Unmoored theory

I’ve written before about the dichotomy of descriptive vs theoretical sciences, but I’ve recently noticed another apparent dichotomy within theoretical sciences—expansionary vs focusing sciences. Expansionary sciences are those whose domain tends to expand—(neo)classical economics seems to claim all human interaction in its domain; formal semantics now covers pragmatics, hand gestures, and monkey communication—while focusing sciences tend to rather constant domain or even a shrinking one—chemistry today is about pretty much the same things as it was in the 17th century; generative syntactic theory is still about the language faculty. Assuming this is true,[1]It’s pretty much a tautology that a science’s domain will either grow, stay constant, or shrink over time the question is, whether it reflects some underlying difference between these sciences. I’d like to argue that the distinction follows from how firm its foundations are, and in particular what I’ll call its empirical conjecture.

Every scientific theory, I think, basically takes the form of a conjoined sentence “There are these things/phenomena in the world and they act like this.” The second conjunct is the formal system that give a theory its deductive power. The first conjunct is the empirical conjecture, and it turns the deductions of the formal system into predictions. While every science that progresses does so by positing new sorts of invisible entities, categories, etc., they all start with more or less familiar entities, categories, etc.—planets, metals, persons, etc. This link to the familiar, is the empirical foundation of a science. Sciences with a firm foundation are those whose empirical conjecture can be uncontroversially explained to a lay person or even an expert critic operating in good faith.

Contemporaries of, say, Robert Boyle might have thought the notion of corpuscles insanity, but they wouldn’t disagree that matter exists, exists in different forms, and that some of those forms interact in regular ways. Even the fiercest critic of UG, provided they are acting in good faith, would acknowledge that humans have a capacity for language and that that capacity probably has to do with our brains.

The same, I think, cannot be said about (neo)classical economics or formal semantics.[2]Now obviously, there’s a big difference between the two fields—neoclassical economics is extremely useful to the rich and powerful since it let’s them justify just about any … Continue reading Classical economics starts with the conjecture that there are these members of the species homo economicus—the perfectly rational, self-interested, utility maximizing agent—and derives theorems from there. This is obviously a bad characterization of humans. It is simultaneously too dim of a view of humans—we behave altruistically and non-individualistically all the time—and one that gives us far too much credit—we are far from perfectly rational. Formal semantics, on the other hand, starts with the conjecture that meaning is reference—that words have meaning only insofar as they refer to things in the world. While not as obviously false as the homo economicus conjecture, the referentialist conjecture is still false—most words, upon close inspection, do not refer[3]I could point you to my own writing on this, the works of Jerrold Katz, and arguments from Noam Chomsky on referentialsm, or I could point out that one of the godfathers of referentialism, Ludwig … Continue reading, and there is a whole universe of meaning that has little to do with reference.

Most economists and semanticists would no doubt object to what the previous paragraph says about their discipline, and the objections would take one of two forms. Either they would defend homo economicus/referentialism, or they would downplay the importance of the conjecture in question—“Homo economicus is just a useful teaching tool for undergrads. No one takes it seriously anymore!”[4]Though, as the late David Graeber pointed out, economists never object when homo economicus is discussed in a positive light. “Semanticists don’t mean reference literally, we use model theory!”—and it’s this sort of response that I think can explain the expansionary behaviour of these disciplines. Suppose we take these objections to be honest expressions of what people in the field believe—that economics isn’t about homo economicus and formal semantics isn’t about reference. Well then, what are they about? The rise of behavioural economics suggests that economists are still looking for a replacement model of human agency, and model theory is basically just reference delayed.

The theories, then, seem to be about nothing at all—or at least nothing that exists in the real world—and as a result, they can be about anything at all—they are unmoored.

Furthermore, there’s an incentive to expand your domain when possible. A theory of nothing obviously can’t be justified by giving any sort of deep explanation of any one aspect of nature, so it has to be justified by appearing to offer explanations to a breadth of topics. Neoclassical economics can’t seem to predict when a bubble will burst, or what will cause inflation, but it can give what looks like insight into family structures. Formal semantics can’t explain why “That pixel is red and green.” is contradictory, but it provides a formal language to translate pragmatics into.

There’s a link here to my past post about falsification, because just as a theory about nothing can be a theory about anything, a theory about nothing cannot be false. So, watch out—if your empirical domain seems to be expanding, you might not be doing science any more.

References

References
1 It’s pretty much a tautology that a science’s domain will either grow, stay constant, or shrink over time
2 Now obviously, there’s a big difference between the two fields—neoclassical economics is extremely useful to the rich and powerful since it let’s them justify just about any horrendous crimes they would want to commit in the name of expanding their wealth and power, while formal semantics is a subdiscipline of a minor oddball discipline on the boundaries of humanities, social science, and cognitive science. But I’m a linguist, and I think mostly linguists read this.
3 I could point you to my own writing on this, the works of Jerrold Katz, and arguments from Noam Chomsky on referentialsm, or I could point out that one of the godfathers of referentialism, Ludwig Wittgenstein, seems to have repudiated it in his later work.
4 Though, as the late David Graeber pointed out, economists never object when homo economicus is discussed in a positive light.

What does falsification look like anyway?

Vulcan vs Neptune

There’s an argument that plays out every so often in linguistics the goes as follows:

Critic: This data falsifies theory T.
Proponent: Not necessarily, if you consider arguments X,Y, and Z.
Critic: Well, then theory T seems to be unfalsifiable!

This is obviously a specious argument on the part of the critic, since unfalsified does not entail unfalsifiable, but I think it stems from a very understandable frustration—theorists often have an uncanny ability to wriggle free of data that appears to falsify their theories, even though falsificationism is assumed by a large majority of linguists. The problem is that the logic falsificationism, while being quite sound, maybe unimpeachable, turns out to be fiendishly difficult to apply.

At its simplest, the logic of falsificationism says that a theory is scientific insofar as one can construct a basic statementi.e., a statement of fact—that would contradict the theory. This, of course, is an oversimplification of Karl Popper’s idea of Critical Rationalism in a number of ways. For one, falsifiability is not an absolute notion. Rather, we can compare the relative falsifiability of two theories by looking at what Popper calls their empirical content—the number of basic statements that would contradict them. So if a simple theoretical statement P has a particular empirical content, then the conjunction P & Q will have a greater empirical content, and the disjunction P v Q will have a lesser empirical content. This is a useful heuristic when constructing or criticizing a theory internally, and seems like a straightforward guide to testing theories empirically. Historically, though, this is not the case, largely because it is often difficult to recognize when we’ve arrived at and accurately formulated a falsifying fact. In fact, it is often, maybe always, the case that we don’t recognize a falsifying fact as such until after one theory has been superseded by another.

Take for instance the case of the respective orbits of Mercury and Uranus. By the 19th century, Newtonian mechanics had allowed astronomers to make very precise predictions about the rotations of the planets, and based on those predictions, there was a problem: two of the planets were misbehaving. First, it was discovered that Uranus—then the last known planet from the sun—wasn’t showing up where it should have been. Basically, Newton’s mechanics predicted that on such and so day and time Uranus would be in a particular spot in the sky, but the facts were otherwise. Rather than cry “falsification!”, though, the astronomers of the day hypothesized an object on the other side of Uranus that was affecting its orbit. One such astronomer, Urbain Le Verrier was even able to work backwards and predict where that object could be found. So in September of 1846, armed with Le Verrier’s calculations, Johann Gottfried Galle, was able to observe an eighth planet—Neptune. Thus, an apparent falsification became corroboration.

Urbain Le Verrier (1811-1877)
Johann Galle (1812-1910)

I’ve previously written about this story as a vindication of the theory first approach to science. What I didn’t write about, and what is almost never discussed in this context is Le Verrier’s work on the misbehaving orbit of Mercury. Again, armed with Newton’s precise mechanics, Le Verrier calculated the Newtonian prediction for Mercury’s orbit, and again[1]Technically though, Le Verrier’s work on Mercury predated his work on Uranus Mercury didn’t behave as expected. Again, rather than throw out Newtonian mechanics, Le Verrier hypothesized the planet Vulcan between Mercury and the sun, and set about trying to observe it. While many people claimed to observe Vulcan, none of these observations were reliably replicated. Le Verrier was undeterred, though, perhaps because observing a planet that close to the sun was quite tricky. Of course, it would be easy to paint Le Verrier as an eccentric—indeed, his Vulcan hypothesis is somewhat downplayed in his legacy—but he doesn’t seem to have been treated so by his contemporaries. The Vulcan hypothesis wasn’t universally believed, but neither does it seem to be the Flat-Earth theory of its day.

It was only when Einstein used his General Theory of Relativity to accurately calculate Mercury’s orbit, that the scientific community seems to have abandoned the search for Vulcan. Mercury’s orbit is now considered a classical successful test of General Relativity, but why don’t we consider it a refutation of Newtonian Mechanics? Strict falsificationism would seem to dictate that, but then a strict falsificationist would have thrown out Newtonian Mechanics as soon as we noticed Uranus misbehaving. So, falsificationism of this sort leads us to something of a paradox—if a single basic statement contradicts a theory, there’s no way of knowing if there is some second basic statement that, in conjunction with the first, could save the theory.

Still, it’s difficult to toss out falsification entirely, because a theory that doesn’t reflect reality, may be interesting but isn’t scientific.[2]Though sometimes, theories which seem to be empirically idle end up being scientifically important (cf. non-Euclidean geometry) Also, any reasonable person who has ever tried to give an explanation to any phenomenon, probably rejects most of their own ideas rather quickly on empirical bases. We should instead adopt falsificationism as a relative notion—use it when comparing multiple theories. So, Le Verrier was ultimately wrong, but acted reasonably—he had a pretty good theory of mechanics so he worked to reconcile it with some problematic data. Had someone developed General Relativity in Le Verrier’s time, then it would have been unreasonable to insist that a hypothesized planet was a better explanation than an improved theory.

Returning to the hypothetical debate between the Critic and the Proponent, then, I think a reasonable albeit slightly rude response for the proponent would be “Well, do you have a better theory?”

References

References
1 Technically though, Le Verrier’s work on Mercury predated his work on Uranus
2 Though sometimes, theories which seem to be empirically idle end up being scientifically important (cf. non-Euclidean geometry)

Chris Collins interviews Noam Chomsky about formal semantics

Over on his blog, Chis Collins has posted the text of a conversation he had over email with Noam Chomsky on the topic of formal semantics. While Chomsky has been very open about his views on semantics for a long time, this interview is worth reading for working linguists because Collins frames the conversation around work by linguists—Heim & Kratzer, and Larson & Segal—rather than philosophers—Quine, Austin, Wittgenstein, Frege, et al.

You should read it for yourself, but I’d like to highlight one passage that jumped out at me. Of the current state of the field, Chomsky says:

Work in formal semantics has been some of the most exciting parts of the field in recent years, but it hasn’t been treated with the kind of critical analysis that other parts of syntax (including generative phonology) have been within generative grammar since its origins. Questions about explanatory power, simplicity, learnability, generality, evolvability, and so. More as a descriptive technology. That raises questions.

p 5. (emphasis mine)

It’s true that formal semantics today is a vibrant field. There’s always new analyses, The methods of formal semantics are being applied to new sets of data, and, indeed, it’s virtually impossible to even write a paper on syntax without a bit of formal semantics. Yet it is also true that almost no one has been thinking about the theory underpinning the analytical technology. As a result, I don’t think many working semanticists are even aware that there is such a theory, or if they are aware, they tend to wave their hands, saying “that’s philosophy”. Formal semanticists, it seems, have effectively gaslit themselves.

