory to Frege rests upon Dummett's. See Dummett, M.A.E.Frege (Duckworth, London, 1973) ch.2 and pp. 516-7. I disagree with Dummett by holding that the Tarskian approach is not just a notational variant of Frege's.
Fregean treatments of quantifiers may be found, for example, in Mates, B.Elementary Logic (Oxford University Press, New York, 1965), pp. 54,Keenan, E. L. 'Quantifier Structures in English', Foundations of Language 7 (1971), p. 262 and passim, and throughout Geach's writings.
6 Dummett, Frege, p. 405.
7 β is a name assumed not to occur already in the sentence. It is convenient to define the relation of extension holding between language so that, as a limiting case, each language extends itself. We define truth not just for English but all the members of a family of languages which extend the stock of English singular terms.
8 See e.g. Marcus, R. B. ‘Interpreting Quantification’, Inquiry 51 (1962), pp. 252–259. For an excellent discussion of substitutional quantification see S. Kripke's ‘Is there a problem about Substitutional Quantification?’ in Evans, G. and McDowell, J.H. (eds.) Truth and Meaning (Clarendon, Oxford, 1975) pp. 325–419.
9 Now that this heuristic purpose has been discharged, I shall in later pages collapse the two principles into something along the more familiar lines of: A sentence of the form ‘Something' is true iff, upon some extension of the language, there is a substitution instance of the form which is true.
10 It is interesting to note that some of the delicacy of substitutional quantification into opaque contexts can be retained by Fregean quantifiers despite the ontological burden — that is to say, despite the fact that we are given licence to consider, for every object, a substitution instance involving reference to it. However, once we are dealing with opacities, we must interpret an object's satisfying a complex predicate A(x) in terms of the truth of some (potential) singular sentence of the form A(t) in which refers to it, and not the truth of any such singular sentence.
11 For cogent statements of this criticism, see Dummett, Frege pp. 3–7, pp. 194ff.
12 I particularly have in mind operators like ‘It is certain that', ‘John believes that'. l disagree with Wallace, J.'s paper ‘Belief and Satisfaction', Nous, 6 (1972), p. 85, in which the converse, Tarskian, direction of explanation is defended.
13 This naturalness has certainly struck Quine; see the accqunt in The Roots of Reference (Open Court, La Salle, illinois, 1973), pp. 93–5, of the child's understanding the satisfaction by an object of a complex predicate in terms of the substitution of singular terms.
14 Those who are interested in the strengths and weaknesses of Fregean truth theory for quantifiers would benefit from reading Baldwin, T.'s paper, 'Quantification, Modality and Indirect Speech', in Blackburn, S. (ed.), Meaning, Reference and Modality (Cambridge University Press, Cambridge, 1975). Baldwin dispenses with the idea of enlarging the singular terms of the language by exploiting the machinery independently needed for dealing with sentences containing demonstratives.
15 See, for example, the truth conditions for the quantifiers given throughout Reference and Generality, and also the discussion in ‘Quantification Theory and Objects of Reference', Logic Matters, pp. 141ff. It is true that it is not always possible to tell whether Geach has in mind purely substitutional or Fregean truth theories.
16 Quine, W.V.O.Mathematical Logic (Harvard University Press, Cambridge, 1965), p. 70.
17 In allowing unrestricted forward and backward ‘pronominalization’ this simple grammar is quite unrealistic, but the tricky syntactical question of demarcating where ‘pronominalization’ is allowed and where obligatory really does not affect the semantical issues I am dealing with.
18 I consider the significance of the departure from homophony below.
19 I discuss the merits of the ‘going proxy for’ idea below.
20 I do not introduce quantifier phrases with relative clauses until section 5.
21 See, for example, the discussions in Lakoff, G. ‘Linguistics and Natural logic', in Davidson, D. and Harman, G. H. (eds.), Semantics of Natural Languages (D. Reidel, Dordrecht, 1972) p. 633, and Bach, E. ‘Nouns and Noun Phrases', in E. Bach and Harms, R.T. (eds.), Universals in Linguistic Theory (Holt Rinehart and Winston, New York, 1968).
22 Reference and Generality, p. 128. The same argument is used many times; see 'Ryle on Namely-Riders’ Logic Matters pp. 89–90, ‘Referring Expressions Again', Logic Matters p. 98 and p. 101.
