languages


Today’s reading: Grammaire générale et raisonnée de Port-Royal, by Antoine Arnauld and Claude Lancelot, published in 1660.  Let’s call it PRG. You can get it here, in the 1803 edition. My understanding was that it was a precursor to Chomsky, and in fact he claimed as much in a book, Cartesian Linguistics (1965).  Spoiler: it isn’t.

grammaire

Undoubtedly your first question will be: as a grammar from Renaissance times, how does it compare to the word of Šm Fatandor Revouse, Pere aluatas i Caďinor? In overall coverage and linguistic knowledge, it’s fairly similar— for instance, PRG, like Šm Revouse, stumbles in the phonology section through not having any vocabulary or notation for phonetics; both are reduced to talking about letters.

On the other hand, PRG is fairly free of the sort of metaphysical and nationalistic nonsense that Šm Revouse indulges.  In particular, they never claim that the ancient languages are better than the modern, nor do they try to find spiritual categories or whatever within language. They acknowledge at several points that many aspects of language are arbitrary, and vary between languages. (They do sometimes appeal to the notion of ‘elegance.’)

By the way, see here for an argument from W.K. Percival that there is really no such thing as “Cartesian linguistics” at all, that PRG was not particularly innovative or Cartesian, and that Descartes’ idea of language, to the extent he had any, had very little resemblance to Chomsky’s.

Anyway, what is PRG? It’s not really a grammar at all, either of French or the ancient languages. It could be called a sketch of a comparative grammar, or an overview of the concepts needed to study grammar. So it starts with sounds, then discusses nouns, pronouns, adjectives, cases, verbs, etc.  It never gives enough information to fully cover any topic or tell you in detail how a language handles it, but it does define all grammatical terms, gives examples, and opines on what the functions of each thing are.

Chomsky felt that his notion of “universal grammar” was prefigured here, but I’d say PRG starts from the pretty obvious fact that a similar grammatical analysis can be used for the major languages of Europe. PRG never really runs into a fact about modern French that can’t be described using the terms of classical grammar.  So, for instance, they are perfectly aware that French nouns don’t have case, but they find it useful to relate subjects to the Latin nominative, PPs with de to the genitive, and PPs with à to the dative.

The languages covered are very few: of ancient languages, Latin, Greek, and Hebrew; of modern, French, Italian, and Spanish. There are a couple of references to German; none at all to English, and nothing on languages the authors surely were aware of: Basque, Bréton, Dutch, Portuguese, Arabic.

Chomsky went so far as to assert that PRG prefigured his “surface and deep structures”. This is completely absurd; PRG talks about things like subjects and predicates and propositions, but this was bog-standard thinking about language since ancient times. They come a little closer in this passage on adjectives:

When I say Invisible God has created the visible world, three judgements occur in my mind, contained in this proposition. Because I judge first that God is invisible. 2. That he has created the world. 3. That the world is visible. And of these three propositions, the second is the principal one, and the core of the proposition; the first and the third are incidental to it.

The idea that the adjective invisible applied to God represents a proposition God is invisible reoccurs in generative grammar. On the other hand, it is not part of a transformational view of language, nor it is part of a systematic treatment of semantics. It’s really a pretty basic observation about adjectives… if you want to say what an adjective is, you’re almost bound to observe that it says what something is like. It doesn’t mean that you’ve invented deep structure, or phrase structure rules.

There are some interesting bits where the authors try to relate meanings to other meanings. E.g. they say at one point that Petrus vivit ‘Peter lives’ is equivalent to Petrus vivens est ‘Peter is living’, or that Pudet me ‘I am ashamed’ is equivalent to Pudor est tenens mihi ‘Shame is had by me’. You could generously relate this to generative semantics, except backwards: GS tends to make verbs primitive, while PRG tries to restate verbs in terms of adjectives or nouns.

