On Epistemic Modal Predicate Logic
In their earlier investigations Frege and Russell have specially turned their attention to logical analysis of complex sentences with subordinate clauses, which are introduced by the connective that and the verbs know, believe, doubt and so on (e.g. ‘Columbus believed that he had paved a new nautical way to India’). Following Russell and Ducass, relations, which are expressed by these complex sentences, are called propositional or epistemic attitudes. The truth of those sentences does not always depend on truth values of the subordinate clauses, it is not their function. Therefore, replacement of the subordinate clause by any of the equivalent sentences can change the truth value of the complex one. For a long time there was no satisfactory theory of logical analysis of these sentences. Unsuccessful was, ultimately, also the search of such criteria of identity of senses and synonymity of sentences, which guarantee permissibility of the above mentioned replacement.
KeywordsInductive Hypothesis Atomic Formula Modal Rank Logical Sign Subordinate Clause
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