Chomsky’s framing here is interesting, too. He could be understood as suggesting that formal semantics could engage in theoretical inquiry while maintaining its vibrancy. It’s not clear that this is the case though. Currently, formal semantics bears a striking similarity to the machine-learning/neural-nets style of AI, in that both are being applied to a very wide array of “problems” but a closer look at the respective technologies very likely would cause us to question whether they should be. Obviously, the stakes are different—no one’s ever been injured in a car crash because they used lambdas to analyze a speech act—but the principle is the same.

But I digress. Collins and Chomsky’s conversation is interesting and very accessible to anyone who familiar with Heim & Kratzer-style semantics. It’s well worth a read.

The Poverty of Referentialist Semantics

(What follows is a bit of a rant. I hope it holds together a bit. If you make it past the inflammatory title, let me know what you think.)

When Gregor Mendel first discovered his Laws of Inheritance, it was a great revelation. To be sure, humanity has perhaps always known that many of a person’s (or plant’s, animal’s, bacterium’s, etc) traits are inherited from their parents, but Mendel was able to give that knowledge a quantitative expression. Of course, this was just the beginning of the modern study of genetics, as scientists asked the next obvious question: How are traits inherited? This question persisted for the better part of a century until a team of scientists showed experimentally, that inheritance proceeds via DNA. Again, this raised a question that has spurred research to this day: How does DNA encode physical traits? But why am I writing about genetics in a post about semantics? Well, to make a point of contrast with the theory that has dominated the field of linguistic semantics for the past few decades: Formal Semantics.

As in the case of inheritance, we’ve always know that words, phrases, and sentences have meanings, but we’ve had a tougher time understanding this fact. In the late 19th and early 20th century philosophers, psychologists and linguists seemed to settle on a way of understanding linguistic meaning: linguistic expression are meaningful by virtue of the fact that they refer to objects in the world. So, “dog” has a meaning for modern English speakers because it refers to dogs. This principle has led the modern field of semantics, although not in the same way as the discoveries of genetics led that field. If semanticists had proceeded as the geneticists had, they would have immediately asked the obvious question: How do linguistic expressions refer to objects in the world? Instead of pursuing this question, semanticists seem to have banished it and, in fact, virtually any questions about the reference relation, and have done so, I believe, to the detriment of the field.

At first blush, it might seem that semanticists should be forgiven for not centring this question in their inquiry. Curiosity about genetic inheritance, to continue my comparison, is quite natural, likely because we can observe its facts objectively. Certainly, it’s a cliché that no one likes to admit that they’re like their parents. There is very little resistance, on the other hand, to seeing such a similarity in other people. The facts of inheritance are unavoidable, but they are not coupled with anything approaching intuition about them. In fact, many of the facts are fundamentally unintuitive: How can a trait skip a generation? Why does male pattern baldness come from the mother’s side? How can a long line of brown-eyed people produce a blue-eyed child? This dearth of intuition about an abundance of evidence means that no one objects to followup questions to any scientific advance in the field. In fact, the right kind of follow-up questions are welcomed.

On the other hand, linguistics, especially generative linguistics, faces the opposite situation. In many ways, the object of generative inquiry is our intuitive knowledge about our own language. It should be obvious here that the average person’s intuitions about language vastly outweigh the objective facts about language.* Our intuitions about language are so close to our core, that it is very uncomfortable for us to entertain questions about it. We like to think that we know our own minds, but a question like what is language?—properly pursued—highlights just how little we understand that mind. This is not to say it’s an unanswerable or ill-formed question; it’s not a species of zen kōan. Language exists and we can distinguish it from other things, so, unlike the sound of one hand clapping, it has a nature that we can perhaps gain some understanding of. In fact, the field of generative syntax shows us that language is amenable to rational inquiry, provided researchers are open to follow-up questions: Chomsky’s initial answer to the question was that language is a computational procedure that generates an infinite array of meaningful expressions, which raised the obvious question: What sort of computational procedure? In many ways this is the driving question of generative syntactic theory, but it has also raised a number of additional questions, some of which are still open.

