Thursday, November 26, 2009

A Failed-Self Reference Argument

Steven Goldberg is an American sociologist. In his book, When Wish Replaces Thought, he proposes the following argument against descriptivism, which he seems to think is completely decisive. I found the argument interesting, because it attempts to use self-reference in much the way Turing's proof that the halting problem is unsolvable does. Unfortunately, Goldberg's argument is flawed in several respects.

Here is the relevant passage, which appears on pp. 193-194:


"People with more than a passing interest in words fall into two groups, prescriptivist and descriptivist. The prescriptivist believes that there is an ideal of correctness in the use of words - shifting and temporally based as it ultimately may be. The descriptivist finds the concept of "correctness" elitist at best and, more often, incomprehensible.

"The one inviolable rule of descriptivism is this: There are no correct definitions, meanings, or usages other than those used by people-in-general; any attempt to substitute a definition, meaning, or usage for that used by people-in-general is invalid. Where the prescriptive subordinates popular usage to correct usage, the descriptivist denies to correctness
and all other criteria parity with use by people-in-general.

"Now consider what happens when you ask a descriptivist how he defines "dictionary" in his descriptivist dictionary.

"The descriptivist might, as his inviolable rule says he must, accept the definition of "dictionary" used by people-in-general. If he does this, he will define "dictionary" as people-in-general really do, as giving correct definitions, correctness being determined by a literary elite. The descriptivist must accept the view of people-in-general that there is a correct usage -- in this case correct definitions -- because his inviolable rule requires that he accept the view of people-in-general. In granting that there is a correct usage, the descriptivist grants what his inviolable rule, his basic premise, denies.

"The descriptivist might, on the other hand, reject the definition used by people-in-general and substitute the definition of "dictionary" implied by his violable rule, the definition that denies there there is a "correct" usage other than that used by people-in-general. But if he does this, he does the one thing that his inviolable rule prohibits. He substitutes a "correct" definition whose existence his basic premise denies for the only definition that his basic premise -- his inviolable rule -- grants as legitimate, the definition used by people-in-general.

"The descriptivist cannot argue that people-in-general are incorrect in defining a "dictionary" as giving correct usage because "incorrect" (or "wrong") has no meaning in the descriptivist universe (except, perhaps, to describe misrepresentation of the usage of people-in-general, which is just what the descriptivist does if he alters the definition of "dictionary" used by people-in-general; people-in-general cannot, according to the descriptivist premise, be incorrect).

"Whether the descriptivist accepts the definition of "dictionary" used by people-in-general or rejects the definition used by people-in-general, the descriptivist's descriptivism is exposed as rotten at its core. Note that the contradiction is not merely an oddity relevant only to a single definition. The problem of defining "dictionary" is but a focused view of a contradiction that infuses all of descriptivism and that can be stated without reference to a definition of "dictionary". The general contradiction is that descriptivism is founded on an axiom that accepts "A" (popular usage) and rejects "B" (any other authority or criterion for correctness) even when acceptance of "A" commits descriptivism to an accepance of "B", which is rejected by the axiom ("A") that requires its acceptance."


I think this argument is flawed for a number of reasons. Here are a few.

1. I think Goldberg caricatures what descriptivists believe. A descriptivist wouldn't say that meaning is determined the use of "people-in-general", because words don't have single meanings. For example, what if exactly 50% of "people-in-general" think a word means one thing, while exactly 50% of "people-in-general" think it means another? Then there is no one meaning held by "people-in-general" at all. For another, words have multiple meanings and shades of meaning. Sometimes these meanings can even be the opposites of each other. What, for example, do "people-in-general" mean by the word "cleave"? On the one hand, it can mean "to stick together". But it can also mean "to cut apart". Then there are words whose meanings have gradually shifted over time, such as "nubile". Originally, it meant "marriageable", but these days it seems to be used more as if it means "young and sexy".

2. I think Goldberg caricatures what "people-in-general" believe about the meaning of the word "dictionary". It may well be that "people-in-general" think of a dictionary roughly like what Goldberg claims: as a book "giving correct definitions, correctness being determined by a literary elite". But if you ask "people-in-general" whether they think a dictionary can ever contain an incorrect definition, or is it necessarily always right, I'd be very surprised if they choose the latter option. Furthermore, there is not a single dictionary accepted by all English-speaking people, but many different ones. "People-in-general" will have to concede that these many different dictionaries may disagree on the meaning of a word. So a descriptivist may well define "dictionary" as "a book containing usually-correct definitions, approved by a literary elite" and still satisfy the beliefs of "people-in-general". But then Goldberg's "contradiction" disappears.

