One can of lexicographical whoop-ass (intra-update)

I was hanging out at Languagehat (here) today and decided to throw caution to the wind. Posting a comment made for some nervousness, akin to that of having all 20 tomes of the OED (plus updates) hanging Damocles-iastically above.

The erudite LH has come up with one popular blog (e.g. 138 comments, so far, on the post in question) on an esoteric subject. And for some, including myself, it can be great fun. But user beware, it can get prickly and one can get run over like Brad Pitt in Meet Joe Black. These linguists can be merciless. So, at my own peril, enter I did… (Keeping a bullet handy in my use of “by” instead of “for” in my introductory “Running the risk that I end up being lambasted by my amateurship…”.)

The discussion was on the usage of “either” in English, ad how in Brit it means “each of two” and in American “one of two”—both definitions are of course valid, but the question was on usage. And there I went, armed with I-don’t-know-what.

The full thread is below (and here), and I will update it as it comes along. But I felt the initial upper-cut (let alone my newfound RAE-stemmed para[e]noia) at: “You seem at least to have mastered the style of the Sphinx. I find it very difficult to make out what you’re saying, from sentence to sentence. Each sentence is shrink-wrapped so indestructibly and tightly around its meaning that I can’t prise it open – like the plastic wrapping around small electronic equipment nowadays, in Germany at any rate.”

So much so that in yet another confessional, I replied that he’d “just given brilliant wordsmith ammunition to every significant other that, in looking for signifiance if my insignificant prose that was meant to convey my heart-felt but locked-in significatum, decided I was too obscure… and dumped me.”

Being the sucker that I am for punishment (which the above quote embodies), here goes the thread…

Re: Either (from way above)

Running the risk that I end up being lambasted by my amateurship…

In Spanish, “or” can be “o” or “ó”. The diacritical accent turns the inclusive form “o” into the exclusive form “ó”. In English, and I think there’s some discussion here, “or” is always inclusive (meaning “and/or”)—and/or, at least, it is ambiguous enough to force the inclusivity. So much so that, when in need of an exclusive form, we have come up with “xor” in logic and computing. In language, we sometimes use “either/or” to mean the exclusive form (personally, when meaning alternatives I try and always [all times] explicitly use “and/or” and/or “either/or” [which is to say that each time I use "and/or" either/or "either/or"]).

Now, does this tells us something about “either”? The fact that “either/or” means exclusion could potentially suggest that “either” is exclusive (as in “one of two” above). But if that was (not were) the case, then we would just use “either” for exclusive alternatives, and there would be no need for “either/or”.

So I posit that our use of “either/or” is just a contraction of “either…or”. And this would suggest that “either” is only exclusive within the “either…or” construction. By exclusion, then, “either” is inclusive (just as “or”).

I.e. the “one of two” version of “either” is incomplete without the “…or” (an incomplete usage contraction, albeit from the 14th c), but not *wrong* (and the “each of two” = “each and/or both” is *right*).

(And in another personal p/reference, I always use the isolated “either” in the “each of two” sense.)

TL

Posted by tlajous at July 16, 2009 02:03 PM

Running the risk that I end up being lambasted by my amateurship…

I’m not so sure about “amateurship”. You seem at least to have mastered the style of the Sphinx. I find it very difficult to make out what you’re saying, from sentence to sentence. Each sentence is shrink-wrapped so indestructibly and tightly around its meaning that I can’t prise it open – like the plastic wrapping around small electronic equipment nowadays, in Germany at any rate. ´

As Huck said: “the statements was interesting, but tough”. I think that I disagree with you at almost every point, but I’m not sure. Let me just start at the beginning of your post and comment on a few sentences, one by one:

In Spanish, “or” can be “o” or “ó”. The diacritical accent turns the inclusive form “o” into the exclusive form “ó”.

This is the only statement I clearly understand, but I just as clearly don’t believe it, off the bat. Granted, my Spanish is nowhere near perfect, but having read a lot of Spanish over decades I’ve never encountered such a convention, and I can’t find anything about it in my grammars or on the internet, for instance in the Diccionario de la Real Academia Española.