Just as what is language? is a difficult question, so are what is meaning? and how do words refer? So semanticists can be forgiven for balking at them initially. But, again, this is not to say that these are unanswerable questions in principle. What’s more, I don’t think semanticists even attempt to argue that the questions are too hard. On the contrary, the answer to the questions are so obvious that they don’t warrant a response. Are they right? Is it a boring, obvious question? I don’t think so. I think it is an interesting question whose surface simplicity masks a universe of complexity. In fact, I can demonstrate that complexity with some seemingly simple examples.

Before I demonstrate the complexity of reference in language, let’s look at some simple cases of reference to get a sense of what sort of relation it is. Consider for instance, longitude and latitude. The string 53° 20′ 57.6″ N, 6° 15′ 39.87″ W refers to a particular location on earth. Specifically it refers to the location of the Dublin General Post Office. That sequence of symbols is not intrinsically linked to that spot on earth; it is linked by the convention of longitude and latitude, which is to say it is linked arbitrarily. Despite its arbitrary nature, though, the link is objective; it doesn’t matter who is reading it, it still refers to that particular location. Similar remarks apply to variable assignment in computer programs, which are arbitrarily linked to a location in a computer’s RAM, or numerals like 4 or IV, which are arbitrarily linked to a particular number (assuming numbers have objective reality). These seem to suggest the following definition of the reference relation.

(R) reference is the arbitrary and objective mapping between symbols and objects or sets of objects.

For a moment, let’s set aside two types of expressions: subjective expressions like my favourite book, or next door, and proper names like The Dublin General Post Office, or Edward Snowden. For the purposes of this post, I will grant that the question of how the latter refer is already solved, and the question of how the former refer is too difficult to answer at this point. Even if we restrict ourselves to common nouns that ostensibly refer to physical objects, we run into interesting problems.

Consider the word “chair”. English speakers are very good at correctly identifying certain masses of matter as chairs, and identifying others as not chairs. This seems like a textbook case of reference, but how are we able to do it?

A chair

Not a chair

In order for reference to obtain here, there must be some intrinsic property (or constellation of properties) that marks the thing on the left as a chair and is lacking in the thing on the right. Let’s skip some pointless speculation and settle on shape as the determining factor. That is, chairs are chairs by virtue of their shape. And let’s grant that that chair-shape can be codified in such a way as to allow reference to obtain. That would be great, except that it still doesn’t fully capture the meaning of “chair”.

Suppose, for instance, a sculptor creates an object that looks exactly like a chair, and an art gallery buys it to display as part of its collection. Is that object a chair? No, it’s a sculpture. Why? Because it no longer serves the function of a chair. So the objective shape of an artifact is not sufficient to determine it’s chair-ness; we need to say something about its function, and function, I would argue, is subjective.

Or consider the following narrative:

Sadie has just moved into her first apartment in a major Western city and she needs to furnish it. Being less than wealthy she opts to buy furniture from Ikea. She goes online and orders her Ikea furniture. The next day three flat-pack boxes arrive at her door: One contains a bookshelf, one contains a bed, and the other contains a chair.

In what sense does that box contain a chair? It contains prefabricated parts which can be assembled to form a chair. Neither the box, nor its contents are chair-shaped, yet we’re happy to call the contents a chair. What if Sadie were a skilled woodworker and wanted to build her own furniture from, say, several 2-by-4s. Would we call those uncrafted 2-by-4s a chair? I don’t think so. Let’s continue the narrative.

Sadie assembles her furniture and other furniture and enjoys it for a year, at which point her landlord decides to evict her in order to double the rent. Sadie finds another apartment and pack up her belongings. In order to facilitate the move she disassembles her furniture and puts them the the trunks of the cars of her various helpful siblings. Her bookcase goes with Rose, her bed with Declan, and her chair with Violet.

Again, we refer to a bundle of chair parts as a chair. What if Sadie had taken out her anger at being evicted by her greedy landlord on the chair, hacking it to pieces with an axe? Would the resulting pile of rubble be a chair? Certainly not.

