An Underspecified Preface

In: Pragmatics, Truth and Underspecification
Ken Turner
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Laurence Horn
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An Underspecified Preface

Very general remarks may be helpful,

and are not always untrue.

It is no doubt perilous to make them.

But that cannot be helped.

Warnock 1958: 52

I was relying upon a reader

who would be ready to meet me half-way—

who does not begrudge a pinch of salt.

Frege 1984: 193

Better to leave matters a little semantically

underdeterminate … than make the language impractical

to use or impossible to learn.

Atlas 2005: 16

The philosophy of language is an old subject, and since 1879 it has been a great one. There is room in it for many books. This is another one. But if each of several books on the philosophy of language, or, indeed, on semantics and/or pragmatics, is concerned, at least in its early pages, with the elements of the subject, then space must be found in the latest for some context and, perhaps, an apology or two.1 Such is the purpose for which the present few paragraphs have been set aside.

Let us begin at the start of the Fregean Era. From 1879 quantifier/variable and argument/function structures (slowly, and through the intellectual filters of others who often neglected to recognise their source) became constituents of logical and philosophical thinking and they (again, slowly) dissolved the inhibiting restraints of Aristotelian and Stoic reasoning. The new ‘system’ was the first modern logical language, with the universal quantifier, the material conditional, negation and identity as the primitive symbols—with modus ponens and an implicit rule of substitution as the inference rules—and the existential quantifier, conjunction and disjunction as the derived symbols. The crucial innovation was to recognise that universally quantified statements were not semantically related to names and other nominal expressions but were, instead, composed from two functions, joined by a propositional connective, and this move enabled the representation of multiple generality and constituted a huge conceptual advance in formal inference.

The coarse-grained notion of undifferentiated content was in time replaced, largely as a result of problems having to do with the informativeness of identity statements, by a distinction between sense and reference. This distinction was accompanied by the notion of force, which was to receive a thorough examination at the hands of certain Oxford ordinary language philosophers, and the notion of tone (or ‘colouring’), which was developed, later, by certain other Oxford ordinary language philosophers as part of the work of attempting to design, with a clever and natural exploitation of the Kantian categories of the understanding, a conversational logic. So, although the seeds were planted by Frege at the University of Jena, the nascent green shoots of contemporary pragmatics most vigorously appeared in and around Corpus Christi and St. John’s Colleges in Oxford (and later at the University of California Berkeley).

The sense/reference distinction eased the problem of identity (think Morning Star and Evening Star; Alice Cooper/Vincent Furnier; John Wayne/Marion Robert Morrison; Lewis Carroll/Charles Dodgson, etc.) but introduced other difficulties to do with the precise nature of sense: (a) its location, in an abstract and timeless and unchanging ‘third realm’ (somewhere beyond the first, the physical, and the second, the mental) didn’t help to convince logicians and philosophers that it was a serviceable tool and (b) ‘grasping’ a sense, from somewhere presumably in the second realm, was always a vague and questionable action.

The timelessness of the inhabitants of the third realm calls to mind certain modern preoccupations having to do with indexicality and other contextually dependent expressions. The issue would seem to be this. On the one hand there is a ‘content’ that fails to be truth-conditional. These cases require that the contextually dependent items must be expanded and made explicit—‘cashed out’ in some of the more modern idioms—so that the context-sensitivity is expunged. The assumption is that all context-sensitivity can be severed, and this assumption can be challenged (think ‘the essential indexical’; cf. Perry 1979). On the other hand there is a ‘content’ that is more than truth-conditional. The original 1879 revolutionary was later to say, probably in 1897, ‘The distinction between what is part of the thought expressed in a sentence and what only gets attached to the thought is of the greatest importance for logic’ (Frege 1979: 141; emphasis added), and a bit later, in 1918, ‘conversational suggestions make no difference to the thought’ (Frege 1977: 9), thus setting part of the agenda for more than the next one hundred years. These ‘attachment’ cases have generated increasingly delicate classifications of such inferences as implicatures (conversational, conventional and the others), explicatures, higher-order explicatures, implicitures and the rest. These two sets of issues leave the modern philosopher of language, and those in collateral disciplines, with The Goldilocks Problem, as they seek accounts that avoid too little ‘content’ (indexicals and their relations), or accounts of too much ‘content’ (implicatures and their neighbours), in search of theories of just the right amount of content.