3. The dictionary definition of "dictionary" doesn't usually claim its definitions are correct. For example, picking a dictionary at random from the web, I find the first definition of "dictionary" as "A reference book containing an alphabetical list of words, with information given for each word, usually including meaning, pronunciation, and etymology." Given that, maybe "people-in-general" don't assume what Goldberg claims they do.

4. "People-in-general" may well believe that a word has a certain definition but that does not necessarily mean that the object that the word refers to actually exists. For example, "people-in-general" might define "unicorn" as "a goat-like animal with magical powers and a single horn", but that doesn't mean that unicorns actually exist or have magical powers. Acknowledging this doesn't violate the descriptivist position; the descriptivist need not be a moron. So "people-in-general" may believe that a dictionary is a book "giving correct definitions, correctness being determined by a literary elite", but that doesn't necesssarily believe that such a book actually exists. Thus, a descriptivist can, without fear of contradiction, believe both that "people-in-general" think "dictionary" has this meaning on the one hand, and also believe that no such book as described by "people-in-general" actually exists in the real world.

So while I find Goldberg's attempt interesting, I think it is a failure.

14 comments:

Sniffnoy said...

I'd like to add one other big mistake that I think actually encapsulates both 4 and 2. It's the mistake of thinking that words are defined by their "definitions". Most non-mathematical terms refer to empirical clusters of related things; the "definition" is just how we attempt to describe the relation that we've already noticed. Even when given a specific definition, we naturally extend the word. It's easy for people to be able to answer the question, "Is this a dictionary?", for a given object, without being able to give a good definition of "dictionary" in general. The whole problem the dictionary-writer faces, is not interviewing people for definitions and then combining them, but coming up with a description *at all* for something that everyone already knows but noone has bothered to specify.

Jeffrey Shallit said...

I'd add that it is not even always easy to answer the question "Is this a dictionary?" For example, would a piece of paper with a single definition on it be a dictionary? How about two definitions? How many would I need before I had a dictionary?

Rachel said...

This guy is a lot like people who try to prove the correctness of their religion by appealing to the holy texts or premises of their religion.

People like this apparently cannot imagine what it means to not believe the tenets of their religion, and assume that the only choices are to submit to their God or willfully rebel against him. They can't remove most of their religious premises from their reasoning about what it means to be outside their religion, and so their arguments sound nonsensical to non-adherents of their religion.

Likewise, this guy doesn't understand what it means to not be a prescriptivist:

The one inviolable rule of descriptivism is this: There are no correct definitions, meanings, or usages other than those used by people-in-general; any attempt to substitute a definition, meaning, or usage for that used by people-in-general is invalid. Where the prescriptive subordinates popular usage to correct usage, the descriptivist denies to correctness and all other criteria parity with use by people-in-general.

In other words, he assumes that descriptivists are really prescriptivists, but their authority figure is the whim of the public and not the traditions passed down by generations of prescriptivist teachers.

This is not, in fact, true. A descriptivist believes that an authority figure dictates the standards of correct usage and that people are obligated to follow them as much as an atheist believes in God. Which makes this nonsense:

Whether the descriptivist accepts the definition of "dictionary" used by people-in-general or rejects the definition used by people-in-general, the descriptivist's descriptivism is exposed as rotten at its core. Note that the contradiction is not merely an oddity relevant only to a single definition. The problem of defining "dictionary" is but a focused view of a contradiction that infuses all of descriptivism and that can be stated without reference to a definition of "dictionary". The general contradiction is that descriptivism is founded on an axiom that accepts "A" (popular usage) and rejects "B" (any other authority or criterion for correctness) even when acceptance of "A" commits descriptivism to an accepance of "B", which is rejected by the axiom ("A") that requires its acceptance.

He totally misunderstands what it means for a descriptivist to make a statement about language. When a descriptivist says that word X means Y in a language, or that grammatical rule Z is present in a language, that is a generalization about speakers' linguistic behavior. That's all it is. They are not (morally?) obligated to use that word as it is used by speakers of the language (or to believe that the word's definition has anything to do with things that exist in reality), or to follow that grammatical rule as speakers of the language do.

