This work addresses the representation problem – to use the jargon of computer scientists. To be sure, they speak of the representation of knowledge, but that is a misnomer, reflecting their intentions rather than the nature of the problem. What counts as knowledge must be true, yet any notation in which we can express what is true must equally allow us to express what is false. The problem, therefore, is how best to represent the meanings of linguistic expressions so that they may be manipulated in accordance with rules, such as rules of inference or of translation. One might call this the ‘semantic form’ of expressions, by analogy with ‘logical form’.

My interest is restricted to expressions of everyday language. This is not a synonym for ‘natural language’. The implied contrast is with technical language, for example the language of mathematics, which might also qualify as natural language. I also assume that, in the case of expressions which are accounted either true or false (propositions), the central core of their meanings will be given by specifying the circumstances under which they would be true, so that semantic form or structure will relate to and should facilitate these specifications.

Identifying the structure is, indeed, the very first step in such a specification, for the meaning of an expression is determined by the meanings of its parts and the manner of their combination; that much is implicit in the possibility of learning a language (see Davidson, 1965).

In the forty-year period surveyed in this concluding section of our venture (1950–1990), etymology can be seen steering a strange course, as if its practitioners and its beneficiaries were sometimes working at cross purposes; in addition, irreconcilably conflicting ideas all too often prevailed inside each group. There are few exceptions from this trend towards diversification at almost any cost. One rare universal is the fact that a single, particular genre of etymological guide is at present clearly doomed to rapid disappearance (not least for economic reasons), namely the dictionary of word origins in Language X expounded in Language Y (assuming, of course, that both X and Y are major living tongues). The nearly-extinct type of lexicographic compilation here hinted at is exemplified by Max Vasmer's meritorious work on Russian and Ernst Gamillscheg's on French, each phrased in German, in conformity with an old tradition. To be sure, there was published a revised translation into Russian, by O. N. Trubacëv, of the former, and a slightly expanded second edition of the latter made its appearance in the original garb without, it is true, producing any stir outside Central Europe. Yet, the more characteristic course of recent events can be illustrated by the fluctuating fortunes of Walther von Wartburg's incomparably more ambitious and influential venture, which concerns Gallo-Romance lexis as a whole, and more. At the outset the monumental project was undertaken as a venture to be worded in German, and was so continued, when the author moved from Lausanne to Leipzig.

So far, we have managed to describe the shifting positions of etymology, at first outside the edifice of historical grammar and later on in close connection with it, in splendid isolation from political events and social changes as it were, with practically no reference to such real-life situations as the Napoleonic Era, the Crimean War, or America's Civil War, to cite three examples at random. In this undertaking we have received support from the oft-cited fact that, between 1871 and 1904, Europe went through a protracted period of relative peace – of respite from involvements in serious wars and from all sorts of revolutionary concussions.

But as one approaches the next half-century, things begin to undergo a radical change, not necessarily for the better. The period 1900–1950, at present visible in clear retrospect, was marked by two world wars which were not only exceptionally devastating, but were also characterized by all sorts of ideological implications and by energetic reshuffling of centres of intellectual prestige. Allusions to the impact of changes of such magnitude can no longer be swept under the carpet. The fortunes of historical linguistics and of etymology alike were very strongly and, I repeat, by no means always favourably affected by the resulting redistribution of intellectual ammunition.

It should suffice, in this context, to mention two influential circumstances. First, by 1900, the reputation of German scholarship, both pure and applied, stood at its zenith the world over.

In different times and at different places, etymology has meant slightly or entirely different things to the few or many people who, under varying sets of circumstances, have used that word, applying it to their own spheres of interests. Basically, etymology always meant something approximating to the paraphrase ‘original meaning, or use, of a given lexical unit or proper name’. But the cultural implications of this lame descriptive statement can be entirely different. The core meaning of a word can be imagined as something wholly independent of the passage of time and endowed with magic messages or mystic overtones.

The appeal to etymology in a magic context may well have started with proper names and be so old as to have its roots in prehistory. Parents, by giving their newborn child a name whose ‘real’ meaning is wholly transparent to those familiar with the given language (like Spanish Dolores, Consuelo, or Amparo, or Hebrew Rachel), or transparent only in part, or else to experts alone, may to some extent be motivated in their choice by this chance to encode a wish for the child's future well-being or expected character (standard of behaviour), even though several alternative motivations may prevail. To the extent that the real meaning of a name titillates the speech community's, or certain outsiders', curiosity, the etymology comes close to resembling the riddle, and the etymologist, in being called upon to solve or clarify it, acts like a magus or a magician.

