Expounding assertion and expanding negations in logic

I. Grattan-Guinness


This article considers two aspects of classical two-valued logic that deserve more attention than they receive: elaborating the details of asserting a proposition, that is, assigning to it one of the truth-values ‘true’ and ‘untrue’; and extending the negation of a proposition to modes when only a part of it is negated. These two modifications are applied to a trio of case studies in logic: the formulation of several paradoxes, the use of indirect proof-methods when the theorem in question is asserted, and the distinction between implication and inference. Attention is also drawn in places to some features of logic that are often treated rather casually; for example, specifying universes of discourse, and theories of truth. Relationships with mathematics are emphasised.


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