23 On the first and second occasions mentioned in footnote 22.
24 The argument with reflexive pronouns occurs in Reference and Generality, p. 132.
25 A similar point is found at many places in Geach's writings. See, for example, 'Logical Procedures and the Identity of Expressions', Logic Matters, p. 112, 'Names and Identity', in Guttenplan, S. (ed.), Mind and Language (Clarendon Press, Oxford, 1975), pp. 139-40.
26 This point is made in Dummett's Frege, p. 14, and, with explicit reference to Geach's treatment of pronouns, by B.H. Partee, ‘Opacity, Co-reference and Pronouns’ in D. Davidson and G.H. Harman (eds.), Semantics of Natural Language, p. 436.
27 Reference and Generality, p. 132.
28 Reference and Generality, p. 188.
29 Reference and Generality, p. 186.
30 Partee, B. H. ‘Deletion and Variable Binding', in Keenan, E. L. (ed.), formal Semantics of a Natural Language (Cambridge University Press, Cambridge, 1975).
31 Hints of this argument are to be found on p. 29 of Partee's paper ‘Deletion and Variable Binding'.
32 H.N. Castaneda, ‘ “He” : a study in the logic of self-consciousness', Ratio 8 (1966), p. 130, and many other papers.
33 This proposal is essentially made in Anscombe, G.E.M.'s paper ‘The First Person', in Guttenplan, S. (ed.), Mind and Language (Clarendon, Oxford, 1975), p. 47. See also Kuno, Susumu ‘Pronouns, Reference and Direct Discourse', Linguistic Inquiry 3 (1972).
34 For an example of confusion on this point see e.g. Wallace's paper ‘Belief and Satisfaction', op. cit. Wallace symbolizes a teleological principle as follows:
It is important to notice that this principle makes essential use of universal quantification into the argument place made available by the relational sense of belief. The reader may if he wishes give notional formulations … but I think he will find any such principles … distinctly implausible the reason being that it appears impossible to capture notionally the idea that Nelson believes of himself that he has the ability to perform the contemplated action.
35 A consideration first stated explicitly in J. Wallace, ‘On the Frame of Reference', in Davidson and Harman, op. cit., p. 237. See also Davidson, D. ‘In Defense of Convention T', in Leblanc, H. (ed.), Truth, Syntax and Modality (North Holland, Amsterdam, 1973), p. 83, and S. Kripke, op. cit., p. 356.
36 It would be an interesting exercise for the reader to attempt to construct a strictly homophonic theory for the simple ‘brace’ notation for co-referentiality introduced above, or for that fragment of English with the devices ‘the former' and ‘the latter'.
37 It is in this way that I would like to account for the fact, made much of by Kripke (see ‘Naming and Necessity’ in Davidson and Harman op. cit.) that if A uses the proper name β with the intention to refer to whoever B was referring to when he used the name β, then the referent of β on A's lips will be the same as on B's. I do not wish to deal with it by so extending (and weakening) the concept of 'epistemological contact’ that one is in such contact with an object x if one has simply come into contact with someone who uses a name to refer to x.
38 In order to accommodate this simple logical relation between A's remark and B's, we must use the apparatus of co-referentiality we have been considering, and must not suppose that B's reference is fixed by the description ‘the item A referred to by his use of the token “John” ‘.
39 Not just expressions like ‘the bastard’ and ‘the fool’ as seems to be suggested by Jackendoff, R.S. on p. 110 of Semantic Interpretation in a Generative Grammar (MIT Press, Cambridge Mass., 1972).
40 I borrow the notion of a description's fixing the reference of a singular term from Kripke, op. cit.
41 See section 4 (D) and section 7.
42 I follow the example of Wexler, K.Culicover, P.and Hamburger, H. in calling the converse of the ‘in construction with’ relation, ‘governs'. See Learning Theoretic Foundations of Linguistic Universals, Social Sciences Working Paper No. 60, University of California at Irvine, 1974, p. 42. I am grateful to Mr. Geoffrey Pullum for the reference to this and other relevant literature in Linguistics.
