Nikolay Ivanov

Pragmatism of Peirce and James overcomed traditional dualism between mind and matter, sense data and conceptions, and the severe differentiation between philosophy, science, art and religion. They made three types of synthesis- epistemological, metaphysical and religious, based on relations between belief, thought, and action. Within the framework of these the problem of relation between science and religion is solved. Peirce founded science on essentially religious metaphysics in such context in which knowledge and thought are grounded and become meaningful. Science exists as a part of evolution of the universe not as end in itself. Without solving the metaphysical problems scientific knowledge is fallible and incomplete. Religious belief is another sort of knowledge for the evolution and in the future it would converge with science.

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘ All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem