A New-old Characterisation of Logical Knowledge

作者：Grattan Guinness Ivor^*

来源：History and Philosophy of Logic, 2012, 33(3): 245-290.

DOI：10.1080/01445340.2012.675631

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of %26apos;sortal terms%26apos;, two theories that will feature prominently. Second, we propose that logic comprises four %26apos;momental sectors%26apos;: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (in) valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its %26apos;external%26apos; negation not-R; and the assertion of R in the pair of propositions %26apos;it is (un)true that R%26apos; belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended.

• 出版日期2012