Language Heedless of Logic - Philosophy Mindful of What? Failures of   Distributive and Absorption Laws
  Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language. They presume semantics under which `and' and `or' are related by the dually paired distributive and absorption laws. However, at least one of each pair of laws fails in the vernacular. `Implicature'-based auxiliary theories associated with the programme of H.P. Grice do not prove remedial. Conceivable alternatives that might replace the familiar logics as descriptive instruments are briefly noted: (i) substructural logics and (ii) meaning composition in linear algebras over the reals, occasionally constrained by norms of classical logic. Alternative (ii) locates the problem in violations of one of the idempotent laws. Reasons for a lack of curiosity about elementary and easily testable implications of the received theory are considered. The concept of `reflective equilibrium' is critically examined for its role in reconciling normative desiderata and descriptive commitments. 
Arthur Merin
cs.CL