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.
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