But we really have to avoid overinterpreting texts in terms of current theories. PRG is, by modern standards, hobbled by a lack of semantic terms and frames of reference. The authors didn’t have predicate calculus to think about, or Minsky’s idea of frames, or Fillmore’s idea of semantic roles, or Rosch’s prototypes or fuzzy categories, or Lakoff’s ideas on categories and metaphors.

They’re doing the best they can with the concepts they have. On verbs, for instance, they reject the old idea that verbs represent actions or passions, pointing out (quite rightly) that there are stative verbs which are neither. They propose that the essence of a verb is that it affirms something— that is, it asserts a proposition about something. The prototypical affirmation is the word est “is”, which is why they restate Petrus vivit as Petrus vivens est. Essentially they’re reducing sentences with verbs to things they have already discussed: objects and attributes.

They have a very short chapter on syntax, whose content is rather disappointing. It amounts to these observations:

  • Some words have to agree with each other, to avoid confusion.
  • Some words require each other (e.g. nouns and subjects), and some words depend on another (e.g. adjectives on nouns).
  • When everything is stated well, without rhetoric, the order of words is “natural” and follows the “natural expression of our thoughts”.
  • However, sometimes people want to be fancy, and they omit words, insert superfluous words, or reverse words.

I’m guessing they were in a hurry to wrap up, because they certainly knew Latin well enough to know that the basic sentence order was different in Latin and French, but also could be more freely varied.

A minor point of interest: PRG frequently, like generative grammar, gives negative examples— things we don’t say. This was by no means common in grammars— Whitney’s Sanskrit grammar, for instance, doesn’t do this.

Should you run out and read it? Eh, probably not, especially as it turns out it’s not a precursor at all to modern syntax. It is interesting if you want to know how early rationalists approached grammar, e.g. if you wanted to write something like Šm Revouse’s grammar for your own conlang.

 

 

 

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I’m up to page 220, which probably means I’m half done with the Syntax Construction Kit. So it’s time for another progress report.

The last book I read, Robert Van Valin’s An introduction to Syntax, is perhaps the least useful on the details of syntax, but the most useful on what syntax has been doing for the last forty years. There are two overall strands:

  • A focus on constituent structure, the path taken by Chomsky.
  • A focus on relations between words: semantic roles, valence, dependencies.

That’s really helpful, and it’s a better framing than the division I learned in the 1980s between Chomskyan syntax and generative semantics.  The problem with that was, in effect, that GS disappeared. So it kind of looked like the Chomskyans won the battle.

But like Sith and Jedi, you can never really get rid of either side in this fight. In many ways GS simply regrouped and came back as Cognitive Linguistics. Plus, it turns out that many of the specific GS ideas that Chomsky rejected in the 1970s… came back in the ’90s as Minimalism. In particular, semantic roles have a place in the theory, and even the semantic breakdown of verbs (show = cause to see) that GS emphasized years ago, and that Chomsky at the time bitterly resisted.

Also, an unexpected side path: in order to understand and explain a lot of modern theories, I’m having to re-read papers I read for my first syntax classes, nearly forty years ago. My professor had pretty good taste in what would prove important.

There’s two challenges in writing this sort of book.

  • How to communicate that Chomsky isn’t the only game in town, without simply writing a brusque travelog of maybe a dozen alternatives
  • How to make this useful and interesting for someone who just wants to write conlangs, man

Van  Valin scupulously divides his page count between the constituent and the relational point of view. I will emphasize relations far more than I originally intended to, but I’m still going to focus on constituent structure. Partly that’s because there’s so much to cover, but it’s also because I’ve already written quite a bit about relations and semantics in my previous books.

But in general, I’m trying for breadth of syntactic data, not depth in Minimalism (or any other school). The problem with the latter approach is that you may learn to create a syntactic tree that your professor won’t scribble red marks over, but you won’t learn why that particular tree is so great. Every theory can handle, say, WH-movement.

