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Informal Lectures on Formal Semantics
This book is an introduction to the current developments in model-theoretic semantics, which has become an essential part of the work in theoretical linguistics over the last decade. The author examines the model structure of Montague's theory and then presents elaborations on this basic model that have been of particular importance in the last few generalized quantifiers, the introduction of more structure in the domain of individuals, properties as primitive elements in the model, situations and similar 'smaller' worldlike entities. Nothing is presupposed about knowledge of the mathematical and logical tools used in formal semantics, and Bach presents the informal with a minimum of formalism.
- GenresLinguisticsNonfiction
150 pages, Hardcover
First published April 1, 1989
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December 21, 2018
Right off the bat, in the first lecture, we are hit with one of Bach’s more debatable premises: “Meanings are things that are not language.” A lot has gone down in Academe in the 30 years since these lectures were delivered in Tianjin, and this view of meaning flies in the face of most, but certainly not all, current cognitive theories of meaning. That said, this slender book of eight lectures offers a prescient glimpse at state-of-the-art semantics from the 1980’s. Here the reader finds no fetishization of densely packed formulas full of lambdas, subscripts, Boolean operators, upside down A’s or backwards E’s. Unlike most work in the Montague tradition, Bach’s explanations of semantic phenomena in this book are truly legible, not to mention fairly painless. Explaining formal semantics without symbolic demonstration is a lot like teaching algebra or calculus without any visual representation of what is being taught. Yet Bach rises to this challenge and manages to convey numerous interesting ideas from semantics without obfuscating the sense to be conveyed in the name of overly precise analyses, and without mystifying the reader with a lot of symbolic junk.
Bach’s exposition is grounded in truth-functional and model-theoretic meaning. Meaning what? Meaning a statement is a proposition which refers to the way the world would have to be for that proposition to be true. Since we can speculate and talk about hypothetical or counterfactual scenarios, and do so all the time, we oftentimes refer to worlds that are not the actual world but are possible worlds just the same. Every use of negation, all talk about the future, and every use of ‘if’ ground meanings in a possible world that is often at odds with the actual world, however that actual world might be defined. In anthropological terms, this ability to talk about how the world might or could be is a large part of what makes us human. I personally see this special, speculative ability as a powerful engine of civilization and culture.
In the Montague tradition, Bach provides a grammar fragment which he calls ‘PC’, standing (I hope) for ‘predicate calculus.’ This simple grammar demonstrates how meaning is composed from parts of discourse: variables (e.g. pronouns), constants (e.g. names of individuals), and predicates (e.g. verbs, adjectives, or nouns). Nouns, especially quantified nouns and noun phrases, are included as predicates because they function to identify sets of properties which each member of a set of entities share. Noun phrases like ‘ugly ducklings’ or ‘unnecessary bloodshed’ or ‘the rent’ are predicates just as much as verbs and adjectives are. Predication may moreover include the mapping of variables (‘here’, ‘I’, ‘yesterday’) to constants (‘here’=’place of speaker’, ‘I’=’person speaking’, ‘yesterday(for me, here, now)’=’December 19, 2018’). For Bach, pragmatics is primarily concerned with this valuing of variables through an interpretation of (or grounding in) discourse context. Otherwise, pragmatics is about flagging referents as unambiguously identifiable, as in the case of determiners like the humble ‘the’.
Bach then plows deeper into Montague-style quantification alternations, analyzing sentences such as “Every child was teasing a tiger.” Depending on the scope and ordering of the quantifiers (‘every’ and ‘a’) in the semantic representation, we get readings like “There is a single tiger that every child was teasing” vs “Every child had his or her own tiger to tease and was teasing it”. Dowty et al. used the sentence “Every man loves a woman” to demonstrate the same form of semantic ambiguity. As has been pointed out before by linguists of a cognitive bent, these kinds of sentences are highly marginal in English and are rare (non-existent?) outside of English. In effect, these sentences are nowadays seen as dwelling at the ragged edge of (English) grammar, and so fail to furnish any kind of insight into core issues related to linguistic meaning.
But luckily for most readers, this book is not full of hackneyed logic problems. It moves in the later lectures away from analytic philosophy and towards theories of meaning that are more germane to students of grammar. Bach recognizes that eventualities can be quantified, although differently from the way nouns are quantifiable. Here he touches on aktionsart, which is the lexically-based (not grammar-based) meaning contribution to a predicate’s organization of time. Some predicates are used to describe states which can take place for a duration of time (‘that barn has always been red’). Other predicates are used to describe events that are momentary and iterable (‘she kept cutting the rope with a knife’). Between these, there are predicates which are used to describe processes which behave a bit like states and a bit like events (‘he is cooking the stew now’). Bach extends this mode of analysis to show the ways language can be used to reify action so as to give to an action or event a certain measure of extent or individuation.
