Geoffrey K. Pullum
online version available
UC Santa Cruz
Generative grammarians have often been accused of playing fast and loose with
data, dismissing counterexamples as "mere exceptions" if they don't like them.
An unsympathetic reader of Hankamer (1978) might portray it as a perfect
example of this tendency. Faced with the direct counterevidence to his claims
presented in Schachter (1977), Hankamer dismisses them as just a bunch of
special cases, and clings to his favored hypothesis. Just the sort of thing
to reduce a hypothesis to vacuity, the methodological moaner might say.
Typical arrogant transformationalist.
I'm going to argue that the unsympathetic reader or methodological moaner
in this case would be making a mistake.
The hypothesis at issue is that of Hankamer and Sag (1976)one of the
great papers on anaphora from the classical period of transformational
generative grammatical description. The thesis of this paper is that
there are two kinds of anaphora, deep and surface, with major differences
between them, the central one being that only deep anaphors can be
exophoric (i.e., take their antecedents from nonlinguistic context).
A clear example of deep anaphora is found in the case of ordinary
anaphoric pronouns. Suppose you and I come upon a place
where just a week ago we admired a beautiful church, and find it
is almost completely demolished, and you stare at me incredulously
as if I might know why this has been done.
I could say:
Don't look at me; I don't know why they've done it.
The pronoun it can be understood
in a normal way even if there has been no prior mention of what they
have done. That is exophoric use.
The clearest example of surface anaphora is VP ellipsis, which firmly
resists exophoric use. In the context just described it would be bizarre
for me to say
#Don't look at me; I don't know why they have.
A demolition scene is not sufficient to permit why they have to be
understood as "why they have demolished that beautiful church", or
"why they have perpetrated this heinous architectural crime", or whatever.
The title of this squib is of course another deliberate example of
deviance: I can't just say Hankamer was! in a title where there is
clearly no linguistic antecedent. But Hankamer was right! is fine;
complete omission of a complement (compare Null Complement Anaphora as in
Well, I tried! or Isn't anyone going to volunteer?, where
whole clauses rather than VPs are missing) acts as a deep anaphor, not a
surface one, as Hankamer and Sag (1976) carefully demonstrate.
Hankamer and Sag gave various talks based on their paper around 1975.
They would carry a big bag of props and act out scenarios as examples.
Hankamer would wordlessly fetch out a nine-inch ball and try to stuff
it through a six-inch hoop, and Sag would say:
#It's not clear that you'll be able to!
(bizarre and uninterpretable), or the perfectly acceptable alternative:
It's not clear that you'll be able to do it!
Even without witnessing any of the live performances, which some say were
pretty neat, I found the data as published in the Linguistic
Inquiry article fully convincing.
Paul Schachter did not. He published a squib (1977) entitled
"Does she or doesn't she?", the title being taken from a Miss Clairol
hair dye advertisement in which the following words appeared without
linguistic context to support the VP ellipsis:
Does she or doesn't she? Only her hairdresser knows for sure.
The interpretation intended for the first clause (deducible from the
nature of the product being advertised) was "Does she dye her hair or
doesn't she dye her hair? Only her hairdresser knows for sure whether she
dyes her hair." There is no linguistic antecedent. This, Schachter said,
was a counterexample to the claims of Hankamer and Sag. And he cited half
a dozen others (they will be listed below).
As his positive proposal, Schachter refers the reader to a then
forthcoming article of his (Schachter 1978) in which he proposed that
there was no VP deletion rule, auxiliaries merely had optional complements
and were pragmatically understood as "propredicates" when the situation
permitted the message to get across. He claimed that "speakers use
antecedentless propredicatesas they use other antecedentless
pro-fromsonly if they can reasonably assume that the content of the
pro-forms is recoverable from the pragmatic context" (p. 766).
Now, messing with Jorge on questions of data can be hazardous to your
health. We are talking about a man who is reliably reported to have
responded to several students' disagreement with some data, in one
particularly grouchy Monday morning Syntax I class, by saying:
"Anyone who thinks that is grammatical has got their head up their ass."
Schachter got similarly short shrift. Hankamer (1978) dismisses
Schachter's own analysis as completely unacceptable. Among other things,
Hankamer points out, powerful arguments had been given by Grinder and
Postal (1971) that told in favor of transformational derivations for VP
ellipsis cases, and Schachter did not address these (indeed, his 1978
paper, which appeared after the 1977 squib, does not even cite the Grinder
and Postal paper, and to this day he has not responded to that point).
