## $1 in the hands of a woman Reader Jacob Baskin wrote with an interesting ambiguity that he was reminded of reading my recent post about "the wife and mother of two men killed in a fire". He writes In the context of third-world development, I recently heard the factoid that "$1 in the hands of a woman is, on average, worth $10 in the hands of a man" (here, for instance). Does this mean, "Each dollar that a woman has is worth, to her, what ten dollars would be to a man"? Or, "Each dollar that a woman has would be worth, if it were in the hands of a man, ten dollars"? Clearly the former meaning is intended, but as with that "duck/rabbit" optical illusion, I can make myself see the sentence in either way. I'm hard pressed to think of other sentences with two possible meanings in direct opposition to each other. I also can't quite figure out what's going on with the sentence to create this ambiguity. Just thought this might be interesting to you. Yes, it’s interesting! Here are my first thoughts, for what they’re worth. I also easily hear both meanings, (plus a third, I discovered as I wrote this) and I think both (maybe all three) patterns are probably common. I think the difference comes from three different kinds of “filling in” that we can do. Consider first the familiar proverb: A bird in the hand is worth two in the bush. This one is about what birds are worth to “me” (or to “one”, generically) depending on where they are. Having one bird in the hand is worth (to me) having two birds nearby but not in my hand. I guess it can also be paraphrased as “A bird, if it’s in my hand, is worth (to me) what two birds are worth (to me) if they’re in the bush”. So we’re figuring out the comparative value to one individual of a bird in two different locations. For a second kind of meaning I don’t know a proverb, but googling on “one dollar in the hands of” turns up quite a number of examples, some with different structure that makes the second meaning clear. Here’s one: The real value of one dollar in the hands of a poor Cambodian is significantly higher than the real value of one dollar in our hands. — This blog post is touching, and it happens to add rich detail about the intended meaning: What is one dollar to us? What is one dollar to those poor Cambodians? When we spend one dollar, they earn one dollar. We will be one dollar poorer while they will be one dollar richer. However, being one dollar poorer can hardly ever affect our standards of living in any way; while one dollar richer can make a significant difference to a poor fellow Cambodian for a day or two. That blogger (who is Malaysian) could have said, using Jacob’s construction, One dollar in the hands of a poor Cambodian is worth fifty dollars (or whatever) in the hands of a Malaysian. And there we’re switching the implicit argument of worth, I think: What a dollar in the hands of a Cambodian is worth to the Cambodian is the same as what fifty dollars in the hands of a Malaysian is worth to the Malaysian. And that’s very different from the ‘bird in the hand’ reading, where we keep the “worth-to” person constant and consider the value to them of these dollars (or birds) when they’re in different locations. And now I think there’s a third reading different still. Suppose I read the Cambodian example a different way: Having one dollar in the hands of a Cambodian is worth (to the world? to ‘impact on economic development’? in ‘real value’ (whatever that means)?) having fifty dollars in the hands of a Malaysian. That’s a meaning that might be of interest to prospective donors – you would do more good giving your dollar to a Cambodian. Oh, and that’s most likely the intention in Jacob’s original post: it’s probably suggesting that directing aid to women will have more economic impact than directing the same amount of aid to men. (That wasn’t the intention in the original source of the Cambodian example, though, where the Malaysian was a tourist discussing the enterprising Cambodian children selling ten postcards for a dollar, etc., and thinking of arguments for buying from them even when you didn’t really want more postcards.) So there are at least three possibilities, and they all seem to revolve around the implicit argument of worth – worth to whom? I haven’t worked on these constructions and what I just said is not a linguistic analysis, just what I would take as a starting point, trying to figure out what the different meanings are and where one might look for some implicit material that leads to the ambiguity. Summarizing: The construction has the surface form “NP1 in Location 1 is worth NP2 in Location 2”, where “NP” means a noun phrase like “a bird” or “one dollar”. Reading A: For the speaker, or a generic individual, or for some understood individual, call him/her S, NP1, if it’s in Location 1, is worth as much to S as NP2 is if it’s in Location 2. (And in this case, both location descriptions may be “anchored” to S. So “in the hand” is “in S’s hand”, and “in the bush” is “in the bush in the vicinity of S”) Reading B: Location 1 is anchored to Person 1 and Location 2 is anchored to Person 2, and the sentence means: NP1 in Location 1 is worth as much to Person 1 as NP2 in Location 2 is worth to Person 2. Reading C: NP1 in Location 1 is worth as much [in some neutral system of values, like “to economic development”] as NP2 in Location 2. Since the “Location n” might be “in the hands of Person n”, that seems to help make it easy to slide from one meaning to another. I think the real “culprit” is the missing argument of “worth”: “me” or “one” in Reading A, Person 1 vs Person 2 in Reading B, and some neutral value like “the world” in Reading C. ## 29 Comments 1. ### mgh said, October 17, 2012 @ 7:56 pm I run into something similar with groupons — I will say there is a$20 for $40 groupon (meaning, I spend$20 for $40 of goods) while the rest of my family thinks this is incorrect and says it is a$40 for $20 groupon (meaning I get$40 of goods for $20). 2. ### Barbara Partee said, October 17, 2012 @ 8:18 pm That's perfect for Jacob, because he was wondering if there were other cases where the two possible meanings were virtually opposites, and you just found one. (My first guess on yours is to look for different meanings of "for" as the culprit.) 3. ### Dick Margulis said, October 17, 2012 @ 8:26 pm Fourth possible meaning: A man can extract ten times as much utility out of a dollar as a woman. If I give a woman a dollar, she can prepare a meal for three people. If I give a man a dollar, he can prepare a meal for thirty people. So a dollar put into the hands of a woman is worth ten dollars if it is put into the hands of a man. I hasten to add that I don't believe this perverse interpretation. I'm just saying it's available, and if I were still a sophomore math major, I could probably prove some sort of theorem about this group that would demonstrate that those are the only four possible interpretations. But I'm not, and I no longer can. So it is left as an exercise. 4. ### Chad Nilep said, October 17, 2012 @ 8:46 pm Is there an actual semantic difference between Reading A and Reading C? There is a pragmatic or ideologically mediated difference between {judgement of some individual = S} and {universal or neutral judgement}. But in semantic terms, isn't the universal judgement from nowhere just another possible value for S? Reading A: worth to S of NP1 in Location 1 = worth to S of NP2 in Location 2 Reading C: worth to neutral system of NP1 in Location 1 = worth to neutral system of NP2 in Location 2 5. ### KathrynM said, October 17, 2012 @ 8:47 pm For what it is worth, I read the sentence initially with Barbara's meaning three: One dollar given to and deployed by a woman will do what ten dollars given to and deployed by a man will do [forgive the paraphrase–but I believe that is what you meant.] Like Dick Margulis, I am not necessarily subscribing to the truth of that interpretation: I'd want to see the data. LOTS of data. But that's how I read the sentence, before ambiguity intruded. 6. ### J.W. Brewer said, October 17, 2012 @ 10:15 pm I think it's pretty clearly Reading C in context, because the context is pitching to potential affluent First-World donors. The problem is conflating the donors' own subjective and often paternalistic preferences (which is not the worst thing in the world – if you don't want to be treated paternalistically, just don't ask for money) as to what uses of their donated money are more worthwhile with a "neutral system of values." 7. ### Barbara Partee said, October 17, 2012 @ 10:25 pm @Dick Margulis, thanks, I agree. After I had posted it occurred to me that I hadn't really gotten Jacob's second meaning among my three, and no two of mine were "opposites", as his intuition had told him. But I think my reading C (the intended reading for his example, I think) and your reading (let's call it D) are indeed 'opposite' — one says give the dollar to the woman, the other says give it to the man. @Chad Nilep — that's an interesting hypothesis, and it would be interesting to try to argue it out. Here's one argument, not a knockdown one though, for C and A not being the same reading with different choices of S. In the case of reading C, the location-descriptions can't be anchored to any 'person', because there isn't any 'person', the "worth" is to the whole world. So for instance the first example, with 'a bird in the hand', can't get a C reading because "the world" or "economic development" doesn't have a hand. If that argument works, I'd predict that the following sentence would pretty much demand an A reading: A crayon picture of oneself made by one's child is worth ten oil paintings of oneself made by a professional. (substitute "you" for "one" to make it more natural, but read that "you" as generic.) But even so, that doesn't prove that A and C are really different; reading A could maybe be like reading C but with the addition of some variable-binding relating the "worth"-argument to implicit arguments present in the Location phrases. 8. ### John Roth said, October 17, 2012 @ 10:57 pm I'd go with interpretation C, but then I'm primed for that interpretation since I've read a bit (not a huge amount, granted) about the kind of micro-finance investment that I think they're talking about. Interpretation A focuses on internal values: what a woman can purchase with$1 provides the same amount of satisfaction as what a man could purchase with $10. Interpretation B implies that women are radically less effective at getting value for money. Dick Margolis' interpretation D is a bit twisty. I can see it, but it slips away as soon as I quit focusing. "A bird in the hand is worth two in the bush" is talking about the risk value of giving up what you have (the bird in the hand) to capture the two that are in the bush. You may wind up with two birds, or you may wind up with none. Althernatively, it may be saying that what you have is worth more than what you might have, but actually don't. In either case, it isn't the same as any of the three interpretations. 9. ### Chad Nilep said, October 17, 2012 @ 11:42 pm @Barbara Partee "the world" or "economic development" doesn't have a hand. Well, according to Adam Smith it does (albeit an invisible one). Just slightly more seriously, if there are three implicit arguments (the object, the location, and the arbiter of value), does that change Dick Margulis's math? I'm also going to have to leave the specifics as an exercise for the reader, but if arbiter and location may or may not coincide, I think we have more than four potential readings. 10. ### Ian Tindale said, October 18, 2012 @ 1:28 am We have a project that takes ten weeks. Later, they say “we’re moving the deadline forward one week”. Does that mean it takes eleven weeks, or nine? 11. ### ajay said, October 18, 2012 @ 4:21 am I'm hard pressed to think of other sentences with two possible meanings in direct opposition to each other. "I have dusted this shelf". Interpretation 1: I am cleaning this room.This shelf does not now have dust on it. Interpretation 2: I am a scene of crime officer looking for fingerprints. This shelf now has dust on it. 12. ### Dakota said, October 18, 2012 @ 4:33 am If you go to the exact words of organizations concerned with third-world development , you will also find there is a bit of a circumlocution involved. The statement is Intercept Poverty: Give Girls Assets and Preparation for Decent Livelihoods and Give It To Them Young Girls and planners need to know that : •$1 in female hands is worth $10 (and in some cases$20) in male hands as women tend to invest money directly back into the family, children, education, health care, etc. while men spend it elsewhere

