The Scope of Semantics

(AKA Katz’s Semantic Theory (Part II). This post discusses chapter 1 of Jerrold Katz’s 1972 opus. For my discussion of the preface, go here.)

If you’ve taken a semantics course in the past decade or two, or read an introductory textbook on the topic published in that time span, you probably encountered, likely at the outset, the question What is meaning? followed almost immediately with a fairly pat answer. In my experience, the answer given to that question was reference1—the meaning of an expression, say dog, is the set of things in the world that that expression refers to, the set of all dogs in this case. Now, I can’t exactly recall my reaction the first time a teacher presented that as an answer to the question of meaning. I might have been wholly unimpressed, or I might have had my mind blown, that way that an impressionable young mind can be blown by someone giving a pat, confident answer to a deep question. Either way, I know that every time I’ve heard that answer2 to the question of meaning since, it’s become less impressive, to the point of being slightly offensive. At best, a pat answer is incomplete; at worst, it’s flat wrong.

Of course, I never really had a better answer to the question of meaning, and most of the other answers on offer seemed much worse. I couldn’t shake the unease I had with reference as an answer, but I couldn’t fully articulate that unease. Which is why I was very quickly drawn into Semantic Theory—Katz pinpoints and articulates the source of that unease on page 3 of the book:

The misconception, it seems to me, lies in the supposition that the question “What is meaning” can be answered in a direct and straightforward way. The question is generally treated as if it were on par with questions like “What is the capital of France?” to which the direct and straightforward answer “Paris” can be given. It is supposed that an answer can be given of the form “Meaning is this or that.” But the question “What is meaning?” does not admit of a direct “this or that” answer; it’s answers is instead a whole theory [emphasis added]. It is not a question like “What is the capital of France?” “When did Einstein retire?” “Where is Tasmania?”because it is not merely a request for an isolated fact, a request which can be answered simply and directly. Rather it is a theoretical question, like “What is matter?” “What is electricity?” “What is light?”

(Katz 1972, p3)

Imagine if, instead of developing theories of matter, electricity, and light, the early physicists had been satisfied with giving a simple answer like Matter is anything you can touch and feel. We wouldn’t have a science of physics, or chemistry. We likely wouldn’t have any science as we know it.

Katz goes on to acknowledge that, if one were to ask a physicist what electricity is, they might give a simple answer, but notes that such an answer would be a highly condensed version of the theory of electromagnetism that has been developed over centuries of inquiry. Similarly, if you were to ask a phonologist what a syllable is, or what pronunciation is, or if you asked a syntactician what a sentence is, or what grammar is, you might get a similar condensed answer with a several big caveats. You certainly wouldn’t get a simple straightforward answer. In fact, one of the first tasks in any introduction to linguistics is to disabuse students of any simple answers that they may have internalized, and even to disabuse them of the notion that simple answers to such questions even exist.

This seems to leave us in a bit of a bind. If we don’t know what meaning is, how can we study it? Katz’s response: the same way we did with chemistry, biology, phonology, etc.—We identify a set of phenomena that are definitely under the umbrella of meaning, and go from there. Not to disappoint, Katz identifies 15 such phenomena which he frames as subquestions to the meaning question:

  1. What are synonymy and paraphrase?
  2. What are semantic similarity and semantic difference?
  3. What is antynomy?
  4. What is superordination?
  5. What are meaningfulness and semantic anomaly?
  6. What is semantic ambiguity?
  7. What is semantic redundancy?
  8. What is semantic truth (analyticity, metalinguistic truth, etc.)?
  9. What is semantic falsehood (contradiction, metalinguistic falsehood, etc.)?
  10. What is semantically undetermined truth or falsehood (e.g., syntheticity)?
  11. What is inconsistency?
  12. What is entailment?
  13. What is presupposition?
  14. What is a possible answer to a question?
  15. What is a self-answered question?

A formidable list to be sure, but, as far as I can tell, modern formal semantics only cares about 11–143. Katz expands on each of these with representative examples. I won’t go into those examples, but they all are based on intuitions that a person would have about linguistic meaning. If one takes these as the leading questions of semantic theory, Katz argues, then the simple answers to the meaning question lose their appeal, as they do not answer the subquestions 1–15, or at least cannot do so without a complex semantic theory to supplement them.

Furthermore, Katz points out that the debates between the competing simple answers all use arguments based on the phenomena that 1–15 as about. Take, for instance, the best known critique of the referentialist answer. If we assume that meaning=reference, then any two expressions that have the same referent, must be synonymous. Gottlob Frege, the godfather of formal semantics, argued that there were expressions which had different meanings but had the same referent, the classic example of which is the morning star and the evening star. The two expressions have different meanings (they differ as to when the star appears in the sky), however they refer to the same object (the planet Venus). And once you start to think about it you can come up with a seeming infinity of such examples.

Katz goes on to show that critiques of other simple answers to the meaning question are based on what hes call “strong pretheoretical intuitions,” all of which raise at least one of questions 1–15. His point here seems to be that we can’t divorce our semantic theory from pretheoretical intuitions such as the ones the form the basis of 1–15, so why not just embrace it? Why not throw away the “leading principles” and just try to build a theory that answers 1–15?

Katz closes the chapter by discussing skepticism with regards to meaning. It’s hard to honestly maintain skepticism, he argues, when we can marshal an extensive body of evidence that meaning exists. That body of evidence starts with an explication of 1–15, but likely extends beyond that. It is even harder to honestly maintain skepticism if we can build a theory that shows the regular and law-like behaviour of the evidence marshaled. Taking a suggestion from Quine (who played a major role in the preface), Katz compares the situation that he finds himself in to that which ancient astronomers found themselves in:

Astronomy found its answer to “What are planets?” by constructing a theory that explained planetary motion on the assumption that planets are physical objects that obey standard mechanical laws. In the same spirit, once we construct a theory that can successfully explain a reasonably large portion of semantic phenomena, we can base our answer to “What is meaning?” on what the theory had to assume meaning was in order to provide its explanations.

(Katz 1972, p10

Semantics, as it is taught and studied today, is commonly considered by non-semanticists to be the most arcane and opaque subfield of linguistics. It’s not clear what is more obscure, the questions that semanticists ask or the formalism that they use to answer those questions. I often wonder if there is something endemic to questions of meaning that make them seem arcane to many, or if it is a failing in the standard answer that leads to this feeling. This chapter of Katz’s book, for me, rules out the former. The questions in 1–15 are far from arcane, or, at least, they’re no more arcane than the questions that occupy the other subfields of linguistics. Maybe if we took Katz’s view of semantics, fewer students would run screaming (or grumbling, or yawning) from semantics classes.

In the next chapter, entitled “On the general character of semantic theory” Katz begins constructing his theory.

Footnotes (the links might not work, sorry)

  1. ^ I learned my semantics in a generative department where reference was the answer. Other departments might have had another answer.
  2. ^ and sometimes I’ve even given that answer as a teacher.
  3. ^ Entailment and inconsistency are the key phenomena. Presuppositions are useful as diagnostics. Questions have only recently gained currency lately it seems.

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.