And they do not have any obligation to believe about language what most speakers believe about language. Most educated speakers of English believe that singular "they" is "grammatically incorrect," even as they use it every day themselves. I, as a descriptivist, believe they're wrong; I believe that the English language is as speakers use it, and not as they say they do (or should). No contradiction there.

Rachel said...

By the way, if you're looking for examples of people not understanding math, you might appreciate this...

David said...

If descriptivism in Goldberg's sense is correct, and people-in-general hold beliefs about meaning that contradict descriptivism, then people-in-general hold false beliefs about meaning. But this is consistent with the truth of descriptivism. Descriptivism is a view about how words acquire meaning; it doesn't, contrary to Goldberg, entail that people-in-general accept descriptivism.

Jeffrey Shallit said...

Thanks, Rachel. The .9999... = 1 thing is definitely going to be one of the topics in my book.

Blake Stacey said...

Maybe Goldberg is just afraid that descriptivists will turn into Nazis?

RichardW said...

I would say that the primary problem with Goldberg's argument is your #1: his characterisation of the descriptivist position is far too simplistic.

One sign of this is the way he lumps together "definitions, meanings, [and] usages", as if the distinctions between these are not important. Yet these distinctions are central. It seems to me that the most significant difference between prescriptivists and descriptivists is that the former emphasise asking sources for definitions of words (or rules of grammar) while the latter emphasise looking at how sources actually use words (and grammar). (That's what the words "prescribe" and "describe" imply.) But Goldberg bases his argument entirely on a distinction over which source to consider: people-in-general or an elite. Instead of describing how people-in-general use the word "dictionary", he gives us their (presumed) prescription for how the word "dictionary" should be used. That's not a descriptivist position. If Goldberg's contention is that descriptivists are not using the word "dictionary" in a manner consistent with how people-in-general use it, the sort of evidence he needs to support the contention would be instances of people refusing to call a book a "dictionary" after they're told that it's based on descriptivist principles!

Playing devil's advocate, I would question your argument #4. Yes, in principle "descriptivists" (as Goldberg imagines them) could escape his dilemma by saying that no such book exists. But they cannot do so without contradiction as long as they continue to refer to some real books as "dictionaries".

RichardW said...

P.S. I should have read Rachel's post before writing mine, as she makes a similar point. However, I would suggest that Rachel is taking too pure a view of descriptivism.

When a descriptivist says that word X means Y in a language, or that grammatical rule Z is present in a language, that is a generalization about speakers' linguistic behavior. That's all it is.

But a descriptivist does more than describe languages. Like everyone else, he is also a user of language, and in choosing his words he must make judgements about which usages are appropriate. Moreover in wider society (and especially as a parent) he will likely make judgements about the usages of other people.

I doubt there are many descriptivists who think a child's language should never be corrected. A descriptivist parent may say "that's not standard English" or "that's not appropriate to the context", rather than "that's not correct", or simply state his preferred version in a suggestive tone of voice. But, in encouraging the child to use one form rather than another, the parent is expressing a judgement about what constitutes appropriate usage. And of course we make such judgements all the time in choosing our own words. To take this to an extreme, if there was absolutely no sense in which language use could be wrong, then I couldn't be faulted for saying "the world is flat", even though I know it's round, because there would be nothing wrong with choosing to use the word "flat" to mean "round".

Of course, in making such judgements the descriptivist doesn't appeal to some theoretical ideal but to how language is used in practise.

I just found this on Wikipedia:

On the other hand, some adherents of a strongly descriptive approach may argue that prescription is always undesirable. Sometimes they see it as reactionary or stifling. A "pure descriptivist" would believe that no language form can ever be incorrect and that advice on language usage is always misplaced. However, this is a very rare position[citation needed]. Most of those who claim to oppose prescription per se are in fact only inimical to those forms of prescription not supported by current descriptive analysis[citation needed].
http://en.wikipedia.org/wiki/Linguistic_prescription#Prescription_and_description_in_conflict

David said...

There is no inconsistency in the descriptivist view as Goldberg as characterized it, even if one assumes that most people do define "dictionary" as "a book that gives the correct definition of words, as determined by a literary elite" and also assumes that dictionaries so defined really exist. Goldberg's descriptivists hold that there are in fact no correct meanings or definitions of words other than those used by people-in-general. This position doesn't preclude the existence of books that give definitions according to some other standard.

