Episode post here. Many thanks to Maria Araújo for this transcription!
Matt Teichman:
Hello, and welcome to Elucidations. I’m Matt Teichman,
and with me today is Greg Kobele,
Professor of Computational/Experimental Approaches to Grammar, at the Institute
for Linguistics at
the University of Leipzig. And he’s here to
discuss mathematical
linguistics.
Greg Kobele, welcome.
Greg Kobele:
Thank you very much for having me, Matt.
Matt Teichman:
Okay. So probably, a lot of our listeners don’t really
know that much about what linguistics is. And especially those of our listeners
who don’t know what linguistics is might be surprised to hear that math is
somehow involved in it. So I was wondering if we could talk about what exactly
linguists do. Is studying linguistics—how is that different from, for example,
me going off to learn French, or learn Chinese? Is learning a foreign language
the same thing as doing linguistics? Or are they somehow different?
Greg Kobele:
That’s a great question, Matt. So linguistics is a broad
field and I’m going to be speaking about a particular narrow aspect of
it. Linguistics has contact points with language revitalization, with language
documentation, with language change—as well as more narrow things like syntax,
semantics and pragmatics. And I’m going to really be ignoring these—from my
perspective—peripheral aspects of linguistics, and just talking about the
narrowly construed, so to speak, theoretical linguistics, simply because that’s
where my interests lie. I don’t mean to offend anybody, linguistics is a broad
thing. It’s all important; it’s all great.
I think linguistics is really a study of human behavior. So I must confess to having some sort of empiricist leanings. It’s really a study of human behavior; it’s akin to psychology in that respect. And the kind of human behavior that we’re studying is human linguistic behavior, broadly construed. And again, behavior is broadly construed as well. You know, neuroimaging I’m counting as behavior as well. The linguist is trying to discover a particular causal power here that’s relevant in linguistic behavior.
And it’s a hypothesis that there is one coherent one, or rather, that the one coherent one is the one that linguists are studying. But the ultimate goal of linguistics, as I see it, is to contribute to the theory of this causal power— which will then integrate itself with other people’s theories of other causal powers that are contributing to linguistic behavior, or to human behavior in general. And so we’re interested in trying to understand, at the first level, how people use language to do things. And one of the abstractions that we make already, at this point, is how people use language to communicate information.
And again, this narrow picture of the broader human behavior—human linguistic behavior—is further subdivided into how the form of people’s utterances contributes to some aspect of the meaning that is regularly associated with it. And, again, meaning is really only observable through people’s behavior. But we often abstract away from that and think about meaning as an inherent property of the utterance, and we try to figure out how the form of an utterance is associated with its meaning. But the reason I’m engaging in this long spiel is because I think that it’s important not to lose sight of the fact that—even though we’re focusing on these very abstract relations between idealized sounds and idealized meanings—it’s all in service, ultimately, to this more data-driven goal of explaining how people act, or contributing to an explanation of how people act.
Matt Teichman:
So I think one question that people might have about
this project is: what’s the mystery about people’s behavior? Why would there
need to be a whole field of study, maybe even a science, looking at how people
can speak a language? Isn’t it just sort of obvious? You know, I say stuff that
occurs to me, and then—well, what do words mean? I don’t know, I figure out
what words mean by looking them up in the dictionary. So, you know, what’s the
big deal here, from an intellectual perspective? Why is it challenging to do
this?
Greg Kobele:
So I think that there are two relevant points here. One
is that it’s intellectually interesting. Or rather, I think it’s fascinating,
because language is such an intrinsic and inherent property of us, right? We’re
the animal who speaks. And so, studying language, really, is studying something
about ourselves that seems so fundamental to who we perceive ourselves to be.
But the difficulty of these questions becomes really manifest once you start trying to write down exactly how you imagine this process of language learning, or of language use, is going. So if you imagine yourself trying to write down instructions for someone that doesn’t speak the language—that really codifies your ability to do so. A lot of the things that we take for granted, suddenly, become much more mysterious than they otherwise do. So one of the aspects of language that is puzzling—or somehow, at a cocktail party, frustrating for a linguist—is just that we all speak a language. We all do it extremely well, and it comes naturally. And so, a lot of the difficulty involved—the inherent difficulty—is opaque to naive introspection. But even lay people, as soon as they start trying to really rigorously write down what they think is going on, they realize: oh, there’s really much more going on here, than it seems to me at first blush.
Matt Teichman:
Yeah, I think that’s right. I think it’s really easy to
underestimate how much work you’re doing, and what kind of mental jiu jitsu is
going on under the hood, if you even just say something simple. And maybe you
can learn how complicated that is, by the exercise of trying to teach somebody
who doesn’t speak English to speak English. It’s really hard to tell them all
the exact rules they have to follow. There’s just millions of rules.
Greg Kobele:
So, I think one of the difficulties, at the outset, is
this notion of ‘rule’. So there’s this notion of ‘prescriptive rule’ that people
often object to, that is now codified in countries like France or Germany, with
the Academie
Française or the
Duden. And that’s not really what we’re
after. We’re not trying to tell people how to speak. What we’re interested in
is, really, understanding the regularities that manifest themselves in people’s
behavior, and we use things that we call rules to describe these
regularities.
But it’s the regularities that we’re interested in. Not the somehow a priori rules that tell you: this is how you speak English correctly. And one of the fascinating things about language, especially in the United States—an immigrant nation—is that many people come here and speak English in ways that are different from, say, my dialect growing up.
We have no problem understanding each other. And so, really, the mode of communication that we engage in is very flexible. And yet, despite this flexibility, there really are substantive and substantial regularities that can be discovered.
Matt Teichman:
So linguists aren’t interested in telling people: this
is the way you should speak English, versus this other way. That’s not part of
the project. The project is, rather, what we call descriptive. So it’s
analogous to if you were going out into the woods and observing the mating
habits of swallows. You’re not telling the swallows: do it this way. You’re
just trying to find out how they do it.
Likewise, if we’re systematically trying to describe the rules that people obey when they know a language, it’s this descriptive project. You’re going out into the wild, as it were, and observing the way people talk and the rules they follow when they know a language. And then you’re just trying to describe: exactly what are the patterns that they’re observing when they know the language?
Greg Kobele:
So, if I can interrupt you a little bit—
Matt Teichman:
—yeah!
Greg Kobele:
I think that it’s actually quite correct to say that it’s
a descriptive project. But I think that what we’re trying to describe—what we
think of ourselves as trying to describe—is one of the causal powers that is
underlying our actual speech behavior. And so, we think that there’s this
coherent system in the world that is, probably, some aspect of our
psychology. And this causal power is something that is causally relevant in our
actual behavior. And we’re trying to understand this system, so to speak.
And so, we’re engaged in a descriptive project—not trying to tell you what you should do, but we’re trying to understand what you do do—as a way of understanding what this causal power is. The reason I want to make this distinction is because we think that we’re engaged in a predictive enterprise. So, by understanding the nature of this causal power, we’re not just categorizing butterflies in the wild, say. We’re also trying to understand the ways in which your speech behavior is influenced by these properties of you. And so, it’s a project that is really attempting to be a predictive one, a scientific one.
Matt Teichman:
And by causal power, you mean something like the
language faculty. The fact that any human can learn a language and can speak a
language once they’re old enough. Something like that.
Greg Kobele:
That’s a word that people usually use to describe
this. But I think it’s also useful to think of it just in terms of one of the
causal influences on our behavior. Just like my not having had very much to eat
for breakfast does influence the actual behavior that I’m engaging in, in some
way. So there are lots of ways that my behavior is shaped by various things.
Some of them seem less structured and more tangential, some of them seem to be really regular in nature. We’re hoping—and it, thus far, seems to be not untrue—that what you’re calling the language faculty, and what I’m calling this causal power relevant to linguistics—or that linguists are studying, that underlies part of our language behavior—is an internally coherent and consistent object that can be investigated. And we’re trying to understand its laws, so to speak.
Matt Teichman:
Okay, right. So we’re not just looking at: oh look,
these 4,592 sentences are the exact sentences Matt said last week. But we want
to understand where they’re coming from; what’s the principle that’s giving rise
to these sentences that—
Greg Kobele:
—why did Matt say those sentences, and not some other
ones, right?
Matt Teichman:
Yeah, good.
Greg Kobele:
So, the explanation for that is, probably, not due to any
one effect, right? So the reason that Matt said one thing, and not something
else, has a lot to do with what else went on with Matt that day; and what’s
going on in the world; and how Matt was feeling at that time. But it also had
something to do, presumably, with the system of conventions that Matt
internalized as a child, and growing up, that was relevant to the way he tried
to convey certain intentions with linguistic forms. And that’s the kind of thing
that we’re trying to understand.
Matt Teichman:
Okay. So, what would be an example of a pattern that
anybody who knows English observes—that you would think is really easy to just
write down, as you said—but which actually is way more complicated than
initially meets the eye?
Greg Kobele:
So one of the things that is very jarring to a native
speaker to hear is
agreement
mismatches. So, we’re used to saying, ‘I am a linguist’. But if someone says, ‘I
are a linguist’—even though you understand them perfectly well—it’s a very
jarring feeling. You really notice that something went wrong; they weren’t
playing by the same rules that you’re used to.
Matt Teichman:
That’s right, it makes you wince a little bit, as a
speaker of English.
Greg Kobele:
Indeed. And other things don’t necessarily do that. But
the generalizations that seem to obtain, about when people feel comfortable with
certain subjects meeting up with certain verbs, is a little more complicated
than just: ‘the subject of the sentence has a certain grammatical
number and the grammatical
number of the subject of the sentence influences the form of the verb’.
And one thing that we can see is that in more marginal constructions—and by that I mean constructions that aren’t as prominent in your mind when you think about canonical sentences, constructions like existential ‘there’ sentences, such as, ‘There were believed to have been two explosions at the factory last week’—here, the subject of the sentence, the grammatical subject ‘there’, is in the subject position right next to the verb. ‘There were believed to have been two explosions’. But the agreement is not obviously being triggered by ‘there’, because we were saying ‘there were believed to have been two explosions’.
Matt Teichman:
Yeah, ‘there’ isn’t plural, right?
Greg Kobele:
Well I mean, you might think it is, in this sentence. But
just change a small aspect of the sentence, and you say, ‘There was believed to
have been an explosion in the factory the other day’—‘there’ stays the
same. And what’s going on is: you’re changing the number of ‘an explosion’
versus ‘two explosions’. Which, if you think about the sentence—if you were
to write it down—you would see that that occurs, actually, far after the main
verb—the ‘were’, or ‘was’ in the sentence. And so, the trigger (or the
governor of the agreement, the agreement trigger) actually isn’t the subject
(the grammatical subject of the thing that’s in the subject position). It’s
actually something that’s farther down in the clause.
Matt Teichman:
Okay, right. So you might initially have thought that
the way you figure out how to inflect your verb, in a language like English, is:
you match it to certain features of the subject, which is usually around the
beginning of the sentence. So if we have the sentence ‘Matt was believed to have
recorded a podcast’, then ‘Matt’ agrees with the verb ‘was’—cause we didn’t
say ‘Matt were believed’, we said ‘Matt was believed’. So ‘Matt’ is
singular, and ‘was’ takes the singular form.
So the normal way we would think about agreement happening, in most cases, is: you look at the subject noun phrase at the beginning of the sentence and you match it. So if it’s singular, then the verb of the sentence is singular. If it’s plural, then the verb of the sentence is plural. But in these cases with ‘there’, it seems like the verb isn’t matching itself to something at the beginning of the sentence; it’s matching itself to something later on. It’s matching itself—in your case—to explosions, which occur later in the sentence: ‘There were believed to have been several explosions’. ‘Were’ is matching with something later, rather than something earlier.
Greg Kobele:
That’s right. And so, these examples, I think, show that
the generalization that we had originally come up with—that the subject agrees
with the verb—is descriptively true in a number of cases; but that’s not
really the right way to describe what’s going on. Or, in other words, this
notion of subject—as in the trigger of agreement—needs to be distinguished
from subject, the thing that appears in (so to speak) subject position.
Matt Teichman:
And then, I guess, the big decision we have here, if
we’re trying to come up with a theory of what an English speaker knows,
is—option one: verb agreement means the verb always agrees with X, and then we
figure out what X is and how that all works, and we have a general rule. Maybe
option two would be: well, if the sentence begins with ‘there’, agreement
follows this rule. And if the sentence begins with something like ‘Matt’—not
‘there’—then it follows another rule. Is that right?
Greg Kobele:
That’s right. And so we’re trying to understand what a
descriptively adequate characterization of these patterns might look like. But
we’d also like to have an explanation of these patterns that seems regular and
simple, one that isn’t simply a list of cases to consider.
Because in this case, the number of cases may be small; but if you try to list down—as individual rules—statements for each kind of construction, you’re going to end up with a potentially infinite list of constructions, an infinite list of statements. And this is not going to be something that is plausibly representable in a finite way. And so, we need to—we want to essentially take these generalizations that you’re making, and compress them, so that we end up with a finite description of this infinite variety that language exhibits.
Matt Teichman:
Okay, right. So that’s one thing, anyway, that’s at
stake, in the decision about whether we want to split up the rule. If we split
up the rule too many times, then it’s like: we just have an ad hoc rule for
every single sentence, at the limit case. Which is not really explaining
anything. What we want is a rule that’s general—that has a little bit of
explanatory power. And, ideally, which could bring these cases with the word
‘there’ and cases that start with ‘Matt’ under the same heading.
Greg Kobele:
That’s one way to look at it. Another way of thinking
about it is that what we ultimately want is to have a system that can be
learned, right? So this notion of explanatory adequacy, I think, is a shorthand
for an idea about what might be possible to be learned. So we might think that
if we have just a huge list of exceptions, it’s going to be unlikely that that’s
going to be the generalization that a learner comes up with. Whereas, if we have
a very simple and elegant statement—that’s the kind of thing that a
generalizer, a learner, is more likely to converge upon. But, ultimately, this
notion of elegance, I think, in the context of linguistics, is really just a
proxy for a theory of learning.
Matt Teichman:
Right, beause you can’t learn an infinite set of
sentences. That would take more than a lifetime, obviously. In order to be able
to come up with a new sentence that you’ve never heard before—that nobody’s
ever said before—you have to be generating new sentences from some finite
stock of knowledge, or some finite set of rules.
Greg Kobele:
That’s right. So the learner’s representation of his or
her, hypothesis needs to be something that’s finitely specifiable. That’s right.
Matt Teichman:
Another thing, I think, that is surprising to a lot of
people about linguistics is that it’s not like we’re just describing the rules
of English, and then maybe somebody over in France is describing all the rules
of French, and somebody over in China is describing all the rules of Mandarin
Chinese. But rather, there’s collaboration happening between these three
cases—and more languages as well. So that someone’s discovery about the way
some construction works in Mandarin could actually impact my study into what the
rules of English are. What’s the relation there? Why would a discovery about
some other language that has nothing to do with English impact the way I decide
to understand English?
Greg Kobele:
So this is something that’s often a point of controversy
in linguistics. Many people object to the idea that there is only one language,
which is an easy way to understand what you were talking about. So, certainly,
there’s no logical reason why the generalizations about French and about
Swahili, for instance, need to look similar. And while there are some people
that think they should, there are also people that think they needn’t.
But what does seem to be the case—what seems to be difficult to avoid—is the thought that there is a common learning mechanism across individuals growing up in different cultures. And that each of these languages that people learn are the result of using this common language-learning mechanism, in these different learning environments. And so, a very useful way of thinking about the way that discoveries about generalizations or regularities that are present in, say, French is relevant for the generalizations that we might think are present in Swahili, is that we expect the generalizations that the learner is able to pick up on to have some sort of internal coherency—internal consistency. And so, the formal properties of these generalizations should be similar.
The reason that that is the case is that there is no general purpose learner—there is no learner that can learn everything. Learners, by virtue of making one generalization, they rule out the possibility of considering another generalization. And so, the space that the learner is able to navigate in is necessarily constrained in a certain way—and so, you expect that the possible outputs of the language-learning process, given that they’re produced by the same generalizer, have things in common with one another.
It’s not clear whether or not the surface forums of these generalizations need to look very similar, or if there’s just a deeper similarity that’s not surface-apparent that lurks between them. But, of necessity, given what we know about properties of inductive inferrers, there are going to be structural properties that learnable languages share with one another.