Hankamer's claim about the data Schachter exhibited was that all he had
come up with was "a limited number of fixed expressions"; they not only
did not exhibit syntactic ellipsis, Hankamer claimed, but they should
actually be listed in the lexicon as special expressive devices of a type
not syntactically derived by productive rules, and in at least
some cases they clearly had special conventional meanings attached.
Now it seems to me that there is a substantive dispute here about what the
data are in this casewhat counts and what can be dismissed. It needs
to be properly settled.
What is necessary if we are to evaluate the support for Hankamer's claim
is to get a quantitative handle on the phenomenon. Over the past two
decades I have often tried to get students interested in working on this,
but no dice, no one would touch it. It involved tabulating and counting
and hunting for data. So I have done the work myself. As always with
such empirical work, it turned out a bit more complex and interesting
than I thought it was going to be, but it was perfectly doable.
It is a significant fact that all of Schachter's examples
involve auxiliary verbs with pronouns: Must you?, Does she or
doesn't she?, You wouldn't!, You shouldn't have, and so
on. Not a single one involves a full NP or a lexical verb. That is, he
has no exophoric uses to show for phrases like Several officials of the
Catholic church have, or Could Henry be expected to?, or
anything of the sort.
This makes the set of all possibly relevant phrases finite.
But how big is it? How many phrases like Can it? or They hadn't
are there? I must admit that my first guesses at this were
wildly wrong. I thought it was going to be a number in two digits,
maybe three. But the full list needs computational assistance to
generate. Let's consider how we get it.
We have eleven auxiliary verb lexemes and two modal idioms to consider:
- be (forms: present am, are, is, preterite
- have (forms: present have, has, preterite
- do (forms: present do, does, preterite did)
- can (irregular preterite: could)
- dare (regular preterite: dared)
- may (irregular preterite: might)
- must (no preterite form)
- need (no preterite form in its modal use)
- ought (no preterite form)
- shall (irregular preterite: should)
- will (irregular preterite: would)
- the special idiomatic construction had better
- the special idiomatic construction would rather
I propose to neglect the modal use of the copula with the infinitive
(You are to go to bed immediately), which represents a separate
construction from all these, on the grounds that it is now somewhat formal
in many syntactic configurations (not many contemporary American speakers
would say things like Am I to? anaphorically, and I know
Jorge wouldn't, so there is not much point in looking for exophoric
Each of the lexemes listed can be either neutral (like are) or
negative (like aren't). Having some finite forms that accept the
negative inflection n't is the defining diagnostic for auxiliary
verb lexemes in English. There are some sporadically non-occurring
negative forms: *amn't, *mayn't, and for most American
speakers today *shan't. For these we can substitue the analytic
negative (I may not for *I mayn't, etc.). I will assume
mightn't and oughtn't still exist, though I recognize that
these too are tottering on the brink of extinction for many American
But we have to allow for combinations of auxiliaries (one of Schachter's
cases is John, you shouldn't have!, which has two auxiliaries).
This means allowing for the modals in either present or preterite tenses
(where they have preterites), and in either neutral or negative form,
each followed by either
(i) nothing or
(ii) perfect have (You shouldn't have) or
(iii) the copula (He might be) or
(iv) both (They couldn't have been), or
(v) the progressive copula followed by the passive auxiliary
(You may be being), or
(vi) have followed by
the progressive copula followed by the passive auxiliary
(You may have been being).
That's a total of
10 · 2 · 2 · 6
= 240 possibilities.
Where the auxiliary is have, in either present or preterite tense,
and in either neutral or negative form, it is possible for it to be
followed by nothing (They have) or the copula (They haven't
been) or the progressive and passive auxiliaries (They haven't been
being), so there are
2 · 2 · 3 · 6
= 12 possibilities with have.
Do cannot be followed by other auxiliaries, so there are just the
present and past neutral and negative forms to consider, 4 possibilities.
The copula can be present or preterite and neutral or negative and
can be followed by either nothing or by another copula (You already are
being), so there are 8 possibilities there.
The number of possibilities for auxiliary combinations, then, is
240 + 12 + 4 + 8 = 264.
Now, for any one of these 264 logical possibilities, the pronoun subject
can be any of the eight personal pronouns he, I, it,
she, one, they, we, and you, or dummy
there. I include one despite its rather formal nature (only
the British royal family seems use this kind of one much in
everyday speech, and Jorge sure doesn't use it) because it does duty for
the informal substitute of unstressed you (spelled ya in
novels): we need to allow for the possibility of phrases like One just
doesn't (i.e. Ya just don't) being used exophorically.
Any of the pairings of any of the pronouns with any of the auxiliaries
can yield a declarative ellipsis fragment (You are) or an
auxiliary-inverted one (Are you?). I am going to ignore what
Chris Gunlogson calls the rising declarative (You are?). As
will be seen below, this represents a major concession to Schachter in
my statistics, making his view look about a third better than it should.
I'm a generous guy.
In addition, we can get a very few negative or positive imperatives: two
with do (Yes, please do, No, please don't), and one
with dare (Just you dare!), so those must be added.
This establishes that the class of cases to be covered is not bigger than
264 · 9 · 2 + 3
= 4755. Vastly bigger than I thought. But in practice the list turns out
to be significantly shorter than this, for several reasons:
- There are some modals without preterites (must, ought,
- There are some syntactically impossible pairings with shall
(we don't get shall with he, it, she, they,
- The modals dare and need are negative polarity items, so
there is a prohibition on plain declarative use of neutral dare and
need (we get He daren't defy me and Dare he defy me?
but not *He dare defy me)).
Allowing for these factors, I built and carefully checked a list of the
entire universe of candidates. (Jorge would have used a C program to build it.
I used a C shell
script, which you may download if you wish. It's not elegantit's
392 repetitive lines longbut I aimed at clarity, not brevity.)
I find that there are 3245 candidates for us to consider. The full list of
HTML form for your browsing pleasure, alphabetically ordered from
You wouldn't have been being.
I have also made available
ASCII file of the raw data.
Some people regard ellipsis after be(en)being
as ungrammatical. (Everyone would accept Don't worry about
whether your phone might be bugged, it already is being!, or
so I presume; but some do not accept It already has been
being for two months!.) This actually amounts to more than
a thousand items, so it could be significant. For the dialects
of those speakers, then, we need to remove the
items in question. This adjusts the number of candidates downward to
I will compute the statistics below both with and without the
questionable be(en)being cases.
My bottom line is that we can evaluate the plausibility of
Hankamer's claim by doing a numerical comparison of
(a) the number of expressions in the language
that are candidates for Schachter-style exophoric VP ellipsis, and
(b) the number that seem actually to occur in use.
Schachter's hypothesis predicts a rich and randomly distributed array of
cases spread right across the list of syntactic possibilities; we should
encounter hundreds of exophoric propredicates, at the very least.
Hankamer's claim will look more and more ridiculous as the number
of confirmed cases of it grows. But Hankamer will be vindicated
if that number is very smallespecially if the items on the list have
idiosyncratic properties that the lexicon would need to record.
The entire list of relevant phrases cited in the relevant
literatureSchachter's papers and the papers by Hankamer and Sagis
listed below. I show the source in red and append a few remarks in green,
if your browser is set up right (Why these colors? Oh, I don't knowone
does these things in web documents simply because one can.)
Does she or doesn't she?
[Schachter (1977), example (1)]
An advertising slogan, as discussed above.
In defense of the view that it is a special fixed phrase, Hankamer
points out that it is modelled on a standard adolescent male euphemistic
question about whether a girl is sexually active or not.
(Schachter reports that he did not know this.)
It isn't productively usable in exophoric mode; Hankamer also points out that
you couldn't even have used the slogan "Does she?" instead;
it wouldn't have been interpretable.
[Schachter (1977), example (3)]
A familiar phrase of warning to tell someone
not to do something that is morally wrong or inadvisable.
Schachter's context is that
John tries to kiss Mary, and she says, "John, you mustn't."
[Schachter (1977), example (4)]
A heavily conventionalized way of indicating reluctance to accept a
proffered alcoholic beverage ("I really shouldn't, Charlie, 'cos I'm
driving, but aw, shucksh, I guesh one more for the road won't hurt..."
says the town drunk, and later on they use the Jaws of Life to pry him
out of his pickup truck).
[Schachter (1977), example (5)]
A heavily conventionalized and singularly old-fashioned way to invite someone
to dance. Don't try this at a rave if you want people to think you are cool.