Hopefully, that will address the second challenge as well.  As the Conlanger’s Lexipedia gives you a huge amount of information about words, my aim with this book is to give you more things to put in your syntax section than you thought was possible. And hopefully some pretty weird things. Wait till you see a Bach-Peters sentence.

Plus, web toys! I don’t know why more syntax books haven’t been written by computer programmers; it’s a natural fit. Though I have to say: Chomsky should have run his ideas on Minimalism past a programmer. Some of Minimalism is beautifully simple: you can set out the basic structure of a sentence with a minimum of rules. Then, to handle tense and case, question, and movements, you have to add an amazing superstructure of arbitrary, hard-to-generalize rules. The idea is to get rid of ‘arbitrary’ rules like Passive, but the contrivances needed to do so seem just as arbitrary to me.

 

Here it is!

Generated sentence did that frog not sit on these fat big mice?

Note, it’s not minimal, it’s Minimalist. By that I mean, it’s generated by a program that uses Minimalist theory to build sentences.  Here’s the final tree:

CP
    C
        C:Q
        T
            V:did
            T:Past
    TP
        D
            D:that
            N:frog
        T
            T:<Past>
            VP
                Neg:not
                VP
                    D:<that frog>
                    V
                        V:sit
                        P
                            P:on
                            D
                                D:these
                                N
                                    A:fat
                                    N
                                        A:big
                                        N:mice

Still not clear?  I’ve spent the last few days creating a program to model Minimalism.  And I don’t even like it much as a syntactic theory! But I like it for its ambition: give some simple rules for building up a sentence word by word.  This is not, as you might expect, using phrase structure rules; it really is built up word by word, from the bottom up. And that makes it a natural match for programming.

For instance, the above derivation started with the word mice, randomly selected from a list of possible nouns. It then searches the lexicon for things that can be linked with a noun— basically, determiners or adjectives.  So it builds up a prepositional phrase (PP), then looks for something that can be linked with a PP.

The verb sit is marked in the lexicon as waning  PP and also a D. We’ve got the PP, so we can merge sit into the tree. The rules do not allow extending the tree downwards, only upwards, so to get a D we have to find another subtree (that frog), then merge to the left.

The stuff above that… well, that takes a lot more explaining than I can fit in a blog post; you’ll have to wait for the Syntax Construction Kit for that. As a teaser, though, when you see <things in brackets>, they’ve been moved up the tree to another spot; and some of the superstructure handles Do-support— that is, the fact that English requires an inserted do to handle questions that have only bare verbs.

Along the way the program handles determiner agreement (which is why we have these mice),  verbal inflections, and pronoun case (which didn’t happen to be triggered here).

Anyway, I’ll show you the program later; I’m not done with it, though it has about all the features I expect to have.  A lot of it is quite general; you could use it for a conlang or something, if you happened to really like Minimalism.  But some things are pretty kludgy, partly because Minimalism is clunky in spots, partly because English is. Do-support, for instance, is a really weird mechanism.

(Also, I know, didn’t the frog… would be more colloquial, but the current output is at least grammatical, so I may or may not fix that.)

 

I was out with a friend last night, and he asked about the book I’m working on, and I said it was on syntax.  So he asked, reasonably enough, what’s syntax?

Well, how do you answer that for a non-linguist?  This is what I came up with.

Suppose you want to make a machine that spits out English sentences all day long.  There should be no (or very few) repetitions, and each one should be good English.

How would you make that machine in the simplest way possible?

That is, we’re not interested in a set of rules that require the Ultimate Computer from Douglas Adams’s sf. We know that “make a human being” is a possible answer, but we’re looking for the minimum. (We also, of course, don’t want a machine that can’t do it— that misses some sentences, or spits out errors.  We want the dumbest machine that works.)

One more stipulation: we don’t insist that they be meaningful. We’re not conducting a conversation with the machine. It’s fine if the machine outputs John is a ten foot tall bear. That’s a valid sentence— we don’t care whether or not someone named John is nearby, or if he’s a bear, or if he’s a big or a small bear.