Matt Teichman:
Yeah, that makes sense. Because if, for some reason, a
baby born in Kenya moves to the US and is raised here, they’re going to pick up
the exact same US English than anybody who was born here originally picks up. We
all learn language from the same biological starting point. And if that’s right,
then any description we might try to give of what you have to know in order to
know English, or what you have to know in order to know Swahili, or etc., is
going to have to be something that is learnable—that’s one constraint we’re
under. But anybody who is learning any language is starting from the same
point: the point of being a baby.
Greg Kobele:
That’s right. And they have the same procedure for
learning languages.
Matt Teichman:
Right. So, maybe that’s how a discovery about Swahili
could impact my research about English. If somebody who’s researching Swahili
discovers that there’s some distinctive feature Swahili has that illuminate some
fact about how every human being can learn a language—that could impact my
description of English, because I want my description of English to be
consistent with what we know about how people learn languages.
Greg Kobele:
That’s right. Although, to be perfectly frank, there’s
much less work on formal learning of language classes that has been brought into
linguistics. And so, much of this discussion—about how the analysts’
inferences about the structure of one language influence other analysts’
inferences about the structure of another language—has been at the level of a
representation of structure as a proxy for the actual learning algorithm. I
think that the deeper generalization—or the deeper justification—is in terms
of learning. But, as many people doing research on language are not also,
simultaneously, doing research on learning algorithms, they have been adopting a
very preliminary approximation to how learnability should shape inferences about
one language, given another.
Matt Teichman:
Okay, this is great, because we’ve talked a bit about
linguistics now. But probably there are also some question marks in the air
about what any of this has to do with math. We said this was going to be about
mathematical linguistics. Why would mathematics play any role in these
descriptions of rules? I mean, we could just write them in English. And indeed,
that’s the kind of thing you see when somebody who’s trying to learn English
picks up a book describing the rules of the language—those rules are in
whatever language that person speaks.
Greg Kobele:
That’s right.
Matt Teichman:
Yeah. So, what kind of role does math have to play in
understanding how people learn?
Greg Kobele:
I think that mathematics is a wonderful tool for making
descriptions very precise, as well as for comparing descriptions with one
another. And I think that—irrespective of whether or not one is using a
formally precise description to describe something—it’s really the thing
that’s being described that we’re interested in. Because we might use, say,
English to describe the language French, but we don’t think that the grammatical
system of French necessarily has anything to do with, say, the number of letters
that the English description of it contains. There are some aspects of the
description that are clearly accidental, and not reflecting deep and real
properties of the thing being described. I could just as well, describe the
grammatical system of French using English or using German, right? And they
would look different, because they are in different languages, but they would be
about the same thing.
And so I think, really, anyone who’s trying to describe something that they think to be a real thing is interested not in the description, but in the thing itself. One of my advisors in graduate school—my professor, Ed Keenan—had this propensity to dish out wisdom in Zen koan form. And one of the most enlightening things he said to me—among many enlightening things that he said to me—was that if you can’t say something in two ways, you can’t say it at all. And what I take that to mean is that if you have just one way of looking at something, then it’s very, very difficult to know which aspect of that description—that way of looking at things—is reflecting a real and true property of the thing you’re describing, and which is just an accident of the notation; an accident of the way that you’re describing it.
And by having lots of different ways—multiple ways—of looking at the same thing, you’re able to triangulate, as it were, and determine which properties all of these descriptions coincide on, and which ones seem to be particular to each description. And the properties that are particular to a description are unlikely to be real and true properties of the thing that’s being described. And so, we want to be able to describe something in multiple ways, so as to really be able to to look into the noumenal world, and to understand what it is that we’re describing—the really essential properties of the thing being described.
And using mathematics, I think, gives us an edge in doing this. If we have a description that isn’t very precise—that isn’t formalized—it’s very difficult to really know what the properties are that it truly ascribes to things in general, right? Whether they’re artifactual properties, or notational properties, or whether they’re real and true properties, right? An unformalized description is just difficult to understand at a precise level. It’s sometimes the right way to communicate, at an informal level of the ideas involved. But if we’re trying to really understand the essence of the thing that we’re describing, it’s—I think—crucial to be able to make very precise the description of that thing. And then, we can use tools that are well-known in mathematics to compare whether or not two descriptions are actually equivalent; and if they aren’t, where they differ.