There is another problem. Consider a typical example from the recent literature:

(i) He handed her the key and she opened the door.

This, it is claimed, really means (ii).2

(ii) He handed her the key and she opened the door with key that he had handed to her.

(i), it is claimed, though meaningful, is meaningful in an ‘incomplete’, or ‘wrong’, way. (ii), on the other hand, with the addition ‘with the key that he had handed to her’ is meaningful in the right way. But, let’s ask: What makes the addition in (ii) the proper difference that converts being meaningful in the wrong way to being meaningful in the right way? Why not also add (iii):

(iii) … to go from the back garden to the kitchen …

and/or (iv):

(iv) … to get the electric carving knife …

and (v):

(v) … in an attempt to fight off the invaders …

and (vi):

(vi) … who had come from the future to kidnap their children …

and (vii):

(vii) … because their eldest son, Johan, would become an evil warlord who would one day subjugate with his armies the civilised Universe …

Etc. So, we must ask: What is a complete thought (a.k.a., in some of the more modern idioms, full propositionality)? Without an answer to this question the matter of what is now called pre-semantic pragmatic enrichment quickly descends into a version of The Mein Herr Problem:

“What a useful thing a pocket-map is!” I remarked.

“That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

“About six inches to the mile.”

“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the greatest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”

“Have you used it much?” I enquired.

“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly so well.”

Carroll 1893: 169

The right amount of content becomes important because that is the source of truth-conditions and an interest in the notions of truth condition and truth value is a pervasive one throughout the Fregean Era. The idea is that a theory of truth can serve as, or be, a contribution to delineating the outlines of some theory of meaning. But there is also a discussion to be had about the absence of truth-value. Some non-declarative sentence types are not truth valued. Some declarative sentence types are not truth valued (the performatives and other non-assertives). And some non-performative declarative sentences are not truth valued (those which contain constituents that lack a reference or are presuppositionally disabled). There have been a number of proposals advanced to accommodate these truthvalueless constituents in larger compositions. On the one hand, it is proposed that all such compositions are false; on the other, that all such compositions are truthvalueless. Both of these proposals betray the logic of the classical semantics of the elementary connectives. On one view, the consistent logic and the amplified truth tables can be given as follows, although there are competing positions. In the case of negation, the negation of a truth-value gapped proposition is a truth-value gapped proposition. In the case of conjunction, the conjunction of a falsehood and a truth-value gapped proposition is false, otherwise it is truth-value gapped. For disjunction, the disjunction of a truth and a truth-value gapped proposition is true, otherwise it is truth-value gapped. And in the case of the single headed arrow, a false antecedent and a gapped consequent, or a gapped antecedent and a true consequent, result in a truth, otherwise the composition is gapped. Note that these are compositions for a gapped bivalent logic, not a trivalent logic. The notion of a trivalent logic doesn’t, to some, make sense. A truth-value gap is the absence of a truth-value, not a third truth value.

Whatever the outcome of these later discussions, especially the last one, concerning the nature and consequences of truthvaluelessness (where the present authors themselves have yet to reach consensus) the introduction of quantifier/variable constructions marks the distinction between the old and the modern worlds.3 In the wake of this innovation, Aristotelian and Stoic (and Boolean) reasoning are left receding in the rear-view mirror of intellectual history.

Enter the theory of denoting. And, in next to no time, in historical terms, exit the theory of denoting. Enter the theory of descriptions. One abrupt difference between the two theories is in the logician’s attitude to natural language syntax. In 1903 it was possible to claim that ‘grammar seems … to bring us much nearer to a correct logic than the current opinions of philosophers; … grammar, though not our master, will yet be taken as our guide’ (Russell 1903/1937: 42). By 1905 the guide has been emphatically dismissed, whence Russell’s unpacking of (1) into (1’) below, which has been described as resulting from an act of butchery (Gareth Evans). The story here is by now a familiar one. The motivation this time was the problem of empty names. This problem can be approached in several ways. Either an appeal is made to the third realm and sense, or it can be assumed that such expressions function referentially and then form a conception of reality such that their denotata ‘exist’ in some extended sense of that term or one can attempt to find an extensional interpretation of these phrases such that the problem of their non-existent denotata does not arise. Bluntly stated, the choice is between (i) going intensional, and falling back on one of the consequences of the 1879 revolution, or (ii) embracing ontological extravagance, and opening to all comers the gates of ‘reality’ or, perhaps most sensibly, (iii) exploiting the quantificational capacity of the new logic Sinnlos. The architect of the theory of descriptions chose the last option and interpreted such expressions not as troublesome subject-predicate structures but as the complex existentially quantified statement corresponding to the conjunction of (1’a-c):

(1) The F is G. (e.g. The king of France is bald.)