What I did find (remembered only vaguely) is this, where the accent is used to distinguish the letter “o” from the zero numeral “0″, when the letter has numbers on each side:

O / Ó

Esta conjunción disyuntiva (que indica alternancia), únicamente será tildada cuando se encuentren números alrededor. Esto sirve para evitar la ambigüedad con el número “0” dada su similitud en forma: “¿Eran 2 ó 3 personas?”.

Perhaps you generalized from this, understanding it in the following way: it doesn’t make sense to ask “were there 2 or 2 persons present?” When used with numbers, “or” makes sense only when the numbers are different. So when “or” appears between two numbers, it “has the exclusive form”. The same would apply to “ó” between two numbers. But it is illicit to generalize to “ó” between any two nouns, because the use of “ó” is explicitly restricted to the “surrounded by numbers” situation (únicamente), and is intended as an aid to reading, not as a tool of logic.

And in any case, “A or B” cannot possibly mean “both A and B, if you so desire” when A is incompatible with B. “To be, or not to be? That is the question”. The answer to that was not, and could not have been: “take both, silly!”.

In English, and I think there’s some discussion here, “or” is always inclusive (meaning “and/or”)—and/or, at least, it is ambiguous enough to force the inclusivity.

I suspect many English-speaking Americans are not accustomed to interpreting “you can have A or B” as implying that they can have both if they so desire. It’s a question of actual usage to be determined statistically, not a question of principle (unless you have PRESCIPTIVIST tendencies). What does “ambiguous enough to force the inclusivity” mean? As a rule, ambiguity does not force anything. On the contrary, it leaves things up in the air.

So much so that, when in need of an exclusive form, we have come up with “xor” in logic and computing.

Now, from my knowledge of the history of mathematical logic, the reason for introducing the “xor” operator, in contrast to what had been called the “or” operator, was precisely to circumvent the ambiguity of “or” in actual English speech, and arguments about ‘the real meaning of “or”‘. With “xor” and “ior” at your disposal, there’s no longer any need to argue. In each context, you specify the operator that does what you intend.

In language, we sometimes use “either/or” to mean the exclusive form (personally, when meaning alternatives I try and always [all times] explicitly use “and/or” and/or “either/or” [which is to say that each time I use "and/or" either/or "either/or"])

I broke my hedge-trimming shears on that sentence, trying to get it open.

Posted by Grumbly Stu at July 16, 2009 04:40 PM

GS – Thanks!

o versus ó

Post-reading your post and checking the RAE, I have become para(e)noid. I am a native Spanish speaker, so I think it’s not that I misunderstood the RAE… It now appears as if I’ve just gone and entirely made this up!

And/or maybe this is an example of sollipsistic usage… Well, at least of ultra-localized (or just technical) usage. I’ve never looked up the exclusivity of ó that I can remember—in a big mea culpa confession. It’s always been a natural convention for me, and comes from days before the Internet allowed for proper sourcing.

My latest, rather than earliest, recollection of a discussion was precisely in re: English’s lack of linguistic (as opposed to logistic) xor. It was in a group of group theorists and none griped. I am a mathematician, and in the School of Sciences, we all used ó as xor (and sneered at the travails of English-speaking group-ers when fumbling for a natural exclusive construction that avoided the logician’s). At the time in question, I was explaining the English “or” (as I thought my English was better than that of most of my peers, and they haphazardly—it now seems—agreed).

**”A or B” cannot possibly mean “both A and B, if you so desire”** (Please excuse my use of ** as I don’t know how to italicize.)

I think they can, and therein lies part of the issue. If I were to ask you to dinner I could say “please let me know of any preference for location or cuisine”. If I used “and”, I would be indicating that I expect “both” a neighborhood and a culinary choice. By using “or”, I allow you to choose to voice an inclination for one, the other, and/or both. If I was of the type that insists on absolute(-ist) fairness, I would need xor to say that you had to opt for an end-geography and I would then decide on the origin-geography, xor vice-versa. I guess this can fall outside the use of “or” for alternatives, so the other example is that when we go “you can have meat, potatoes, or fruit”.