What does this tell us about how the word “chair” is linked to the object that I’m sitting on as I write this? That link cannot be reference as defined above in (R), because it’s not purely objective. The chair-ness of an object depends not only on its objective form, but also on its subjective function. And this problem will crop up with any artifact-word (e.g., “table”, “book”, “toque”). If we were to shift our domain away from artifact-words, no doubt we’d find more words that don’t refer in the sense of (R). Maybe we’d find real honest-to-goodness referring words, but we’d still be left with a language that contains a sizable chunk of non-referential expressions. Worse still, modern formal semanticists have expanded the universe of “real objects” to which expressions can refer to include situations, events, degrees, and so on. What’s the objective nature of an event? or a situation? or a degree? No idea, but I know them when I see them.

“So what?”you might say. “Formal semantics works. Just look at all of the papers published, problems raised and solved, linguistic phenomena described.Who cares if we don’t know how reference works?” Well, if semantics is the study of meaning, and meaning is reference, then how can there be any measure of the success of semantics that isn’t a measure of it understanding of what reference is?

Again, consider a comparison with genetics. What if, instead of asking follow-ups to Mendel’s laws, geneticists had merely developed the laws to greater precision? Our current understanding of genetics would be wildly impoverished. We certainly would not have all of the advances that currently characterize genetic science. Quite obviously genetics is much the richer for asking those follow-up questions.

No doubt semantics would be much richer if it allowed follow-up questions.


* It is precisely this situation that makes it so difficult to communicate the aims of generative linguistics, and why the main type of linguistics that gains any sort of traction in the mainstream press is the type that looks at other people’s language. Consider the moral panic about the speech patterns of young women that surfaces every so often, the NY Time Bestseller Because Internet, by Gretchen McCulloch, which looks at the linguistic innovation on the internet, or even the current discussion about the origins of Toronto slang. To paraphrase Mark Twain, nothing so needs research and discussion as other people’s language.

I’m being generous here. In fact, most paradoxes of reference are about proper names (See, Katz, J. J. (1986). Why intensionalists ought not be Fregeans. Truth and interpretation, 59-91.)

Katz’s Semantic Theory (Part I)

(This is intended to be the first in a series of posts in which I work my way through Semantic Theory by Jerrold Katz)

Through a somewhat meandering intellectual journey that I undertook when I probably should have been writing, I found myself reading the late Jerrold J Katz’s 1972 book entitled Semantic Theory. While I began that book with a certain amount of cynicism—I think I’ve been disappointed by virtually every book that tries to develop a theory of semantics—that cynicism evaporated very quickly. It evaporated as soon it became obvious that the theory that Katz intended to develop was radically different from the theory of semantics that contemporary linguists assume and that the source of that radical difference was that Katz shared the core assumptions of generative grammar.

That last sentence, or rather its implication, may be a bit inflammatory, but I think it’s justified, for reasons that Katz elucidates.

In his preface, Katz gives something of a historical narrative of linguistics and logic in the first half of the 20th century. He picks this time frame because of what he views as an unfortunate schism that occurred in those years. His basic story is as follows. Throughout most of their history, logic and linguistics were united by their interest in what Katz calls “the classical problem of logical form,” which is clear when you consider, for instance, that the notion of subject and predicate comes from Aristotle’s logical treatise On Interpretation, or that one of the leading logical works from the renaissance to the 20th century, The Port Royal Logic, was written and published along with the Port Royal Grammar. In the 20th century, though, something happened and the two fields went their separate ways, away from the classical problem.

By Katz’s estimation, there are three factors that led to the schism: (i) The professionalization of the fields, (ii) the difficulty of the classical problem, and (iii) the dominance of empiricism in the fields. Since the story of linguistics in this period has been covered quite a bit, Katz doesn’t waste much time on it, and neither will I. The story of logic, however, interests Katz (more of a philosopher than a linguist) a great deal, and I think is useful in understanding current theories of semantics. Logicians in the early 20th century, influenced by the Katz’s three factors, abandoned the problem of logic form and sought out “manageable problems.” The problem, or perhaps program is the better word for it, that they landed on was the development of artificial languages with which to represent thought. These artificial languages, unlike natural language, wore their logical form on their sleeves, to borrow Katz’s formulation.