RichardW said...

David's post has prompted me to try to clarify the premises of Goldberg's argument. He gives two:
P1. According to descriptivists, "there are no correct definitions...other than those used by people-in-general".
P2. People-in-general define a dictionary "as giving correct definitions, correctness being determined by a literary elite".

But his argument depends on two additional, unstated premises:
P3. According to descriptivists, the books we typically call dictionaries contain descriptivist definitions.
P4. Descriptivists refer to such books as "dictionaries".

I think these last two premises are true, and I would say they were implicitly assumed by Goldberg. Adding them excludes Jeff's objection #4 and David's objection. Given all 4 premises I think Goldberg's conclusion follows: descriptivists are caught in an inconsistency. But the argument is unsound because P1 is false. (P2 is also questionable.)

RichardW said...

P.S. Oops. I think the word "descriptivist" in my P3 was unnecessary, since, according to P1, descriptivist definitions are the only definitions. For greater clarity, please replace P3 and P4 with the following:

P3*. Descriptivists refer to the books we typically call dictionaries as "dictionaries", and to the definitions contained therein as "definitions".

Putting it like that, it seems too obvious to mention. But Jeff's argument #4 and David's argument are, in effect, challenges to that premise.

RichardW said...

P.P.S. I've gone through Goldberg's argument again carefully, and realised that no third premise is needed. But in doing so, I found some other problems.

Goldberg starts off by stating his supposed "inviolable rule" of descriptivism in a negative way (about what a descriptivist can't do):

The one inviolable rule of descriptivism is this: There are no correct definitions, meanings, or usages other than those used by people-in-general; any attempt to substitute a definition, meaning, or usage for that used by people-in-general is invalid.

But when he begins his argument, he switches to a positive rule (about what a descriptivist must do):

The descriptivist might, as his inviolable rule says he must, accept the definition of "dictionary" used by people-in-general.

So I now take this positive rule as a premise in place of P1, giving:
P1*. According to descriptivists, they must accept the definitions used by people-in-general.
P2. People-in-general define a dictionary "as giving correct definitions, correctness being determined by a literary elite".

Goldberg begins his argument as follows:

Now consider what happens when you ask a descriptivist how he defines "dictionary" in his descriptivist dictionary.

As soon as the descriptivist tries to answer this question, he must ask himself what he means by a dictionary. And, by P1* and P2, he must accept that a dictionary gives "correct definitions, correctness being determined by a literary elite". But that's not a descriptivist understanding of definitions. So, on these premises, a "descriptivist dictionary" is an oxymoron. Replacing "descriptivist dictionary" simply with "dictionary", the descriptivist can continue, but, when he tries to say how the word "dictionary" would be defined within a dictionary, he runs into the dilemma that Goldberg describes.

Note that there's no need to assume that any dictionary actually exists. Goldberg could be asking what a descriptivist dictionary would contain if it existed. The point is that, given the premises, the idea of a "dictionary" is incoherent.

I would also add that Goldberg runs into the problem of being unable to completely separate definitions from propositions. The definition in P2 is also a proposition about what constitutes a correct definition. This leads Goldberg to write:

The descriptivist must accept the view of people-in-general that there is a correct usage -- in this case correct definitions -- because his inviolable rule requires that he accept the view of people-in-general.

So now the descriptivist must not only accept the definitions of people-in-general. He must accept their views too! Once he went down that route, Goldberg could have made the dilemma much more obvious:

P1a. According to descriptivists, one must accept the views of people-in-general.
P2a. People-in-general deny that one must accept the views of people-in-general.

I think Goldberg could have avoided this issue (or at least minimised it) by leaving out any mention of correctness. He could have taken the following premises:

P1b. According to descriptivists, all definitions are supplied by people-in-general.
P2b. People-in-general define a dictionary as a book containing definitions supplied by a literary elite.

These premises still lead to the same kind of dilemma. The descriptivist cannot say who supplies the definitions in a dictionary.

D. Swart said...

I'm trying to get a feel for the output of this argument.

I wonder what consequences of discrediting descriptivism are that would make Goldberg so vehement and passionate about his stance.

Is it (however indirectly) about helping people communicate their ideas better?

Is there some other argument further in his book that needs this result?

Is it just an argument for practice sake?

Is it to guide speakers, editors, writers, readers, and listeners to one authority over another?