Lesniewski’s Systems Protothetic

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In the period between the two World Wars, Stanislaw Lesniewski, a prominent Polish logician, created his system of the foundations of mathematics, a system comprising three deductive theories: protothetic, ontology, and mereology. Lesniewski initiated his research programme in the foundations of mathematics in 1914 with his studies on a general theory of sets (to be later renamed mereology ). The construction of ontology in the period between 1919 and 1921 marked the next step in the formation of Lesniewski’s system. In order to combine mereology and ontology into a logically rigorous system, he constructed protothetic - the system of first principles . Lesniewski’s system of the foundations of mathematics was the most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics (Z. Jordan). This volume is a collection of the major contributions to protothetic, and includes the protothetic bibliography.