Colloquium: Reciprocity and asymmetry

October 27, 3:30-5pm, Cobb 201
Alda Mari, Institut Jean Nicod, CNRS/ENS/EHESS

It is well-known that reciprocal sentences exhibit a great variety of interpretations (e.g. Langendoen, 1978; Dalrymple et al. 1998; Sabato and Winter, 2011). A sentence like (1) is interpreted as ’each man in the set of men knows every other different man in the same set of men’. This interpretation is called ’strong reciprocity’.

(1) The men know each other

Another interpretation is called ’inclusive alternative orderings’. A sentence like (2) is interpreted as ’each table in the set of tables is either on top of or at the bottom of a different table in the same set’.

(2) The tables are stacked on top of each other

A common strategy has been to assume that this variety is due to the ambiguity of the reciprocal quantifier each other and different truth conditions have been proposed (e.g. Dalrymple et al. ibid, Beck, 2001) . The main problem with this strategy is that it predicts that all the sentences that satisfy the truth conditions for ’inclusive alternative orderings’ are true (and acceptable). This prediction is wrong, as illustrated by (3).

(3) #My mother and I gave birth to each other (Sauerland, 1998)

In the talk we claim that each other is not ambiguous between a series of quantifiers and propose new truth conditions for it.

These are casted in a branching time framework (Thomason, 1984). In a nutshell, we claim that a reciprocal each other sentence is acceptable if it describes a relation that is either actually or possibly true on a strong reciprocal interpretation. We pose some constraints on the possibilities, appealing to inertia branches (Dowty, 1979). This will allow us to account for new data related to the inclusive alternative ordering interpretation and explain why (3) is unacceptable.

Selected references

Beck, Sigrid 2001. Reciprocals are definites. Natural Language Semantics 9 : 69-138.

Langendoen, D. Terence 1978. The logic of reciprocity, Linguistic Inquiry 9 : 177-197.

Dalrymple, Mary, Makoto, Kanazawa, Yookyung, Kim, Sam, Mchombo, and Stan- ley, Peter 1998. Reciprocal expressions and the concept of reciprocity, Linguistics and Philosophy 21 : 159-210.

Dowty, David 1979. Word Meaning and Montague Grammar. Dordrecht: Kluwer Academic Publishers.

Sabato, Sivan and Winter, Yoad 2011. Relational Concepts and the Logic of Reci- procity. Ms. University of Utrecht.

Sauerland, Uli 1998. Plurals, derived predicates and reciprocals, in U. Sauerland and O. Percus (eds.). The interpretative tract. MIT Working Papers in Linguistics 25, 177- 204.

Thomason, Richmond 1984. Combinations of tense and modality, in D. M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic: Extensions of Classical Logic, vol. II, Dordrecht: Reidel, 135-165.