And I don't think it can freely be used outside of a dancing context.
If we hear on the radio that volunteers are needed to help with the
local NPR station's pledge drive, it would not be normal for me to look
at you and say, Shall we? to me "Shall we volunteer to go to the
station and help out with answering the phones next week?"not even if
it is perfectly clear in context and we did it last year.
You shouldn't have!
[Schachter (1977), example (6)]
Feigned disapproval to indicate how pleased one is with an unexpected gift
("Oh, darling, you shouldn't have! It's beautiful!").
[Schachter (1977), example (7)]
A conventional way of asking permission to take something in a public
situation (e.g. a chair or the condiments in a restaurant).
This is conventional enough that a number of times I have asked people
in a noisy restaurant setting "Is anyone sitting here?", indicating an
apparently unneeded chair, and they have answered "Sure"the answer
to the May I? or Can I take this one? that they thought
I was going to ask.
[Schachter (1977), example (7)]
This a conventional way of granting a permission that is requested
with May I?.
Person A, indicating the Grey Poupon mustard on its silver tray, says
"May I?" and person B says "Oh, please do, old chap."
The exchange is decidedly formal and old-fashioned.
If you can, I can.
[Schachter 1977, p. 766, n. 2, example (i)]
It was suggested to Schachter by Susumu Kuno that if someone has just
lifted 300 pounds in a weight-lifting contest, the other person says, "If
you can, so can I." More generally, it is reasonable to imagine hearing
If you(/he/she/they) can, I can or If you(/he/she/they) can, so
can I. The phrase is really a semi-conventionalized way of indicating
that one expects parity. It is also used as an equivalent of "What's
sauce for the goose is sauce for the gander": on seeing that his older
brother has stripped to his underpants for a post-picnic swim in the lake,
a younger brother can say to his parents, "If he can, I can!" But there is
no generalized availability of this sort of exophora. If you and I are
waiting to make a phone call at a line of airport phone booths several of
which we have found not to be working, I cannot say as someone finishes up a
clearly successful call, #If he can, then it must.
Obviously it would mean "If he can talk on that phone, then it must work."
But linguistically the exophora is not available here.
[Hankamer and Sag (1976), p. 409, n. 19;
Not in my wastebasket, you don't;
Hankamer brandishes a cleaver and advances on Sag, and Sag cries:
Don't! My God, please don't!]
This is footnoted by Hankamer and Sag (1976) as an example of a class of
exceptions. The illocutionary force here is that of commanding, or
perhaps pathetic pleading (I didn't see how Sag played it in live
performance, but I imagine he really hammed it up). Hankamer and Sag
note that the constraint they are studying is primarily active in declarative
sentences, or perhaps they should have said, utterances that make
statements. They offer no reason for its weakening in orders, requests,
exclamations, etc. It should be noted, though, that
Schachter (1977, 7667) points out that "statements
may be about anyone or anything, but requests are restricted to actions
to be performed by the addressee and questions to information presumably
possessed by the addressee" and hence the meaning of an utterance that does
not make a statement "is more determinate than that of a declarative," so
"it is not surprising if speakers can more often use antecedentless
propredicates in nondeclarative than in declarative sentences." In other
words, Schachter takes this kind of case to further confirm his view,
since he can provide a pragmatic rationale for the greater ease of
exophoric interpretation in non-statements.
[Hankamer and Sag (1976), p. 409, n. 19,
example (iii): you see that an acquaintance has dyed his hair green,
and you exclaim: You didn't!.]
Highly conventionalized; this phrase is used in circumstances
where a person who has expectations about the likely behavior
of another (their partner, perhaps) discovers the unexpected:
they come home to find the walls have been painted cherry red,
or the tree in the front yard has been felled, or a new Porsche
has been purchased. Despite the declarative form, this phrase
is an exclamation; it can hardly be taken to have as its main
semantic point the conveying of a truth claim, since it is used
solely in situations where it is obviously false!
Now, surprisingly, that is it, as far as the literature is
concerned; this dispute turns on just ten invented examples!
