O stosowalności niektórych modalnych reguł inferencji w rozumowaniach pozalogicznych

Abstrakt

The presented paper takes up the attempt to analyse and specify the suspicion that some modal rules of inference are paralogical in application to non-logical reasonings (s.c. modal fallacy). The considerations have been limited to modal prepositional calculi: K and S5, which are intended to be a formal base of these non-logical reasonings - proofs of so called specific thesis on the grounds of the particular specific theories. Pointing out the properties of being permitted, being valid and being derivable in case of inferences rules and also semantical relations of point, structure, frame and inferential consequence in standard semantics of possible worlds, enables to define two kinds of paralogism: point and structural. Justification of the suspicion of modal fallacy occurrence in the case of a given inference rule, depends on pointed metalogical properties of this rule and also on what kind of the notion of paralogism is being discussed. It appears that when a given rule is paralogical only pointly (and not structurally), the sufficient condition of avoiding modal fallacy is to consider the specific axioms of the given specific theory as the sentences which are structurally true (structural truth is of course not equivalent to logical truth). If we want to treat these axioms as sentences which are pointly true, we have to eliminate pointly paralogical rules. In this case it is enough to construct such axiomatisation of calculi K and S5, in which we use the notion of modal closure (it eliminates the primitive rule of Goedel and all rules derivable from it - rules which are structurally but not pointly correct).