Matt Teichman:
So what would be an example of two different
descriptions of the same phenomenon that you might mistake for being two
different phenomena—because you’re getting confused by superficial features
of the notation used to describe each one?
Greg Kobele:
So, I can give you a very abstract characterization of
something, which isn’t exactly what you asked for—you asked for a
‘phenomenon’, but I think maybe an abstract characterization is going to be
sufficient here.
There are many ways of describing a set of strings, maybe a set of strings of letters, of sets of words, of sequences of characters. On the one hand, you can describe them in terms of a logic. You can view a sequence of characters—i.e. a word—as representing a relational structure—i.e. a graph— and you can use a logical sentence to talk about the properties that the graphs you’re interested in need to have. And the sequences of characters that have those properties—all and only those sentences that have those properties—are then singled out by this logical description. That’s one way of describing a pattern.
Another way of describing a pattern is in terms of a machine. You might have a machine that sequentially walks through, or consumes, each of these letters, and it might move from one state to another. And at the end of walking through these sequences of letters, you look at the state that it ends up in. And if it’s a particular state, then you say: this sequence of letters is one of the ones I’m looking for. And if not, then you say: it’s not one of the ones I’m looking for.
Yet another way of describing things is in terms of an algebraic characterization of the patterns you’re interested in—where you might say something like, ‘I’m interested in a pattern where I have a letter, or another letter repeated some number of times, followed by yet another letter repeated some number of times.’
So, it turns out that all of these ways of describing patterns—let me actually be a little more precise. If we use a monadic second-order logic as the logical language, and we use finite-state machines as the machine language, and we use regular expressions as our algebraic description language—all three of these ways of describing patterns, or describing sequences of letters, are equivalent to one another. So you have a logical characterization of a pattern that ends up being inter-translatable into a machine characterization of a pattern, which is itself also inter-translatable with an algebraic characterization of a pattern.
And so, this tells us not only that these different ways of thinking about patterns are the same; it also tells us, I think, that there is some sort of object of study here. There is a ‘realness’ to the kind of pattern that can be classified in any of these ways. There’s some sort of essence of patterns that can be described this way. And the reason that I have that intuition is because the same class of things is identified in a number of very different-seeming ways.
Matt Teichman:
I see. So if we have any big list of, let’s say, strings
consisting of either the letter A or B—so it’d be, like, AB, ABBA, ABBAAAA,
etc. etc.—and we’re trying to analyze the patterns that obtained in that set
of strings, it’s actually kind of an amazing discovery that you can give a
mathematical proof that what looked like three different ways of describing how
complex the patterns underlying a set of the strings are are actually just
interchangeable. Once you have one, you can just mechanically translate into the
other. You can go back and forth between the three.
Greg Kobele:
That’s right. So they’re good for different things, right?
These different description languages do have their individual strengths and
weaknesses. For example, using a logic to describe something can be very elegant
and concise. And using a machine to describe something—in terms of how a
machine acts on it in a step-by-step way—can be less concise. But it can also
be more suggestive of how you might write a computer program that would do that
for you.
And also, certain properties that these patterns have can be more easily proven using one description language than another. But what the equivalence of these description languages tells us—in terms of the things that they’re describing—is that none of them have a monopoly on the properties of the objects that are being described. There is something real there to describe, and we can get at it in very many different ways.
What, I think, this tells us is that when we want to understand where we should have arguments about what the real-world object of investigation is like, it shouldn’t be at the level of: are we using a logic to describe it, or are we using a machine to describe it? These are really just alternative ways of describing the same kinds of things. The disagreements that we should have should be focused not at this level, but at some other level.
Matt Teichman:
How do some of the mathematical methods you’ve just
described fit in with the rest of linguistics? Is it just one super specialized
sub-field of linguistics, or would it be valuable for every linguist to learn a
little bit of some of what’s happening in this area? How does it connect up with
what’s happening in the rest of the field?
Greg Kobele:
I think it’s valuable for everyone to learn a little bit
of this stuff. But I think that the life-cycle, as I like to think of it, of
linguistics works in the following way—or rather, I think it should work in
the following way.