**”ambiguous enough to force the inclusivity”**

As you well point out, Hamlet allowed his context to define the exclusivity. And most times that works. But by the above I mean that since “or”‘s exclusivity or inclusivity is context-dependent, and in some cases the context leaves the ambiguity open (as in our dinner), then the natural form is inclusive (or we would go insane). [As the inclusive form includes in correct context the exclusive but the opposite does not hold. In a sense, the inclusive for "is larger".]

**With “xor” and “ior” at your disposal, there’s no longer any need to argue.**

In Logic there is no need to argue, granted (or I could say that there is always need to argue, just not for this). My point exactly is that English (as opposed to logician-English) has no such operators and so we need use “or” = “and/or” = ior and “either/or” = xor when we want to make sure the inclusivity and/or exclusivity is explicit.

On the more marginal

**unless you have PRESCIPTIVIST tendencies). **

I am not of a PRESCRIPTIVIST bend, or so I hope (hence my “not *wrong*”). Just seeing the word in caps makes me feel like I am watching a trailer for LH vs DFW Redux…

**
I broke my hedge-trimming shears on that sentence, trying to get it open.**

Let me try and explain my convoluted writing (though I can’t say that as for my convoluted self):

we sometimes use “either/or” — I.e. as if it was a word.

I try and always [all times] explicitly use “and/or” and/or “either/or” — Every time I mean choice, when “or” is normally used, I *substitute* “or” for something else. that something else is sometimes “and/or”, sometimes “either/or”. So, in general, I use one “ior” the other.

which is to say that each time I use “and/or” either/or “either/or” — But each specific time, I cannot use both; each sepcific time I *substitue* “or”, I use one “xor” the other.

**You seem at least to have mastered the style of the Sphinx…. **

You’ve just given brilliant wordsmith ammunition to every significant other that, in looking for signifiance if my insignificant prose that was meant to convey my heart-felt but locked-in significatum, decided I was too obscure… and dumped me.

TL

Posted by tlajous at July 16, 2009 11:31 PM

In Spanish, “or” can be “o” or “ó”. The diacritical accent turns the inclusive form “o” into the exclusive form “ó”.

My Hispanic students say no; it’s only used for numbers. They agree with Grumbly. Example–the numbers 9 or 10:
In words: nueve o diez
In numerals: 9 ó 10

And this would suggest that “either” is only exclusive within the “either…or” construction.

What about this example: “You can plant the tree on either side of the gate.”

the reason for introducing the “xor” operator, in contrast to what had been called the “or” operator, was precisely to circumvent the ambiguity of “or” in actual English speech,

Not quite. They describe computer gates–electrical circuits, if you will–with exact outputs which are described by a “truth table”. The output of an “or” gate is either a one or a zero–that is, either on or off-depending on the inputs. Only one input has to be a one to get a one at the output. If both inputs are one, the output is still one. If both inputs are zero, however, the output is zero.

The “exclusive or” gate is slightly different in that a one at both inputs will produce a zero at the output. You must have a one at one input or the other but not both in order to get a one output.

I broke my hedge-trimming shears on that sentence, trying to get it open.
How about this: “You can have either the chocolate cake or the chocolate ice cream.” “You can have the chocolate cake and/or the chocolate ice cream.” …ooooorrrrrr…(back to the exclusive “either”) “You can have either piece of cake.” “You can have either kind of ice cream.”

Posted by Nijma at July 16, 2009 11:36 PM

Nijma -

**What about this example: “You can plant the tree on either side of the gate.”**

See above on Hamlet.

**They describe computer gates**

That came after both the chickena dn the egg. The truth table pre-dates computer gates. It’s from our friend Frege, I think. It permeates Fregean logic and then moves to language, and appears in THE Tractatus, etc. Within mathematics (which also serves to give context to my usage of the exclusive ó), the “xor” operator generates a group and the “or” operator does not. (Hence the discussion among group theorists, where “ó” generates a group and “o” doesn’t.) The electrical/computer circuitry is just an application… And if you follow the truth tables, you get to exactly the meaning I posit above. I am basically saying tha the truth table for English-”or” and “either” is the same as that for Logician-”or” and to force the “xor” truth table, the “either…or” construction is necessary.