(1’) There is at least one object x such that

a. x Fs, and

b. For any object y, if y Fs then y is identical to x, and

c. x Gs

This analysis of the sentence entails, by conjunction elimination, that there is an object that Fs so the conjunction is false if (1’a) is false. The negative of (1) can be represented by placing the negative operator before (c), or before the entire conjunction. If true, the two negative sentences are true for different reasons. The former is true if there is a unique, extant object which Fs which fails to G and the latter is true if there is no object which Fs or because there is more than one or because a unique, extant object fails to G. The main consequence of this analysis is that sentences containing empty names or defective descriptions can now, without appeal to the third realm, be said to be meaningful and have truth values and the law of the excluded middle shown to be preserved. The architect of the theory that generated analyses like (1’) was not modest about the virtues of this solution. He said that it ‘clears up two millennia of muddle-headedness about “existence” ’ (Russell 1961: 785).

Some more modern readers are not impressed. Jay David Atlas, for example, makes two claims: (i) not is not scopally (much less lexically), ambiguous, but rather sense-general and so, because logical forms cannot be the semantic representations of sense-general sentences, (ii) sense-general sentences do not have underlying logical representations of the kind in (1) or indeed of any other kind. The punch line for these claims is that speakers do not select from the logico-linguistically given readings of a syntactically or lexically ambiguous sentence but that, from a meaningful but radically sense-general sentence, they construct a contextually determined interpretation of an utterance. This can be put in the Kantian-esque slogan: ‘Pragmatic inference without sense-generality is blind; sense-generality without pragmatic inference is empty’ (Atlas 1989: ix). In short, and more colloquially: ‘one is reading meaning into the words, not reading meaning out of them’ (Atlas 1989: 26). There is some merit in examining the arguments for these claims in more detail to see what kind of run we get from them for our money.

The argument is principally founded on some diagnostics to distinguish between ambiguity and generality. Philosophers have been none too careful in attending methodologically to this distinction but linguists, on the other hand (in particular Zwicky and Sadock 1975), have designed a battery of tests to facilitate the distinction and the required basis is provided by one of them. Consider (2a) which has possible interpretations (2b–c) and impossible interpretations (2d–e):

(2) a. A likes visiting relatives and so does B.

b. A likes going to visit relatives and B likes going to visit relatives.

c. A likes relatives who are visiting and B likes relatives who are visiting.

d. A likes going to visit relatives and B likes relatives who are visiting.

e. A likes relatives who are visiting and B likes going to visit relatives.

The parallel interpretations in (2b–c) and the impossibility of the crossed interpretations in (2d–e), under the legislation provided by the Conjunction-Reduction Identity Test (CRIT), are taken as evidence for the ambiguity of (2a).

The CRIT consists of the propositions (A) and (B):

(A) The impossibility of a crossed, literal paraphrase for a conjunction-reduced sentence S entails the ambiguity of S. (The distinct, parallel paraphrases express distinct senses.)

(B) The possibility of a crossed, literal paraphrase for a conjunction-reduced sentence S entails the non-ambiguity of S. (The distinct parallel paraphrases do not express distinct senses.)

In parentheses we note that the following sentences (3–5) permit crossed interpretations and are, therefore, general with respect to whether A or his or her circumstances change:

(3) A became as strident as any of the Brexiteers and then the same thing happened to B.

(4) A became more strident than the average Brexiteer and then the same thing happened to B.

(5) A became the most strident Brexiteer in the party and the next year the same thing happened to B.

The CRIT is then applied to the theory of descriptions’ most iconic examples: Given (6a) we can derive (6b):

(6) a. The King of France is not bald and the Queen of England is not bald.

b. The King of France is not bald and the same goes for the Queen of England.

And given (7a) we can derive (7b):

(7) a. It is not true that the King of France is bald and it is not true that the Queen of England is bald.

b. It is not true that the King of France is bald and the same goes for the Queen of England.