43 There is a range of transformations - passivization, conjunction reduction, Neg-placement, amongst them- which are only ‘meaning preserving’ when they apply to singular sentences. (See, for example, Partee, B.H. ‘Negation Conjunction and Quantifiers: syntax vs. semantics', Foundations of language 6 (1970), pp. 153–165). This strongly suggests to me that the best course is to restrict such transformations to singular sentences, and to allow quantifiers insertion to take place at any stage in the transformational cycle. If Fregean truth conditions are given for the quantifiers, this will enable us to give the meaning of any sentence affected by these transformations in terms of the equivalence of meaning between transformed and untransformed singular sentences. This is simply an extension of the strategy we have adopted for singular pronouns.
44 It was this example which showed that the relevant relation is ‘in construction with’ rather than Langacker's notion of ‘command', for ‘Fido’ does command 'him'. I am very grateful to Deidre Wilson for pointing this out to me, and for suggesting that the relevant relation might be ‘in construction with'.
45 See e.g. Reinhart, T. ‘Syntax and Coreference', Papers from the Fifth Annual Meeting of the North Eastern Linguistic Society (Harvard University, 1974), p. 92, and Culicover, P.W. ‘A Constraint on Coreferentiality', Foundations of Language 14 (1976), p. 109.
46 ‘Quine's Syntactical Insights', Logic Matters, p. 118.
47 Reference and Generality, pp. 125 and 126.
48 Harman op. cit. p. 45.
49 A quantifier is existential in force iff, if a sentence of the form A(Q +Common Noun + Relative Clause), in which Q is the quantifier with maximum scope, is true, then A('Some’ + Common Noun + Relative Clause), with ‘Some’ as the quantifier with maximum scope, is also true. ‘Any’ and ‘No’ are the most important quantifiers which do not have existential force; ‘many', ‘few', ‘most', 'all’ and each of the numerical quantifiers has existential force (as used in English).
50 ‘Back-Reference', op. cit., p. 204.
51 This sentence certainly does present difficulties for Geach, but actually belongs with the sentences like ‘Most men who own a donkey beat it,' discussed under d) below. However, Geach's remarks, if appropriate at all, belong at this point, since his ‘two-quantifier’ solution obviously does not deal with the general problem presented by the sentences we shall consider under d).
52 ‘Referring Expressions Again', Logic Matters, p. 100. It is worth pointing out to those who might otherwise be misled that Geach's views on the treatment of pronouns in such sentences have undergone a complete change. In 1963 ('Referring Expressions Again’) the suggestion made by L. Cohen, ('Geach on Referring Expressions — A Rejoinder', Analysis 23 (1962-3), pp. 10–12) that such pronouns should be treated as pronouns of laziness was rejected with a certain amount of brusqueness. In ‘Back-Reference', op. cit. (1975), p. 195, without a word of acknowledgement, Geach makes the same proposal himself. The pronoun-containing sentence for which Cohen proposed a ‘pronoun of laziness’ account was:
The only man who ever stole a book from Snead eventually made a lot money by selling it.
The sentence for which Geach proposes a ‘pronoun of laziness’ account is
The youngest man who brought a girlfriend to the party kissed her.
I do not myself favour the laziness account, but agree with Cohen that some other account than the bound-variable one must be given.
53 Geach is not alone in proposing a ‘two-quantifier’ solution to these and related difficulties; it is also to be found in N. W .Tennant's contribution to his joint paper with J.E.J.Aitham, ‘Sortal Quantification', in E.L.Keenan (ed,) op. cit. pp. 46–60. (See especially examples (4) and (6) on pp. 53–4). Tennant's claim is that adopting a ‘sortal logic’ (apparently a binary structure for quantified sentences of natural languages, enables him ‘to provide many English sentences with more congruous logical forms than they would receive in the classical predicate calculus'. Insofar as this claim concerns sentences which are problematical because of the occurrence of E-type pronouns, it is entirely spurious. No essential use is made of the binary structures in dealing with these pronouns; the ad hoc introduction of an additional quantifier is a manoeuvre available to those working within the unary structures of the classical predicate calculus.