I think that there are people that are really phenomenal at going out and talking with speakers of languages, and collecting data about how languages are used. And there are people that are really phenomenal—and sometimes they’re the same people—at taking these collections of data and trying to systematize them in various ways. I think there are people that are really amazing at that. And there are also people that are very good at—and, again, maybe they’re the same people—that are very good at looking at different people’s systematizations of different datasets—perhaps even from different languages—and coming up with ways to systematize even those. Or ways of describing regularities that seem to crop up in these different peoples’ descriptions of these different languages.
And then, the role that mathematical linguistics can play in this is that: after this is done, the mathematical linguist can look at these descriptions, and these statements of regularities that people have made, and they can identify what kinds of alternative ways of stating the same kinds of generalizations—or even, alternative ways of stating generalizations that are very close to the ones that were previously stated—that cover the same data, that might diverge from them in various ways.
And the mathematical linguist is, I think, trained in understanding different levels of complexity of description—in ways that, often, other people who haven’t studied this aren’t. Certain descriptive generalizations can be proposed that are actually impossible for a computer to actually compute. And that, I think, is not a desirable situation to be in. If we’re claiming that people are computing things that we know that no computing device can actually do, then we either need to say that people are magical, in a certain way—which might be true, but it seems to be something that we wouldn’t want to immediately jump to—or we want to find an alternative way of describing the generalization that’s being made. One that is computationally more respectable and responsible.
And so, I think once the computational linguist, or the mathematical linguist, looks at the generalizations that are being made, suggests ways of unifying them or phrasing them in a different way—they can give them back to the linguist and say, ‘Well, could you talk about them in this way?’ And the linguist can give them back to the descriptive linguist, and that person can go out into the field, collect more data, trying to understand, ‘Is this thing that the mathematical linguist told me to look for—is this out there? Is this going to show that this way of describing things can’t actually be done? Or is it going to show that it isn’t impossible to continue to describe things in this way?’
And I think that this is a continual feedback loop—with people collecting more data, people systematizing that data in a preliminary way, and the mathematical linguist trying to understand what this is telling us about the kinds of deep properties that natural language has, or may have. And then, that feeding back into questions about what new sorts of data should be gathered in order to verify or falsify these ideas. I think that’s a way that mathematical linguistics, and really mathematical approaches to different fields in general, can interact with people that are already in these fields. I think it wouldn’t be desirable if everyone became a mathematical linguist; because then, no one would be out there collecting the data. And no one would be out there making the preliminary systematizations, or generalizations, about the data that mathematical linguists need to have, in order to understand what the properties that language might have could be.
Matt Teichman:
Yeah. So, I have to say—I’ll put my cards on the table
here. I am very excited about this area of research in the field, because it’s
the first time I’ve seen an attempt to unify a lot of disparate theories. Maybe
that’s the kind of thing we associate a little more with physics. Like, there’s
this division of labor where we have theoretical physicists and experimental
physicists. And at least part of what some of the theoretical physicists are
doing is: coming up with a description that just makes it clear how this
discovery and this theory over here hooks up with this other discovery and this
other theory over here.
Because at the end of the day, we’re trying to have a theory that describes one world. And, maybe, it’s a similar thing with language. At the end of the day, we’re trying to describe human language—the ability of humans to learn things—which is one giant, hugely complex phenomenon. And at some point, that’s probably going to involve integrating a bunch of really detailed, specific accounts of really specific phenomena into a bigger whole—in such a way that that whole does not come out looking like a Frankenstein monster, but something with a coherent structure.
Greg Kobele:
Yeah. I’d like to think that one of the things that
mathematical approaches—to theories in general, but to linguistics in
particular—can offer is a way of integrating different sub-fields of
linguistics with one another, and of integrating linguistics with other fields
of study. So, ultimately, we’re going to need to describe how our
generalizations about the structure of language are actually able to be used in
predicting—or describing—actual languages, as they are used. So, we think
that there is this deep and regular structure that is manifesting itself in
language use. But, ultimately, that’s a hypothesis about the best way of
explaining what actually happens in the world. And I think that in order to
really cash out these hypotheses, we need to have them formalized. So that, in
essence, using mathematics as the glue that can connect the different theories,
and different fields, and different sub-fields together.
Matt Teichman:
Greg Kobele, thanks for a discussion that I’m sure was really
stimulating, and it wasn’t just a feature of the way you said things.
Greg Kobele:
Thanks, Matt.
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