A new proposal for the interpretation of sentences with the anaphor "each-other"
It is well-known that sentences with expressions such as each-another in English, exad et-haSeni in Hebrew, and un-l'autre in French can have various the interpretations with different logical strengths (in terms of entailments). This state-of-affairs has repeatedly raised the following questions, using Dougherty's (1974: 18-19) words: "How is a specific input linked to a specific output? That is, what is the rule of semantic interpretation for each other sentences?… how a specific interpretation (or range of interpretations) is assigned to an arbitrary sentence?"
Naturally, there are at least two competing directions for answering these questions:
Strongest Meaning Hypothesis (SMH) (Dalrymple et al. 1998; Sabato & Winter 2012): The meaning of the reciprocal sentences varies from one sentence to another and is taken from a small inventory of meanings. It is possible to predict a context-sensitive meaning of every reciprocal sentence: in a given context, a sentence takes the strongest meaning that is consistent with known facts about the specific context.
The Unspecified Constructions Hypothesis (UCH): The relevant constructions are ‘unspecified constructions’, described by the following definition: expressions used in relations between two (defined) sets (or more) without specifying which set occupies which position. Accordingly, the basic meaning of these constructions has a much weaker meaning than what SMH argues for, because it only necessitates that each member of the set stands in a single relation to another member. Although this is necessarily true for all sentences with these expressions, these are not sufficient conditions to capture only true sentences in many cases.