54 It should be pointed out that the difficulty presented for the ‘pronouns as variables’ view by sentences like these was mentioned in two important papers by Karttunen, Lauri: ‘Pronouns and Variables', in Papers from the Fifth Regional Meeting of the Chicago Linguistic Society (Department of Linguistics, University of Chicago, Chicago, 1969), and ‘Definite Descriptions and Crossing Co-Reference’ Foundations of Language 7 (1971). See especially footnote 12 of the latter paper where Karttunen writes: ‘Thus he (Geach) completely overlooks the fact demonstrated above that pronouns are sometimes used in a way which is not possible With variables in the more restricted syntax of the predicate calculus.'
55 The fact that we consider pairs of sentences rather than a single sentence is a reflection of the fact that I regard these quantifiers as binary in form. But the current point does not depend upon that; we could impose a unary structure in the normal way, in which case the substitution instance would be
If John owns some sheep then he vaccinates them in the spring,
a sentence of the form considered under a) above.
56 This is implicitly conceded by Geach in the reply (19) given to B in an imaginary dialogue in ‘Back-Reference', p. 199.
57 Harman, op. cit., p. 45
58 Geach makes a similar appeal to intuition in ‘Referring Expressions Again’ (Logic Matters, p. 100). See the sentence: ‘All the same the relation of the dangling pronoun ‘it’ to its antecedent ‘a book’ is pretty clearly the same as (1) as it is in (10)'.
59 See e.g. the discussion in Reference and Generality, pp. 6ff. and in ‘BackReference', pp. 203–4.
60 Reference and Generality, p. 126. I have changed the number of the example to agree with our ordering in this and subsequent quotations.
61 For denotation clauses of this character see e.g. M.A.E. Dummett ‘What is a Theory of Meaning?', in Guttenplan (ed.) op. cit., p.110-111, and Burge, T. ‘Truth and Singular Terms', Nous 8 (1974), pp. 309–325.
62 Reference and Generality, p. 52.
63 ‘Quine's Syntactical Insights', in Logic Matters, p. 118.
64 ‘Logical Procedures and the Identity of Expressions', in Logic Matters, p. 11.
65 I use the concept ‘talking about’ in a way quite different from the concept 'referring to'. One talks about an item x in uttering a sentence S which contains the predicate F in such a way that 5 entails that something is F, iff, in uttering S, one is expressing a belief about x to the effect that it is F. Thus one may be talking about something even though one manifestly refuses to let one's audience know which item it is that one is talking about, and this is inconsistent with my, and I think any decent, concept of (speaker's) reference.
66 This is ignored by C. Chastain ('Reference and Context', unpublished mimeo, due to appear in a future volume of the Minnesota Studies in the Philosophy of Science) who invokes the concept of reference to give the truth conditions of sentences containing expressions like ‘A man', at least partly ‘because of the possibility of subsequent E-type pronouns. For reasons mentioned in fn 65 I would also reject Kripke's suggestion (made in the John locke lectures for 1973) that succeeding pronouns should be dealt with by invoking the concept of speakers’ reference in connexion with sentences containing expressions like’ A man'; Kripke quite rightly insists upon leaving their truth conditions unchanged. Neither proposal seems necessary.
67 Incidentally, this shows that Geach's two sentences (16) and (17) are not contradictories because they can both be false; it is not possible to use a sentence containing an E-type pronoun to form the full contradictory of another sentence containing and E-type pronoun, because the mere use of an E-type pronoun carries with it a commitment to the existence of a referent. E-type pronouns are like definite descriptions which insist upon widest scope.
68 This is why the change Geach has made in the concept of ‘pronoun of laziness’ does matter. The original idea — of an expression ‘eliminable in paraphrase by a repetition of its antecedent’ — ‘might correspond to some underlying syntactic reality, whereas with the later addition ‘ … or by a repetitious phrase somehow reconstructible out of its antecedent’, the possibility of such a correspondence seems to be ruled out.
69 It was comforting to read the recent paper by Hankamer, Jorge and Sag, Ivan 'Deep and Surface Anaphora', in Linguistic Inquiry 7 (1976), pp. 391–428. In it, they propose as generally applicable a distinction between anaphoric processes which corresponds to the distinction I have made in the case of pronouns. In their terminology, I am proposing that E-type pronouns are deep anaphors, and pronouns of laziness are surface anaphors. By their tests, which include an ambiguity test similar to that used in the text, deep anaphors are certainly what E-type pronouns turn out to be. See also O. Dahl, ‘On So-Called Sloppy Identity', Synthese26 (1973), pp. 81–112.
70 To guard against confusion it is worth distinguishing the binary structure here adopted from the binary structure suggested by Geach for the ‘just one man' quantifier, and criticized above. The break in Geach's binary structure was to come at the point marked by ‘and’ in the sentence
Just one man opened the box and he went home
and there is no evidence whatever that’ Just one’ sentences are ill-formed unless they have two such constituents. The binary structure I am suggesting for all quantifiers would discern in the initial conjunct into the two constituent general terms ‘man’ and ‘opened the box', and there is evidence that we need both of these constituents to have a well-formed sentence, though when we wish, in English, to approximate the effect of unrestricted quantification, the first constituent is the universal predicate ‘thing’ or 'object'.
71 The Appendix is to be published in the next issue of the Canadian journal of Philosophy (Vol. VII, No. 4).
72 This is essentially the account given by Quine, in Word and Object (M.I.T. Press, Cambridge, 1960), pp. 110–114, and Roots of Reference, pp. 89–92.
73 By McCawley, J.D. in ‘Where Do Noun Phrases Come From?', in Jacobs, R.A. and Rosenbaum, P.S. (eds.), Readings in English Transformational Grammar (Ginn, WalthamMass., 1970), pp. 176-7.
74 That such sentences pose a problem for the ‘pronouns as variables’ position was clearly indicated by Harman (op. cit., pp. 41–3).
75 Harman considers a sentence of this kind, namely:’ A boy who was fooling them kissed many girls that loved him’, and claims that it seems ‘roughly equivalent to'
A boy who was fooling many girls that loved him kissed and was fooling many girls that loved him.
(Harman, op. cit., pp. 42–3). Notice here the lengths to which one must go to produce a reading which depends upon the occurrence of E-type pronouns without actually acknowledging them. Essentially Harman treats the pronoun 'them’ in the original sentence as a pronoun of laziness, but this yields only
A boy who was fooling many girls that loved him kissed many girls that loved him,
which does not entail that he was fooling all the girls he kissed (nor, in fact, that he was fooling any of them). So, mysteriously, instead of ‘kissed', the sentence's predicate somehow becomes ‘kissed and was fooling'. It is no wonder Harman ruefully observes that ‘it is not at all obvious what transformations would be used’ to get away from his deep structure to the original sentence. Anyway, Harman's ruse does not work generally, as can be seen from the nonequivalence of:
A boy who was fooling them kissed exactly two girls that loved him A boy who was fooling exactly two girls that loved him kissed and was fooling exactly two girls that loved him.
76 Truth and well-formedness cannot be simultaneously and interdependently defined, on pain of ill-formed sentences being presented to the semantic theory for evaluation. In order to avoid this objection, presented to me by Barry Taylor, we should regard the notion of affirmative embedding being defined over a fragment of English that does not contain E-type pronouns, and for which truth and well-formedness are independently defined. Then the grammatical rule extending the fragment to allow for E-type pronouns will be understood as relating to contexts certified in the smaller fragment as being of a type in which one sentence is affirmatively embedded in relation to another. The semantical theory for the larger language will differ from that for the smaller only in containing a single additional clause for the evaluation of E-type pronouns.
77 See, for example, J.D. McCawley, ‘A Program for Logic', in Davidson and Harman, op. cit, especially p. 530, and Keenan, E. ‘On Semantically Based Grammar', Linguistic Inquiry 3 (1972).
78 See Dummett, Frege, pp. 12–14.
79 The point of the clause ‘and there is no larger sentence frame in Σ which has σ as a constituent and which does not have σ’ as a constituent’ is to ensure that the description which fixes the reference of the E-type pronoun has as wide a scope as does not include the sentence containing its quantifier antecedent. This will secure the referential rigidity which we observed these pronouns to display. At the same time, the scope of the description is not the whole sentence; so we do not end up with the inaccurate result that a sentence like
Either John does not own a donkey or he keeps it very quiet
is true iff
The donkey which John owns is such that either
John owns no donkey or he keeps it very quiet.
(and thus false if John owns no donkey).
80 I would like to thank the following for reading the paper and offering comments and encouragement: M. K. Davies, G. H. Harman, P. F. Strawson, B. Taylor, D. Wiggins, D. Wilson and M. J. Woods.