Sunday, November 25, 2012

Confusion about Reciprocals

There is an obvious difference between the literal meaning of an expression and its actual usage. Consider the phrase ``scared to death,'' which everyone knows is rarely used in its literal meaning. When it is, in fact, people usually add the adverb ``literally,'' as in, ``there's no apparent cause of death; the victim seems to have been literally scared to death.'' However, if one were to simply survey attested usage of the phrase in an attempt to determine its literal meaning, one would of course be deceived.

How does one distinguish literal meaning from usage? One could simply ask a native speaker; all native speakers of English, for example, could tell you the distinction between the literal meaning of the expression ``scared to death'' and its actual usage. This does not always work, however. Another example, though, can point to some ways to get at literal meaning. Consider the phrase ``a minute.'' If one were to survey its usage, particularly when spoken to antsy children, as in ``we'll be there in a minute,'' one would conclude that it denoted a time period of quite extended range, perhaps up to one hour. But if one were to limit the context of utterance to those contexts that required greater precision in time durations, one would quickly discover that the phrase's literal meaning is a time period of 60 seconds. One such context is a race: if the TV announcer says, ``the winner beat the next runner by a minute,'' the phrase ``a minute'' means 60 seconds (give or take a few decimal points). Another context is a court of law: if the prosecutor, seeking to establish a timeline, asks me, ``How long did you leave the victim alone?'', and I answer, ``A minute,'' I would be lying if I had actually left the victim alone for two minutes or more.

Hence, it is a simple truism that people use expressions in non-literal ways. Importantly, these non-literal uses in no way require that semanticists posit truth-conditional meanings for expressions that differ from the literal meaning. The meaning of ``a minute,'' for instance, is a time period of 60 seconds; it is in actual usage that this time period extends beyond that. (If you asked someone, they would say that ``We'll be there in a minute'' is literally false if it will take more than 60 seconds to get there.)

For some reason, though, the simple distinction between literal meaning and linguistic usage is frequently ignored in studies of reciprocals. A huge literature now exists examining the possible meanings of reciprocals (e.g., Dalrymple et al. 1998, Beck 2001, Schein 2001, and now Sabato and Winter 2012). Much of this literature (Dalrymple et al. 1998 in particular) surveys attested usage of reciprocals in an effort to figure out what they mean. As with the phrase ``scared to death,'' this method runs the risk of obscuring the actual meaning by not distinguishing that from non-literal usage. This is exactly what has happened; while there is a significant amount of complexity to reciprocals, I believe that they are actually much less complex than they appear to be. The problem is exactly that described above: people use language in non-literal ways.

The kinds of meanings that reciprocals have been argued to have can be illustrated with examples like the following:

(1) The three thugs respect each other.
(2) The three thugs shot each other.

The example in (1) requires that every thug respect every other thug. This interpretation is called Strong Reciprocity, and it seems to be required by stative predicates like respect. This strong interpretation is not necessary with the eventive predicate in (2), which seems to require (minimally) that each thug shot one of the other ones, and got shot by one of the other ones. This interpretation is usually called Weak Reciprocity. I believe that these two interpretations are the only ones that reciprocals have: statives require Strong Reciprocity, while eventives require Weak Reciprocity.

This is not what most of the literature has concluded, however. Dalrymple et al. (1998) introduced a whole range of possible reciprocal meanings in order to account for attested examples like the following:

(3) The third-grade students in Mrs. Smith's class gave each other measles.

In this example, world knowledge tells us that each student can get measles only once, and one of the students must have gotten measles from a non-student, leaving at least one student with no student to give measles to. So, if Weak or Strong Reciprocity were the only meanings a reciprocal could have, sentence (3) could never be true. Yet speakers of English utter and accept sentences like (3). Dalrymple et al. (1998), and researchers after them, therefore added additional meanings for reciprocals.

The obvious alternative, though, is that sentence (3) is literally false, just like scared to death is (almost) always literally false. This is in fact my judgment: it is literally impossible for a group of children to give each other measles. But one can still say ``the children gave each other measles,'' with the meaning that measles passed from one child to another; we just allow two exceptions at either end of the chain (and possibly more, depending on the size of the group). If we switch to a context that requires more precision, though, the literal meaning of the reciprocal comes out. Consider a context where two epidemiologists are talking, and they are trying to determine the source of a measles outbreak. Dr. Q asks how the third-grade students in Mrs. Smith's class got measles. Dr. Z would never reply with the sentence in (3); if he did, he would be saying that measles was not introduced into the class from an outside source, and must have had a spontaneous genesis within the class.

This context makes it clear that the literal, precise meaning of the reciprocal expression is something other than how it is used in (3). In fact, the literal, truth-conditional meaning is Weak Reciprocity, which requires that each member of the subject set act on one other, and be acted upon by one other. That is, each child gave another child measles, and each child got measles from another child. The literal, precise meaning could never be true, which is why in a context that requires it to be, no one would use it. Outside of such contexts, however, people make general statements that have exceptions, they exaggerate, they understate, they speak metaphorically, and so on.

As another example, consider the famous example, ``The people on this island used to eat each other.'' It was probably not true that every single person ate at least one other person and in turn got eaten by someone. For some reason this is thought to be significant in discussions of reciprocals; but take a similarly general statement not involving reciprocals, like ``The people on this island used to eat dodos.'' It was probably not true that every single person ate a dodo; surely some people on the island did not like dodo, or some were vegetarians; the statement is made as a generality, which of course will have some exceptions. The reciprocal statement is no different.

Similar issues are at work in examples involving linear configurations, such as ``The children followed each other into the schoolhouse,'' or ``The acrobats stood on each other's shoulders.'' The members of the subject set at the ends of the lines (or stacks) are exceptions: they participate in the relation in only one way. That they are exceptional is shown by the fact that the size of the set matters, as pointed out by Beck 2001: people would not use ``The children followed each other into the schoolhouse'' when there are only two children, and in fact acceptability goes up with the number of students. Same with acrobats: if there are only two, they have to alternate, first one standing on the other, then they switch. This, it seems to me, points to the actual, literal truth conditions of (eventive) reciprocals being Weak Reciprocity.

Yet another publication has recently appeared in which the distinction between literal meaning and actual usage is not properly made, namely Sabato and Winter 2012. While it may be that I am wrong that there are only two possible meanings for reciprocals, the distinction between literal meaning and usage needs to be carefully kept in mind in trying to figure out what the truth-conditional meaning of an expression is. Many (possibly most) utterances that humans make are not literally true, so just surveying attested usage will not be a good guide to actual meaning.


Beck, Sigrid (2001). Reciprocals are Definites. Natural Language Semantics 9: 69--138.

Dalrymple, Mary, Makoto Kanazawa, Yookyung Kim, Sam Mchombo, Stanley Peters (1998). Reciprocal Expressions and the Concept of Reciprocity. Linguistics and Philosophy 21: 159--210.

Sabato, Sivan and Yoad Winter (2012). Relational Domains and the Interpretation of Reciprocals. Linguistics and Philosophy 35: 191--241.

Schein, Barry (2001). Adverbial, Descriptive Reciprocals. Proceedings of Semantics and Linguistic Theory XI, edited by Rachel Hastings, Brendan Jackson, and Zsofia Zvolenszky. Ithaca: CLC Publications.

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