This book argues that the meaning of negation, perhaps the most
important logical constant, cannot be defined within the framework
of the most comprehensive theory of proof-theoretic semantics, as
formulated in the influential work of Michael Dummett and Dag
Prawitz. Nils Kurbis examines three approaches that have attempted
to solve the problem - defining negation in terms of metaphysical
incompatibility; treating negation as an undefinable primitive; and
defining negation in terms of a speech act of denial - and
concludes that they cannot adequately do so. He argues that whereas
proof-theoretic semantics usually only appeals to a notion of
truth, it also needs to appeal to a notion of falsity, and proposes
a system of natural deduction in which both are incorporated.
Offering new perspectives on negation, denial and falsity, his book
will be important for readers working on logic, metaphysics and the
philosophy of language.
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