That machine is a generative grammar.

The rules of Chomsky’s Syntactic Structures are in fact such a machine— though a partial one.  And along with the book I’m creating a web tool that allows you to define rules and let it generate sentences with the Syntactic Structures rules, or any other set.  It works like a charm.  But the SS rules were not, of course, a full grammar.

Now, besides the amusement value, why do we do this?

  • It’s part of the overall goal of describing language.
  • It puts some interesting lower bounds on any machine that handles language.
  • As a research program, it will uncover a huge store of facts about syntax, most of them never noticed before.  Older styles of grammar were extremely minimal about syntax, because they weren’t asking the right questions.
  • It might help you with computer processing of language.
  • It might tell you something about how the brain works.

I said we wouldn’t worry about semantics, but in practice generative grammar has a lot to say about it. Just as we can’t quite separate syntax from morphology, we can’t quite separate it from semantics and pragmatics.

You might well ask (and in fact you should!), well, how do you make such a machine?  What do the rules look like?  But for that you’ll have to wait for Chapter Two.

At this point I’ve written about 150 pages, plus two web toys.  (One is already available— a Markov text generator.)

I mentioned before that my syntax books didn’t extend much beyond 1990. Now I’ve got up to 2013, kind of. I read a book of that date by Andrew Carnie, which got me up to speed, more or less, on Chomsky’s middle period:  X-bar syntax, government & binding, principles & parameters. The good news is that all this is pretty compatible with what I knew from earlier works, especially James McCawley.

I’m also awaiting two more books, one on Minimalism, one on Construction Grammar.

Fortunately, I’m not training people to write dissertations in Chomskyan (or any other) orthodoxy… so I don’t have to swallow everything in Chomsky.  (But you know, rejecting Chomsky is almost a full time job. He keeps changing his mind, so you have to study quite a lot of Chomsky before you know all the stuff you can reject.)

I’ve been playing with Markov text generators.  There was a little too much for a blog entry, so see my results here. Also includes links to web pages where you can run the generators yourself, or even download my C code to run against your own texts.

Someone over at Metafilter had a great question: What syntactic category are mathematical operands? (Their username is notsnot, in case this needs to go in a dissertation someday.)

Let’s start with something like

Three plus four is seven.

For now, we’ll say the numerals are NPs.  In a construction NP <word> NP, the <word> could be various things: a verb, a conjunction, a preposition. We can immediately rule out verbs, since plus and its friends (minus, times, over, etc.) are not conjugated.

We should also look at non-mathematical sentences, like

Determination plus luck means victory.

Let’s do some syntax. There are some standard though fallible tests for prepositions.  For instance, they can usually be modified by right:

He fell right in the river.
She lives right down the street.
Go to the cave right in the forest.

*Determination right plus luck means victory.
*Three right plus four is seven.

Prepositional phrases (PP) can often be fronted:

Up the hill she walked.
*Plus four three is seven.

You can front a PP and replace the NP with an interrogative, or front just the questioned element:

Sam is the king of England.  Seven is three plus four.
Of what is Sam the king? *Plus what is seven three?
What is Sam king of?  *What is seven three plus?

PPs allow gapping:

Sam is king of England, and Joe, of France.
*Seven is three plus four, and eight, plus five.

These tests aren’t definitive, but plus is failing every one of them. A better match might be conjunctions. Plus, like and, can link NPs or sentences, and can be used multiple times:

Bill and Anne and Rahesh came.  Two plus two plus one make five.
Bill came, and Anne left.  Bill came, plus Anne left.

On the other hand, this transformation sure doesn’t work:

Sam is a king and Sam is a dancer.  >> Sam is a king and a dancer.
X is 4, plus X is sin θ >> *X is 4 plus sin θ.

It looks like the construction S, plus S isn’t really the same plus as in two plus two.  And other operators don’t allow it at all:

*Bill left, minus Anne stayed.
*Bill left, over Anne stayed.

