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Throughout his career, Keith Hossack has made outstanding
contributions to the theory of knowledge, metaphysics and the
philosophy of mathematics. This collection of previously
unpublished papers begins with a focus on Hossack's conception of
the nature of knowledge, his metaphysics of facts and his account
of the relations between knowledge, agents and facts. Attention
moves to Hossack's philosophy of mind and the nature of
consciousness, before turning to the notion of necessity and its
interaction with a priori knowledge. Hossack's views on the nature
of proof, logical truth, conditionals and generality are discussed
in depth. In the final chapters, questions about the identity of
mathematical objects and our knowledge of them take centre stage,
together with questions about the necessity and generality of
mathematical and logical truths. Knowledge, Number and Reality
represents some of the most vibrant discussions taking place in
analytic philosophy today.
Throughout his career, Keith Hossack has made outstanding
contributions to the theory of knowledge, metaphysics and the
philosophy of mathematics. This collection of previously
unpublished papers begins with a focus on Hossack's conception of
the nature of knowledge, his metaphysics of facts and his account
of the relations between knowledge, agents and facts. Attention
moves to Hossack's philosophy of mind and the nature of
consciousness, before turning to the notion of necessity and its
interaction with a priori knowledge. Hossack's views on the nature
of proof, logical truth, conditionals and generality are discussed
in depth. In the final chapters, questions about the identity of
mathematical objects and our knowledge of them take centre stage,
together with questions about the necessity and generality of
mathematical and logical truths. Knowledge, Number and Reality
represents some of the most vibrant discussions taking place in
analytic philosophy today.
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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