In order to formulate an artificial logical language, Quine—one of the Katz’s chief villains—sought to identify and highlight the “logical particles” of natural language as distinct from the extra-logical vocabulary. The logical particles (e.g., and, or, not, if—then) are those that have inferential powers, while the extra-logical words (e.g., dog, bachelor, Moira, lamp) are those that have only referential powers. This seems fairly intuitive, but Katz argues that there is no non-arbitrary way of dividing logical vocabulary from extralogical vocabulary. This is certainly an odd assertion. I mean, it’s pretty obvious that and is a logical word and dog isn’t, right? While it might be a valid intuition that these are different sorts of words, what Katz argues is that the set of words that have inferential powers is much larger than what we might call the logical particles.

To show this, Katz walks us through a possible method for identifying logical particles and demonstrates that this method cannot actually rule out any word as a logical particle. The method starts by examining a valid inference such as (1)–(3).

 (1) All terriers are dogs.
  (2) All dogs are animals.
  (3) Hence, all terriers are animals.

We can see that (1)–(3) remains valid regardless of the meaning of dogs, animals, and terriers; that is, we could replace the tokens of those words with tokens of virtually any other nouns and we’d still have a valid inference. By the same token, though, the validity of (1)–(3) depends on the meaning of all, are, and hence. So, we remove from our list of candidates for logical particles, the words that can be factored out of such valid inferences. Katz argues that, while this method gives the expected results for classical syllogisms and perhaps some other logical inferences, things get messy when we look at the full range of valid inferences

Katz presents (4) and (5) as a valid inference, but argues that the method of factoring we applied to (1)–(3) gives different results here.

 (2) Socrates is a man.
 (3) Hence, Socrates is male.

We can factor out Socrates here, but not man or male. The inference from (4) to (5) seems to depend on the meaning of the latter two words. If we follow our methodology, then we have to add male and man to our logical particles, because they seem to have inferential powers. With a few moments of thought, we can see that this leads to a situation where there is no logical/extra-logical distinction, because every word is a logical particle. Thus Quine’s program is doomed to failure.

As anyone who has leaned any formal logic knows, though, Quine’s program became the orthodoxy. And, in fact, his conception of logic is, in many ways, the basis for semantics as practiced by contemporary generative grammarians. Katz identifies the work of George Lakoff and that of Donald Davidson as early attempts to apply Quinean logic to language, and it continues to today.

As something of an aside, formal semanticists, seem to take as given the assertion that there is a privileged class of logical particles, and try to analyze a portion of the vocabulary that lies outside of that class so that it can be expressed using the logical particles and some simple atomic extra-logical “words.” what belongs to that analyzable portion of vocabulary is not well defined; I know that know, and should are in that portion and I know that dog and wallet are outside of that portion, but I can’t really get much more specific than that.

What’s stranger is that even some of those words that correspond to logical particles are up for analysis. And, triggers some implicatures which are often analyzed using the Quinean tools. The meaning of if—then, is also up for debate. I almost wrote a paper as part of my PhD on conditionals and the one thing that the semantic literature seems to agree on is that the meaning of if—then is not the material conditional (→). Being a naive syntactician, with no understanding of the history of logic, I basically took formal logic as gospel. It never occurred to me that the logician’s conception of conditional statements could be flawed.

Of course, if Katz is correct, then logics built on Quine’s logical/extra-logical distinction are the proverbial houses built on sand. And if I’m correct that formal semantics is built on Quinean logic, then formal semantics is a proverbial house built on a house built on sand. End of aside.

Having argued that the empiricist theories of logic such as those of Quine, Frege, and Carnap are unsuited for inclusion in a rationalist theory of language such as generative grammar, Katz moves on to the next task, the one that occupies the remainder of his book: the task of constructing a rationalist and scientific theory of semantics. According to Katz, this task was viewed by the philosophers of his day as an impossibility, and I don’t know if much has changed.