Although Bach is clearly of the opinion that meanings are out there in the world and not (at least not merely) representations in our heads, he does give credence to semantic theories which limit and constrain the rather cumbersome ontology (and possibly impossible epistemology) of possible ‘worlds’. There are some interesting ideas here regarding how situations, and more metaphorically, files, can narrow the scope of context for a sentence’s meaning interpretation (‘meaning’ still identified with a sentence’s truth conditions). Why refer to an entire world when parsimony and Okham’s razor demand, or at least suggest, a consideration of meaning as grounded in a particular situation or a particular range of background information (a mental ‘file’)?
But with Bach's notions of semantics, reality clearly comes first, then mental representations follow. All in all, there is a very thingy approach to reality in these lectures. As I have already noted, this work focuses on sets—sets of things, sets of properties of things, sets of events as abstract ‘objects’, modality defined in terms of set theory ('must'=in ALL worlds=necessarily, while 'may'=in SOME world=possibly). Even intensionality—the abstract, language-internal 'sense’ of an expression—merely functions to help pick out the extension or intended ‘reference’. Bach’s central notions are once again based on the assumptions inherent in Montague's theory of English quantification. In this respect, Bach's work is similar to that of Ronnie Cann, Barbara Partee, James McCawley, and David Dowty, four linguists who have written extensively on formal semantics as systems of logic for combining categories in order to derive entity mappings and predication relations (truth conditions) If Bach had more than just entertained the prospect that meaning should be regarded as cognitive rather than referential (I.e. referring in the world or between worlds), that is to say if he had followed a path more like the ones followed by George Lakoff or Ray Jackendoff, then in THAT possible world his work would certainly be far more central to linguistics today.
But in the end I consider these eight lectures to be a resounding success. Even with the not insignificant over-simplification which the omission of pseudo-algebra and quasi-calculus engender, and even with his Bloomfieldian phobia of the brain/mind, it is apparent that Bach has given the world (yours and mine) a magnificent, very high level overview of (1980’s) core semantic theory. He clearly selects his complexities with care, and with a concern for the likely readership's fore-understandings and presuppositions. Most significantly, Bach shows that the formal can be represented informally (even orally). In my opinion, the interests of both linguistics and philosophy would be better served IF more scholars could jettison their arcane formalisms and instead provide the reader with a clearer view of meanings, even IF in some world those ‘meanings’ are ‘things’ that are ‘not language.’ As a final word, this work should be considered a classic of natural language philosophy and of philosophically-minded linguistics.
Bach’s exposition is grounded in truth-functional and model-theoretic meaning. Meaning what? Meaning a statement is a proposition which refers to the way the world would have to be for that proposition to be true. Since we can speculate and talk about hypothetical or counterfactual scenarios, and do so all the time, we oftentimes refer to worlds that are not the actual world but are possible worlds just the same. Every use of negation, all talk about the future, and every use of ‘if’ ground meanings in a possible world that is often at odds with the actual world, however that actual world might be defined. In anthropological terms, this ability to talk about how the world might or could be is a large part of what makes us human. I personally see this special, speculative ability as a powerful engine of civilization and culture.
In the Montague tradition, Bach provides a grammar fragment which he calls ‘PC’, standing (I hope) for ‘predicate calculus.’ This simple grammar demonstrates how meaning is composed from parts of discourse: variables (e.g. pronouns), constants (e.g. names of individuals), and predicates (e.g. verbs, adjectives, or nouns). Nouns, especially quantified nouns and noun phrases, are included as predicates because they function to identify sets of properties which each member of a set of entities share. Noun phrases like ‘ugly ducklings’ or ‘unnecessary bloodshed’ or ‘the rent’ are predicates just as much as verbs and adjectives are. Predication may moreover include the mapping of variables (‘here’, ‘I’, ‘yesterday’) to constants (‘here’=’place of speaker’, ‘I’=’person speaking’, ‘yesterday(for me, here, now)’=’December 19, 2018’). For Bach, pragmatics is primarily concerned with this valuing of variables through an interpretation of (or grounding in) discourse context. Otherwise, pragmatics is about flagging referents as unambiguously identifiable, as in the case of determiners like the humble ‘the’.
Bach then plows deeper into Montague-style quantification alternations, analyzing sentences such as “Every child was teasing a tiger.” Depending on the scope and ordering of the quantifiers (‘every’ and ‘a’) in the semantic representation, we get readings like “There is a single tiger that every child was teasing” vs “Every child had his or her own tiger to tease and was teasing it”. Dowty et al. used the sentence “Every man loves a woman” to demonstrate the same form of semantic ambiguity. As has been pointed out before by linguists of a cognitive bent, these kinds of sentences are highly marginal in English and are rare (non-existent?) outside of English. In effect, these sentences are nowadays seen as dwelling at the ragged edge of (English) grammar, and so fail to furnish any kind of insight into core issues related to linguistic meaning.
But luckily for most readers, this book is not full of hackneyed logic problems. It moves in the later lectures away from analytic philosophy and towards theories of meaning that are more germane to students of grammar. Bach recognizes that eventualities can be quantified, although differently from the way nouns are quantifiable. Here he touches on aktionsart, which is the lexically-based (not grammar-based) meaning contribution to a predicate’s organization of time. Some predicates are used to describe states which can take place for a duration of time (‘that barn has always been red’). Other predicates are used to describe events that are momentary and iterable (‘she kept cutting the rope with a knife’). Between these, there are predicates which are used to describe processes which behave a bit like states and a bit like events (‘he is cooking the stew now’). Bach extends this mode of analysis to show the ways language can be used to reify action so as to give to an action or event a certain measure of extent or individuation.