The choice of an accurate and, at the same time, appealing title for this book has, I confess, cost me considerable headaches. The point is that etymology (unless one is willing to equate it with some such indifferent rendering as ‘the discipline of word origins’), has tended to mean, in its actual applications and, above all, implications, entirely different things to successive generations of scholars and laymen alike, from Antiquity to the concluding years of the twentieth century.

In certain remote periods, the literal meaning of a given proper name and the messages encoded into it (especially but not exclusively in reference to proper names of persons) meant incomparably more to an average member of the speech community in question than the provenance of any common nouns. After all, parents in many places enjoy the privileges, within the framework of tradition, of selecting, for their newborn children, names not infrequently endowed with special messages or associations. Conversely, few individuals are invited, encouraged, or allowed to coin novel designations for, let us say, dishes or pieces of furniture. In the second half of the last century, which was marked by a new enthusiasm for science, accurate etymologizing mattered chiefly to those eager to reconstruct a plausible evolutionary chart of sounds and forms, viewed across the ages, since their development, as was then firmly believed, was governed by strict laws, best discoverable by those familiar at first hand with reliably established starting points for word trajectories.

Almost exactly a century ago etymological research reached its all-time peak of appeal and recognition, at several levels of intellectual life. The legitimacy and even desirability of etymological inquiries went unchallenged in practically all advanced countries, as did the inclusion of etymology in the ensemble of historico-linguistic disciplines. Ambitious scholars made a point of their ability to engage in etymologizing, while editors of respected learned journals, usually characterized as ‘philological’, were only too eager to reserve a prominent section of each number for brief, pungent discussions of this kind. Earlier pronouncements of the ‘pre-scientific’ era were mentioned, at best, in more or less casual manner and, not infrequently, in an ironic or condescending tone.

Such a favourable situation does not at all obtain at present, but strangely enough, the current state of affairs in the ‘linguistic’ domain is self-contradictory, with participants and policy-makers (as if to complicate things still more) seldom stooping to ventilating such inconsistencies. A dispassionate observer quickly becomes aware of a certain confusion of values, but may search in vain for any enlightening analyses of what makes etymology ‘unscientific’ (subjectivity of pronouncements? insufficiently objective tone? the general air of archaicity?).

There obtains, to begin with, a hazardous discrepancy between the degrees of attention our societies tend to reserve for dictionary-style compilations of comments on word-origins as against monographic investigations into them.

Modelling intensions

In Chapter 9, an interpretation of the modal adverbs necessarily and possibly was presented in terms of possible worlds, but the other contexts in which extensional entailments fail were not discussed. As proposed in Section 9.2, the general solution to the problem of referentially opaque contexts lies in the concept of intensionality, but the interpretation of modality given above was not stated in terms of this concept and it has not been made clear how possible worlds enable a formal definition of intension to be made. Let us now remedy the situation and provide a general semantic theory for opaque contexts, thus completing our survey of formal semantic theory.

The definitions for the interpretation of modal formulae given in Chapter 9 embody the idea that formulae may be true in some worlds but not in others, i.e. that the extensions of formulae (i.e. truth values) may vary from world to world. Furthermore, it was suggested at the end of Section 9.2 that an intension is something that picks out the extension of an expression in any state of affairs. The intension of a formula may thus be defined as something that specifies its truth value in every state of affairs. Equating states-of-affairs with possible worlds, we interpret the intensions of formulae as functions that map possible worlds onto truth values: functions that map a possible world onto 1 if the formula is true in that world and onto 0, otherwise.

The variety of noun phrases

We have so far in this book been looking at the meaning of sentences primarily in terms of the properties that entities have and the relations that hold between them. This has meant a concentration on the interpretations of verbs and verb phrases, with the meanings of the phrases that serve as their arguments, noun phrases, taking second place. Indeed, only two sorts of English noun phrase have been analysed in the grammar fragments so far: proper names and simple definite noun phrases. But there are, of course, many other types of noun phrase in English, including indefinite noun phrases like those in (1.a & b), quantified noun phrases as in (1.c & d), noun phrases containing adjectives or relative clauses (1.e & f), noun phrases with possessive modifiers (1.g), and many more.

1. a. a book.

2. b. some cat.

3. c. every dog.

4. d. each person.

5. e. the happy student.

6. f. any student who gives a good report.

7. g. Ethel's friend's dog.

