The algebraic theory of propositions and belief reports
Keywords:
intensional contexts, propositions, identity conditions, modes of presentation, operationsAbstract
Intensional contexts are those contexts in which the principle of substitution of co-referential terms salva veritate fails. A particular case within these contexts are reports of propositional attitudes, that is, contexts in which relations expressed by transitive intensional verbs (“believes”, “doubts”) link an agent and a proposition. Traditional conceptions that reduce propositions to possible worlds have failed to account for these contexts because they posit coarse grained identity conditions. This has been one of the motivations for the formulation of algebraic theories of properties, relations and propositions. The objective of this work is to explain how this theory accounts for these failures. According to these conceptions, propositions are 0-adic properties that appear as elements within intensional algebraic systems. The identity conditions of propositions are determined by their constituents and the structure imposed by algebraic operations. It is argued that algebraic theories cannot accommodate belief reports by appealing only the structures of propositions, so it is necessary to complement the theory with modes of presentation.
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