And now it is asked whether there are crossed, in addition to the parallel, interpretations:

(8) a. The King of France is not bald (because France is not, currently, a monarchy), and the same goes for the Queen of England (because she is a typical hirsute Windsor).

b. It is not true that the King of France is bald (because France is not, currently, a monarchy), and the same goes for the Queen of England (because she is a typical hirsute Windsor).

The argument hinges on whether there are native speakers who accept (8a–b). If there are such speakers then there is evidence that “ ‘Not’-sentences are semantically less specified, and theoretically more complex, than the two-thousand-year tradition in logical theory has heretofore recognized” (Atlas 1989: 91).4

The second, more general, claim, that sense-general sentences do not have underlying logical representations of the kind in (1) or indeed of any other kind is a very interesting one. The question may be about whether formal methods have comprehensive application on natural phenomena. The 1879 analysis was confined to providing a semantics and a proof theory for arithmetical statements. The formalism and especially the proposals about multiple generality were perfectly adequate to this principal purpose. But there were no proposals then, nor subsequently with the theory of descriptions, for phenomena from the natural world that can be found outside the relatively narrow bandwidth of arithmetical discourse: demonstratives, indexicality, opacity, modality, temporality, information structure and more. The few remarks about first person pronouns seemed to result in parts of the objective third realm becoming private, non-objective, places, inaccessible to others, and the attempts to deal with opacity, and, with multiple embeddings, the potential infinity of senses, make natural languages, on certain assumptions, unlearnable.

Frege was quite clear that (i) formal methods have little purchase on natural language and (ii) natural language is no guide to a formal language for pure thought: ‘It cannot be the task of logic to investigate language and determine what is contained in a linguistic expression. Someone who wants to learn logic from language is like an adult who wants to learn how to think from a child’ (Frege 1980: 67–68); and this because ‘the excessive variety of logical forms that has gone into the shaping of our language makes it difficult to isolate a set of modes of inference which is both sufficient to cope with all cases and easy to take in at first glance’ (Frege 1953: 103e).

The papers that follow are all ‘attached’, in one way or another, with the thought—or topics themselves ‘attached’ to the thought—of Jay David Atlas (e.g. Atlas 1989, 2005). This branch of the philosophical tree has, over the years, become a large one, with its own branches (with branches). So, the papers treat such themes as the ambiguity/underspecification distinction, dynamic syntax and social interaction, erotetic reasoning, metaphor, Moore’s Paradox, presupposition, radical pragmatics, the semantics/logic interface, the syntax, semantics and pragmatics of negation, and truth-meaning determination (modulo Davidson). We thank Jay for giving us so much to learn from, to think about, to reflect upon, and to argue with.

The purpose of prefatory and introductory remarks is to ease the reader’s transition from the all too frequent great bloomin’, buzzin’ confusion in the outside world provoked by, for example, unpredictable world leaders, weak self-destructive governments, price inflation, commodity shrinkflation, climate change, cybercrime and sudden and seemingly inexplicable currency fluctuations in the planet’s most powerful and prosperous nations, to the tranquil Elysium where real reflection and thought, one might almost say timeless Fregean thought, can take place.

We hope that these remarks have assisted—in some perhaps small way—that transition.

Ken Turner and Laurence Horn


The first apology goes to Quine, of course. Cf. Quine (1952).


Crucially, as Bach 2001 and others have noted, (i) doesn’t SAY this; the question is whether (i) MEANS (ii) or whether all we can assert is that the speaker of (i) is likely to have intended to COMMUNICATE (ii).


There is at least one, and perhaps at most one, object such that that object is a co-author of this Preface and that object is convinced of the truth of this statement. (Apologies to Dummett: cf. any of Dummett 1973, 1981, 1991, 1994.)


There is a complication that might be noted. Zwicky and Sadock (1975) regard their CRIT and other identity of sense diagnostics for ambiguity as inapplicable to cases of “privative opposition” in which one understanding unilaterally entails the other. The opposition between internal (narrow-scope) and external (wide-scope) negation is unfortunately just such a case, given that the former entails the latter but not vice versa (Horn 1985: 126–127). Atlas (1989: § 2.2) rejects this part of the Zwicky/Sadock thesis.

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