It is amusing to note in passing that Schachter's own exophora examples,
apart from the hair dye ad that provides his title, are all
formulaic phrases typical of superficial social interaction in a
restaurant or night club. In fact all of them involve scenes from the
wooing of a passive female called Mary by a courteous but insistent suitor
called John: he asks for a chair near her by saying "May I?" and she
answers "Please do"; the band starts to play and he asks her to dance
with "Shall we?"; he pours her a drink she doesn't want and she says
"I really shouldn't"; pushing his luck, he attempts a kiss and is
rebuffed with "You mustn't"; he persists and buys a gift, which
she blushingly accepts with "You shouldn't have". Does she or doesn't she
indeed! He certainly seems to hope she will. Schachter's final example
has John asking Mary Will you or won't you? and Mary -
illustrating the fact that exophora attempts sometimes failresponds
with Will I or won't I what?. It seems a little odd that
she can't guess. She should talk it over with her hairdresser.
But I digress. Apart from the half-dozen formulaic phrases in John's
courtship of Mary and the four other cases listed above, that is it. How
many more might there be? We face quite a problem with the data gathering
here, as Arnold Zwicky perceptively pointed out to me. We can really only
rely on happenstance example gathering from real life or reading;
searching of corpora is beside the point unless for each example we find
the source and examine the whole context.
The task is reminiscent of the one that Guy Carden faced in his
investigation of whether a pronoun before its antecedent within a sentence
is always linked to an earlier occurrence of a coreferential phrase
earlier in the discoursei.e., whether intrasentential cataphora is
always really intra-discourse anaphora. His investigative method (see
Carden (1982)) was to read through forty novels, watching for
intersententially cataphoric pronouns. When he caught one he would study
the whole of the prior context to see if there had been a previous mention
of the referent of the pronoun. (He found cases where the cataphora was
not discourse anaphoric, but only at a rate of about one per novel.)
A similar technique is needed here, whether the example is culled from
a novel or from a scene at the bus stop in real life.
It is not enough to know that a woman came up to her friend and said,
It doesn't. Everything that went on before that must be
available to us; we need to know whether they had been talking earlier,
and what exact words were said. Only that can tell us whether a
linguistic antecedent for the missing VP was available.
In over twenty years of being interested in the issue,
I have caught only a very few new exophoric VP ellipses on the hoof.
In the circumstances, the only way I can be full fair to Schachter's
hypothesis is to suggest a few invented or vaguely recollected
cases that I think would not be implausible.
I think someone wearing their best clothes who saw that a friend
was apparently about to do something strikingly threatening and
undesired, like turning a playful garden hose on them, might cry out,
(Notice again that this is not a statement; it is an exclamation
that would be used only where the statement appeared to be false.)
Don't you dare!
In similar circumstances one might say,
Don't you dare!, or You dare!, or Just you dare!;
I feel I have heard this often enough.
(The observation about being an exclamation rather than a statement
This is a conventional way of getting someone to stop doing something
annoying, like tapping a pencil on the desk, or practicing drumming
patterns with their fingers on a desktop, or playing with their pet
scorpion at the dinner table. I am pretty sure I have heard this now
and then, possibly even addressed to me when I was jiggling my foot.
I think one might use Should I? or Shall I? to ask a
companion for on-the-spot moral advice about whether to do something,
typically mischievous. We come upon a pompous colleague whom we detest,
bending down to tie up a shoelace; I happen to have a paintball gun, and
I take aim and whisper, "Shall I?".
In similar vein, I think one might perhaps ask a companion for on-the-spot
moral support before doing something risky, like jumping off a rock into a
river. I'm not sure about this one, but maybe I can imagine it in use.
I have grouped Should I? and Shall I? together,
and done likewise with Dare I/Dare you/Dare we,
because I take them to be single idioms with an option on the choice of
pronounlike pull someone's leg, which is a single idiom in which
the someone is freely replaceable by other NPs.
But I have exhausted my imagination with these.
I can find no more, after some years of occasionally
reflecting on the question and some hours looking up and down the
So by my count we have a total of not thousands of new idioms but rather
about 15 special phrases that under Hankamer's view have to be added to the
Doing the statistics both ways (for people who do and who do not
accept ellipsis fragments ending in be being), we have either
or 15/2243 =
of the candidates actually being found in use.
In other words, for each thousand candidate phrases that could
logically have had an exophoric use, only about half a dozen can actually
even be cited as plausible. And that is on an accounting that is quite
generous to Schachter: limiting ourselves to the closed set of cases with
pronouns, omitting modal is to, allowing all of Schachter's data
without question, adding everything that Hankamer and Sag admit as
possible exceptions, adding a few more of my own, and ignoring the rising
declarative construction despite its differences from the declarative.