Although Bach is clearly of the opinion that meanings are out there in the world and not (at least not merely) representations in our heads, he does give credence to semantic theories which limit and constrain the rather cumbersome ontology (and possibly impossible epistemology) of possible ‘worlds’. There are some interesting ideas here regarding how situations, and more metaphorically, files, can narrow the scope of context for a sentence’s meaning interpretation (‘meaning’ still identified with a sentence’s truth conditions). Why refer to an entire world when parsimony and Okham’s razor demand, or at least suggest, a consideration of meaning as grounded in a particular situation or a particular range of background information (a mental ‘file’)?
But with Bach's notions of semantics, reality clearly comes first, then mental representations follow. All in all, there is a very thingy approach to reality in these lectures. As I have already noted, this work focuses on sets—sets of things, sets of properties of things, sets of events as abstract ‘objects’, modality defined in terms of set theory ('must'=in ALL worlds=necessarily, while 'may'=in SOME world=possibly). Even intensionality—the abstract, language-internal 'sense’ of an expression—merely functions to help pick out the extension or intended ‘reference’. Bach’s central notions are once again based on the assumptions inherent in Montague's theory of English quantification. In this respect, Bach's work is similar to that of Ronnie Cann, Barbara Partee, James McCawley, and David Dowty, four linguists who have written extensively on formal semantics as systems of logic for combining categories in order to derive entity mappings and predication relations (truth conditions) If Bach had more than just entertained the prospect that meaning should be regarded as cognitive rather than referential (I.e. referring in the world or between worlds), that is to say if he had followed a path more like the ones followed by George Lakoff or Ray Jackendoff, then in THAT possible world his work would certainly be far more central to linguistics today.
But in the end I consider these eight lectures to be a resounding success. Even with the not insignificant over-simplification which the omission of pseudo-algebra and quasi-calculus engender, and even with his Bloomfieldian phobia of the brain/mind, it is apparent that Bach has given the world (yours and mine) a magnificent, very high level overview of (1980’s) core semantic theory. He clearly selects his complexities with care, and with a concern for the likely readership's fore-understandings and presuppositions. Most significantly, Bach shows that the formal can be represented informally (even orally). In my opinion, the interests of both linguistics and philosophy would be better served IF more scholars could jettison their arcane formalisms and instead provide the reader with a clearer view of meanings, even IF in some world those ‘meanings’ are ‘things’ that are ‘not language.’ As a final word, this work should be considered a classic of natural language philosophy and of philosophically-minded linguistics.
February 6, 2013
This is still the best overview of the various ways to deal with natural languages in a model-theoretic way, even though the material he cites is now dated in some respects. I agree with his approach to presenting that material. Present a few implications of one theory. Provide some evidence suggesting that they can't be true (or can't all be true). Suggest ways to revise theory. Repeat. After a few different theories are on the table and subjected to this treatment, a picture of the basic problems of the field started to materialize for me. One could have all of these insights just by going through the old literature first-hand. But only so much wheel-reinventing is useful, I guess. As far as I know, the only book that treats this literature with the same sweep is Blackburn and Bos's Representation and Inference for Natural Language. Emmon Bach's papers on "natural language metaphysics" are also worthwhile if you find that dimension of semantics interesting.
July 22, 2009
I haven't finished this, but I thought the first few chapters were a decent introduction to Montague semantics: in particular, they show how one can extend the resources of the propositional calculus---first by including times and possible worlds, then by doing some cool stuff with the lambda calculus and set theory---to give a uniform account of the semantics of natural languages.
A couple of quibbles. First, there are some typos which really hinder the exposition (incorrect numbering of examples, inconsistent examples). Second, I felt that the informal approach occasionally hindered more than it helped. It's hard to see exactly who these lectures are aimed at really. 'Informal' amounts to minimising formal notation, which makes some sense re: the set theory etc., but I felt that some of the account (particularly the sections on generalized quantifiers) would have been more perspicuous if Bach had introduced at least a bit of formal notation.
Also, these lectures are over 20 years old now, and I have no idea how much they have been superseded by later work. Presumably some of the live issues Bach mentions are no longer quite so current.
A couple of quibbles. First, there are some typos which really hinder the exposition (incorrect numbering of examples, inconsistent examples). Second, I felt that the informal approach occasionally hindered more than it helped. It's hard to see exactly who these lectures are aimed at really. 'Informal' amounts to minimising formal notation, which makes some sense re: the set theory etc., but I felt that some of the account (particularly the sections on generalized quantifiers) would have been more perspicuous if Bach had introduced at least a bit of formal notation.
Also, these lectures are over 20 years old now, and I have no idea how much they have been superseded by later work. Presumably some of the live issues Bach mentions are no longer quite so current.
Displaying 1 - 3 of 3 reviews