The "elsewhere", as I recall, is gambling and prostitution, but you can hardly say that to potential donors.

Phrased more elegantly, and indicating the intent of the statement, the organization also says, "Increased female control of income has far stronger returns to human capital and other investments than comparable income under male control"

13. ### Michael Cargal said,

October 18, 2012 @ 8:31 am

My immediate thought on reading it was that a woman would pay $1 for an amount of stuff that a man would have to pay$10 for.

14. ### Bobbie said,

October 18, 2012 @ 10:03 am

" I'm hard pressed to think of other sentences with two possible meanings in direct opposition to each other." Ajay added the example of "I have dusted this shelf" meaning either to remove the dust from or to add dust to (in a search for fingerprints.)
The children's book series about Amelia Bedelia (by Peggy Parish) is all about such misunderstandings. She is told to "dress the chicken" so she puts little outfits on each bird. When she makes a "sponge cake", she puts in real sponges. When she "weeds the garden", she replants the weeds. And when she "pitches a tent", she throws it into the woods. She "draws the drapes" on a piece of notebook paper and "puts out the lights" by hanging them on the clothesline.

15. ### Rachael said,

October 18, 2012 @ 10:05 am

Interesting example. I think the ambiguity lies in how you bracket the sentence. So
$1 in the hands of a woman is, on average, (worth) ($10 in the hands of a man) means the woman's $1 achieves as much as the man's$10 (the intended meaning), but

I started thinking in that direction too, but I couldn’t figure out what to do with the “$1 in the hands of a woman” part then. You could be right, but I couldn’t see how to get the two (or more) readings out of different ways of parsing it. I also at first was playing around with different readings of the Locative phrase – whether it would make a difference if we construe it as a simple locative (where the dollar is) or as a conditional “if it were in the hands of X”, but I don’t think that makes any obvious difference either, not when all the interpretations we’re talking about are generic and not referring to specific dollar bills. Proof of the pudding will be to make the structures explicit and figure out compositional semantic interpretation rules that will deliver all (and only) the interpretations we think the sentence can actually have. (And as Chad Nilep notes, maybe there could be more than four.) @John Roth – I wouldn’t actually want to put the “risk” business into the semantics, or even the idea that you would have to give up the bird you have in hand to try for the two in the bush. I think those things are added pragmatically as a way of making sense of what the point of the proverb is. “Conversational implicatures”, I think, in Gricean terms. So I stick to that proverb being an instance of Reading A. 22. ### Edward Vitasek said, October 19, 2012 @ 3:31 am Rachel: Interesting example. I think the ambiguity lies in how you bracket the sentence. So$1 in the hands of a woman is, on average, (worth) ($10 in the hands of a man) means the woman's$1 achieves as much as the man's $10 (the intended meaning), but$1 in the hands of a woman is, on average, (worth $10) (in the hands of a man) means that that$1 would achieve 10 times as much if given to a man (the opposite meaning).

Barbara Partee:

I started thinking in that direction too, but I couldn’t figure out what to do with the “\$1 in the hands of a woman” part then. You could be right, but I couldn’t see how to get the two (or more) readings out of different ways of parsing it.

I'm thinking, it depends on how you parse the sentence.

NP1 (One dollar in the hands of a woman) is worth NP2 (10 dollars in the hands of a man).

Or

NP1 (One dollar in the hands of a woman) is worth NP2 (10 dollars) Adverbial (in the hands of a man). [The adverbial would function as a conditional.]

I might get the terminology wrong, but I that's the direction I'm thinking in.

23. ### Edward Vitasek said,

October 19, 2012 @ 3:41 am

In case I didn't express myself well, here are the rephrased sentences:

(One dollar that is in the hands of a woman) is worth (10 dollars that are in the hands of a man).

vs.

(One dollar that is in the hands of a woman) is worth (10 dollars), (when it is in the hands of a man).

24. ### Diane said,

October 19, 2012 @ 4:20 pm

The alarm went off.

Meaning 1) The alarm was quiet, and has now started making a loud noise.
Meaning 2) The alarm was making a loud noise, and has now stopped.

25. ### Barbara Partee said,

October 19, 2012 @ 5:03 pm

@Edward Vitasek — So do we have to think of the tense-modality different in the two parts, do you think? I'm beginning to think I can see what you mean. For that second one, the parsing that I couldn't see what to do with, you think it might be something like:

Consider one dollar that is now in the hands of a woman. That dollar would be worth 10 dollars if it were put into the hands of a man.

(For the linguists: we give that subject phrase wide scope, I guess, and then the rest of the sentence is interpreted as implicitly modalized. Is there precedent for that? But the subject phrase is also generic in some sense — how get the two different operators it looks like we would need?)

If there is indeed a reasonable way to interpret such a structure in such a way, it looks like that might be a way to get Dick Margulis's D reading, the opposite of my C reading. Thanks.

26. ### JB said,

October 20, 2012 @ 12:47 pm

Jacob Baskin: "I'm hard pressed to think of other sentences with two possible meanings in direct opposition to each other."

Terry Pratchett has a funny line (about a clowns' school nearly burning down) that runs something like "It would have been a blow for entertainment in this city."

That has the two possible meanings running against each other, doesn't it?

27. ### Chandra said,

October 20, 2012 @ 2:15 pm

@Sevly – I guess I have less confidence in my ability to catch birds than you do.

28. ### David W. Hogg said,

October 21, 2012 @ 10:40 am

"A nuclear reactor cannot have too much water!" (from the Simpsons)

29. ### ajay said,

October 22, 2012 @ 5:04 am

David Hogg: yes, that's particularly good – is it impossible or just inadvisable?

A rather more serious example: "Let him have it, Chris!" – which could mean either "surrender your gun to the policeman" or "shoot the policeman". The difference in interpretation was, literally, vital.