(Adding in the rising declaratives would swell the ranks of candidates by
about a third, and would push those percentages down a point or so.)
Schachter's predicted exophoric propredicates simply aren't turning up.
From the invented and intuitively checked data we have, less than one
percent of what you'd expect are turning up. And as I have
documented in my remarks above, most of those that do have something
special and conventional about their usethey are not entirely free with
regard to the properties that provide their interpretation.
It is perfectly reasonable under these circumstances for Hankamer to suggest
that they should be recorded in the lexicon as idioms. Certainly, they
have the form of VP ellipsis fragments, and have occurred frequently as VP
ellipsis fragments; but they have taken on a lexical life of their own, as
commonly heard phrases often do. They do not indicate that exophora is
freely available for VP ellipsis fragments, they indicate that phrases can
become lexically fossilized.
As Arnold Zwicky points out to me, such fossilization through
conventionalization of pragmatically natural patterns is
widespread. One example is found with conditionals: we use the
conditional adjunct If you would excuse me for a few moments... to
mean that we want to be excused for a few moments. The main clause is not
supplied either because it is embarrassing (...I can try to
fix this zipper), because it is unimportant (...I've got
some boring stuff to do out in the kitchen), or because it
is already known (...I need to take this phone call alone
because, as you can tell, I'm setting up a hot date).
The suggestion that you excuse me is enough. But that does not
mean that main clauses can be filled in from the nonlinguistic
context any old time you like.
So I say that a bit of counting shows that Jorge was almost
certainly right. Anyone got any problems with that?
If you do have problems with it, all you have to do is identify attested
cases of exophoric VP ellipsis that are not on my list. You can take them
from novels or plays or films or TV or radio or everyday conversation.
Just mail them to me (xerographically to this address or electronically to
In the case of written sources, send me a xerocopy or transcript with enough
context and descriptive detail for me to be able to see that they are
genuinely exophoric (remember, if there is any prior context providing a
VP with the right sense, then they can be treated as ordinary VP ellipsis
cases, with their semantics allowed for along the lines suggested in Ivan
Sag's dissertation, Sag 1976).
In the case of examples from ephemeral sources like TV, radio, or live
conversation, it would be best if we observed the late Vicki Fromkin's
rule regarding documentation of slips of the tongue: two independent
observers both present at the time must attest to what was uttered.
For every verified case mailed in, I will update the version of this squib at
and recompute the statistics. So this is not a fixed document but an
interactively expanding computational electrosquib of a truly futuristic
kindquite fitting for a tribute to a man who has devoted the bulk of
his energy since 1980 to very serious computational linguistics. (Of course,
if there are no textual changes between the version you're reading now and my
updated futuristic expanding computational electrosquib, the link above
will just take you to a page saying so.)
Send your examples in, and we can start to make a serious attempt to test
Hankamer's claim and perhaps support Schachter's view that VP ellipsis can
in general be exophoric where the context provides the necessary
self-evidence. I'm here, and I'm waiting. I'll treat all submissions
fairly and with scientific detachment.
Not that I have no opinion about the outcome. My money, frankly, is on Jorge.
I've worked with him for twenty years. Happy birthday, Jorge.
Carden, Guy (1982) Backwards anaphora in discourse context.
Journal of Linguistics 18, 36187.
Grinder, John and Paul M. Postal (1971) Missing antecedents.
Linguistic Inquiry 2, 269312.
Hankamer, Jorge (1978) On the nontransformational derivation
of some null VP anaphors.
Linguistic Inquiry 9, 6674.
Hankamer, Jorge and Ivan Sag (1976) Deep and surface anaphora.
Linguistic Inquiry 7, 391428.
Sag, Ivan (1976). Deletion and Logical Form.
Doctoral dissertation, MIT.
Schachter, Paul (1977) Does she or doesn't she?
Linguistic Inquiry 8, 763767.
Schachter, Paul (1978) English propredicates.
Linguistic Analysis 4, 187224.
* Arnold Zwicky gave me some insightful comments
on this note, and helped me clarify a couple of things I had been thoroughly
confused about (this often happens). Many thanks, but no attendant
responsibilities, to him. [Back]