chapter  1
Logical form
Pages 15

Paradoxes limit concepts in an especially striking way, unless we are obtuse to their impact, requiring us to rethink cherished positions as we try to negotiate passage through an unexpectedly complex conceptual terrain. The solutions offered to logical paradoxes are sometimes supported as stopgaps, provided that they do not entail serious disadvantages, even if they are not regarded as perfectly satisfactory on all counts, as the only way to preserve an otherwise useful formalism. This chapter examines a representative selection of four main types of paradox: paradoxes of conditionals; self-non-applicational paradoxes; the paradox named after its discoverer Kurt Grelling; and inductive paradoxes. The idea is to think about logic in terms of the challenges introduced by paradoxes, and about how logic develops and is refined in light of and in response to the problems that paradoxes pose for a symbolism's formal logical and semantic integrity.