The noun phrases in (1) all require a more sophisticated interpretation than the one supplied for proper names and definite descriptions in earlier chapters. Both of these expressions have been translated as expressions of type e, denoting entities in the model. Such an analysis is, however, not ultimately tenable for proper nouns, is suspect for definite noun phrases and cannot be sustained at all for the other types of noun phrase in (1).

Although billed as an introduction to formal semantics in general, this textbook is concerned primarily with what has come to be called Montague Semantics and is therefore based primarily on Montague (1970a; 1970b; 1973). A good deal of research within Montague's general framework has been carried out since the 1970s and this has led to many changes in, and many variations of, the original theory. Other research has also led to reactions to Montague's programme and the development of rival theories. Only a few of these revisions and extensions to Montague's theory have, however, found their way into the text of the book. This may seem retrogressive, but it is my conviction that many of the questions being asked in formal semantics and the directions of research are best understood by learning about the more radical elements of Montague's original approach, particularly the semantic analysis of noun phrases and the theory of intensionality. Once these have been grasped, later developments can be understood more easily. For this reason, the exposition develops an account of the now classical version of Montague's theory, but references are given for the major revisions and extensions at the end of each chapter for readers to pursue as their interests dictate. Furthermore, there is no attempt in this book to give more of the logical and mathematical background than is necessary to understand how such things can help in the analysis of the semantics of natural languages.

Compound sentences

The grammar presented in Chapter 2 generates some very basic sentences of English and the translation procedure enables each one to be associated with at least one representation in Lp (more than one, if it contains a homonym). While the number of sentences generated by the grammar, G1 is relatively large (and can be made larger if more words are added to the lexicon), the language it generates is still finite. One of the properties that all natural languages are assumed to have is that they contain an infinite number of sentences. Since one of the goals of a theory of semantics, as we saw in Chapter 1, is to pair each sentence in a natural language with an interpretation, the theory must contain the means to provide an infinite number of interpretations. Furthermore, because natural languages are here being interpreted indirectly via a logical representation, the logical translation language must itself be infinite.

The reason that natural languages are infinite is that they are recursive. This means that expressions in certain categories may contain other expressions of the same category. For example, sentences may contain other sentences conjoined by the expressions and or or, or they may be connected by if…then, or a sentence may contain one or more repetitions of the expression it is not the case that. Some examples based on the grammar G1 are given in (1).

Temporal contingency

The grammar fragment developed in previous chapters generates sentences only in the past tense form. This has been a matter of expediency to allow more natural English to be used for the examples. However, the temporal properties of the sentences implied by the use of this tense have, in fact, been completely absent from their interpretation. The models we have been working with only contain a set of basic entities, A, and a function F which assigns an extension to each lexeme in the language. The denotations assigned by the latter are, however, static and no notion of change or development is (or could be) incorporated. This means that really the model theory treats all formulas as universal truths or universal falsehoods, as if they were all of the same sort as sentences like e = mc2, All humans are mortal, No bachelors are unmarried, The square root of nine is seventeen, and so on. The propositions expressed by such sentences have the same truth value at all times and so may be thought of as ‘timeless’. Most of the sentences generated by the grammar fragment, however, translate into formulae that could vary in truth value according to time and place, and other contextual factors. For example, A lecturer screamed may be true if uttered today but false if uttered the day before yesterday. Such sentences do not denote universal truths or falsehoods but contingent ones, ones whose truth depends on what is happening or has happened at a particular time.

The passive

In discussing the translation from English into Ltype in Chapter 4, rules for generating and interpreting simple passives were omitted. Although it is possible to define the extension of a passive verb phrase like kicked by Jo as the characteristic function of the set of things that Jo kicks, it is not possible with the apparatus we currently have to link this function directly with the extension of the active verb kick, kicks, kicked. The appropriate relationship between the two voices is that, in the relation denoted by the passive, the entity denoted by the object of the preposition by corresponds to the entity denoted by the subject of the active and the entity denoted by the passive subject corresponds to that denoted by the object in the active. This correspondence was handled in Chapter 2 directly in the translation for the passive rule by switching around the individual constants translating the two noun phrases in the passive rule to yield an identical translation to that of the active. So, for example, Jo kicked Chester and Chester was kicked by Jo are both translated into Lp as kick' (jo', Chester'). Unfortunately, this simple expedient is no longer open to us because of the existence in G2 of a verb phrase constituent. This prevents subject and complement NPs from being ordered with respect to each other in a translation rule because they are no longer introduced by the same syntactic rule.