In fact, it seems to me that among semanticists and a number of generative syntacticians, there is a strong hostility towards rationalist conceptions of semantics as put forth by Katz (and also Chomsky). As an illustrative anecdote, I recall once I was talking with an established linguist, and I expressed some skepticism towards modern formal semantics. When I suggested that a more rationalist, intensionalist theory of semantics might be fruitful, they responded that, while I might be right, if I decided to pursue that line of research, I would never be hired as a semanticist. Luckily for me, of course, I’m a syntactician, but that’s still a rather chilling thing to hear. End of second aside.

Katz concludes his preface by putting his program in context, and outlining the structure of the book. I won’t bore you with the details, but only preview chapter 1 “The scope of semantics,” wherein Katz considers the question what is meaning?, and gives a shockingly sensible answer: That’s a complex question, we’ll need to answer it scientifically.

A test of the language vs communication contrast

One of Chomsky’s more controversial claims regarding language is that it is not a communication system, rather that it evolved as a system of thought which was then externalized and used for communication. It’s perfectly understandable why this would be controversial, as it seems false on its face. We use language all the time to communicate. In fact it may seem like that’s all we use it for. If we think about it briefly we can come up with many non-communicative uses of language. We talk to ourselves to help ourselves think, we use it for play, we use it to aid our memory, and so on. It’s uncontroversial both that language is used communicatively and non-communicatively, but the question is: Which came first?

While there are arguments on either side of the debate, there isn’t a tonne of evidence that speaks directly to it. We don’t have time travel to go back and observe the early development of humanity, and our tools for objectively testing either claim on present-day humans are still too blunt to be of any use. What we can do is compare language to an unambiguously communication-first system: physical gestures. We certainly use gestures to augment language, but we certainly can use language without gestures and gestures without language. When we gesture without language we are certainly communicating but we aren’t using a language.

So, If you’re on board with me so far (language and gesture are distinct systems, and gesture is communicative), we can get some evidence that language is not inherently communicative. If it were communicative, we would expect it to operate like a communicative system (i.e., gesture) in a context where communication is not called for.

The test is as follows: First, be alone (the next time you find yourself alone in a room would be a good time to try it out). Second, don’t be reading, watching TV/Movies, or listening to anything (Isolate yourself from virtual people). Once you’re isolated, say something aloud. It doesn’t matter what, whatever comes naturally. Next, gesture. Point at something, shush the room, make an obscene gesture. But make sure it’s not accompanied with any language. Consider how unnatural one of these tasks felt compared to the other. If you’re like me, one will feel a bit odd, and the other will feel like one of the strangest things you’ve ever done.

A tiny note on language as communication technology

In The Language Myth Vyvyan Evans presents the proposal that human language is a species of communication technology like writing systems, telephones, or computer networks. Just as we have no innate capacity for reading/writing, dialling phones, or clicking on links, we have no innate capacity for language. Instead, we humans were endowed with increased general cognitive ability, which allowed us to iteratively develop language, writing, telephony and computer networks. We know from archaeology, historical records and our own memories that communication technologies such as writing systems, telephony, and networked computing (along with a host of non-communication technologies) have undergone periods of exponential improvement. Science, philosophy, and math has shown in some cases that certain technologies (e.g., computer programming languages) have advanced to their logical or physical limits, or in other cases (e.g.,Audio encoding) have advanced to the limits of human cognition. 
This proposal makes a prediction about language. Either it is still advancing,  it has reached its logical limits, or it is at the limits of human cognition. The second option has been shown to be false as there are classes of language which are more expressive than human language. The first and third, however, are viable hypotheses. The first hypothesis, that language continues to improve like, say, photovoltaic cells, seems like it would be quite demonstrable if it were true. Since we have known for centuries that the language spoken by a given generation varies, albeit slightly, from that of the previous generation, a scientist seeking to provide evidence for the first hypothesis would only have to demonstrate a general trend of improvement in a language across generations. I know of no studies that provide such a demonstration. This leaves the third hypothesis: that language has developed to the limit of human cognition. Notice that the third hypothesis is the UG hypothesis: that humans are born with an innate capacity for language. Absent any evidence of language improvement, Evans’ proposal is the UG hypothesis.