A theory of modal dialectics (Q1084388)

The paper provides a discussion of the normative foundations of modality from the point of view of argumentation and debate (rather than semantics). The introduction of a necessity operator is motivated as a way to get rid of the portmanteau character of implication and negation. In noncumulative dialectics these operators serve two purposes at the same time, viz., to indicate a level of strictness and their ordinary purpose as propositional operators. This is rather awkward [see the author's earlier paper, ibid. 14, 129-168 (1985; Zbl 0571.03003)]. In the modal dialectic systems, on the contrary, the necessity operators are the only ones to indicate strictness. The normative foundation of modal dialectics proceeds from the following fundamental norm of many-leveled dialectics: A (local) thesis is to be defended, ultimately, on the basis of concessions that are as strict as or stricter than this thesis. (There are systems for any number of levels of strictness.) This norm is then implemented by sets of rules that rigorously regiment discussions: modal dialectic systems. These systems are invertible, whereas the noncumulative systems are not invertible. The paper provides derivational and semantic systems of modal logic that correspond to the modal dialectic systems. The equivalence of these systems is proved in the Full Circle Theorem. (So this is a kind of completeness theorem for modal dialectics.) The last section contains some remarks about classical modal systems, i.e., systems based on classical propositional logic. The rest of the paper, however, takes constructive (intuitionistic) or minimal propositional logic as basic, and the modal dialectic systems based upon one of these stand out as the most attractive systems.