A bigger problem is that English sentences allow literally infinite amounts of inserted material.

Sam and Alice are nobles.
Sam and Alice are fine, just nobles.
Sam and Alice are still nobles.
Sam, prince of Florin, and Alice, duchess of Guilder, are nobles of Sylvania.
Sam and possibly Alice are, as of Tuesday, nobles.

How much of this can we do with mathematical expressions?

Three plus four is seven.
Three plus lovely four is seven.
Three plus four is still seven.
Three, square root of nine, plus four, half of eight, are seven.
Three and possibly four are, as of Tuesday, seven.

These are not impossible, but at best they sound jocular.  The additions are not math; they’re intrusions of ordinary English.

There’s also the complication that mathematical plus and minus can be unary: you can say Minus three plus four is one. You can have a conjunction beginning a sentence (And the Lord said to Moses…), but that’s not how minus is working here; it’s obviously a modifier for three.

Not to belabor the obvious, but many of the basic things we can do with a sentence don’t really work in mathematics.  You can’t really put a mathematical expression in the past tense, or use the present perfect, or use pronouns, or passivize, or insert a relative clause, or nominalize, or cleft, or topicalize.

And all this is looking at a very basic expression that probably did arise out of normal syntax.  It’s even harder to apply our notions of normal English syntax to something like

x equals minus b plus or minus square root of b squared minus four a c over two a.

or

e to the i n equals cosine of n plus i times sine of n.

I’ve gone into this much detail to convince you (and myself) that ordinary English syntax doesn’t really explain mathematical expressions.  I hope my conclusion doesn’t shock or appall you: mathematical expressions don’t follow English syntactic rules; they follow mathematical rules.

Now, maybe you could shoehorn the quadratic formula or Euler’s formula into the syntactic framework of your choice. I will bet you, however, that you’ll end up with a pile of very idiosyncratic special rules and special syntactic categories, and a bunch of ad hoc exclusions of normal English rules.

And there’s an alternative formulation that would end up far simpler than that: mathematical expressions have their own cross-linguistic syntax, based on their written form, and languages have conventions on how to say them aloud.

I don’t think this is terribly surprising… it’s like discovering that the Russian of Tolstoy’s War and Peace contains a number of passages which are written in the Roman alphabet and don’t follow ordinary Russian syntax.  Is this a revolutionary discovery about weird undercurrents of Russian?  No, it’s just that Tolstoy included quite a bit of French in the text.  Similarly, English sentences can have embedded mathematics.

Still, I hadn’t thought about it this way, and I find it interesting that a pretty ordinary part of English turns out to be, well, not really English at all.

Now, for historical and practical reasons, there’s a certain overlap, especially with basic arithmetic. People undoubtedly said “Two and two are four” (or “twá and twá sind féower”) long before international mathematics was formalized. So these behave more like ordinary English than the quadratic formula does.

Plus, the conventions for speaking math out loud were, of course, invented by speakers of the language out of existing (or newly borrowed) words, and follow ordinary language conventions– where possible.  So you can read cos (2θ) as “cosine of two times theta”.  On the other hand you can just read it as “cos two theta”, which probably has no non-math analogue in English.

(I should add that programmers are very familiar with the idea that math expressions have a particular syntax.  They don’t bother with linguistic categories at all; they define their own, such as operators, variables, constants, functions, and statements.)

 

 

The book of mine which I use the most is The Conlanger’s Lexipedia. Enough, in fact, that my paperback copy is getting too worn. So I created a hardcover edition!

clex-hard

Lulu charges more than I’d like, but on the other hand I can put it on sale! So for now, you can pick it up for $28.76. That’s less than it costs to go out for dinner! And heck, I’ve put the hardcover Language Construction Kit on sale too.

I also took the opportunity to update the text, correcting a few embarrassing errors. Also, the latest copy of Word, amazingly, can hold the whole book in memory at once without crashing. So I was able to add the first few chapters to the index.

Go buy a few!

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