TL

Posted by tlajous at July 17, 2009 12:05 AM

UPDATE:

I am basically saying tha the truth table for English-”or” and “either” is the same as that for Logician-”or” and to force the “xor” truth table, the “either…or” construction is necessary.

TL, now I understand what you mean!! I did have the distinct suspicion that Anglophone utility-shed Grumbly was up against Hispanic baroque-chapel TL. No offense meant with the Sphinx: it does have a fascinating expression on its face.

For text in italics, type this: <i>text</i> This site supports basic HTML tags.

xor generates a group. How curious! Can you give a brief description? There are a few mathematicians floating around here (I am 1/4 of one), so it would be of some interest, even though not general interest.

Posted by Grumbly Stu at July 17, 2009 01:04 AM

tlajous,
Before Frege, Boolean algebra (I’m more on the practical side), but yes, an apt parallel to the either~or language question.

And this would suggest that “either” is only exclusive within the “either…or” construction. By exclusion, then, “either” is inclusive (just as “or”).

“You can plant the tree on either side of the gate.”

“Either” used by itself in my gate/tree example above (chosen for its parallel with the “There is a tree on either side of the gate” example further upthread) is exclusive. The Hamlet example was about “or”, and there it’s used with “be”–it’s like pregnancy, you’re either dead or you’re not. If you wanted to test whether “either” is inclusive, you would need an example with no contextual clues that was not ambiguous.

Most of the usual codes work here. For italics:

<i> to begin italics

</i> to close italics

Posted by Nijma at July 17, 2009 01:16 AM

Thanks for the italics tip, my only meta-language is LATEX.

How curious! Can you give a brief description?

I’ll back up. Using Rotman’s excellent An Introduction to the Theory of Groups (it’s in Amazon, but one day I’ll learn to add links, I’ll stick to italics for now):

“A semigroup (G,*) is a non-empty set G equipped with an associative operation *.”
AND
“A group is a semigroup G containing an element e such that: (i) e*a = a = a*e for all a in G; (ii) for every a in G there is an element b in G with a*b = e = b*a.”

(We could go into the differing usage of all and every in here…)

Use the set {Y,N} (where Y is “yes” and N is “no”) with the operator xor. Then we must only show that it needs no parens when we compose it. Hhhhmmm, now, Y xor Y = Y, N xor N = N, Y xor N = Y, and N xor Y = Y. Then we only need show that for any three operands this (the no-need for parens) holds (as there are only two elements in the set). And it’s easy to do explicitly, so I’ll leave it to you. So xor generates a semigroup. Now e (the identity) is Y because Y xor Y = Y = Y xor Y and Y xor N = Y = N xor Y. And b (the inverse), is N for Y, as Y xor N = Y = N xor Y, and Y for N as N xor Y = Y = Y xor N. Note that I seem to be repetitive because we have not shown commutatitvity (i.e. a*b = b*a). But that one, I think, is clear and trivial from the truth table (Y xor N = N xor Y) and from the fact that the definition of e already showed it for all elements in G as there are only two. So the group is in fact, abelian (every pair commutes).

Now, try the same with or. It’s clearly a semi-group as it is associative (more easily shown than for xor, again, doing so explicitly in sets of three is the fastest route). But with or, there is no identity: it cannot be Y as Y or N = Y, and it cannot be N as if it was, then Y would have no inverse.

And that’s where my ó versus o comes from…

TL

Posted by tlajous at July 17, 2009 01:51 AM

Nijma -

you would need an example with no contextual clues that was not ambiguous

If there is such a thing as an ambiguous example, then it is inclusive. See above on how inclusivity is larger than exclusivity (which intuitively makes sense too).

Before Frege, Boolean algebra

On Boole, I can just say that I drool…

TL

Posted by tlajous at July 17, 2009 02:03 AM

INTRA-UPDATE:

Much has happenned at Languagehat (which I’ll add to this post later), but I was really on the verge of getting pummelled. Phew!, am happy to have just read (about me) that GS “even wondered briefly whether a real mathematician would flub such a simple example. Only later did I go sleuthing on the net to find out who he was, and had to slink back home wet and bedraggled. And he did say later that it was only a typo …”