In our research lab, we have developed such a theory: the axiomatic theory of abstract objects. It is proposed by Edward N. Zalta (Ph.D./Philosophy), a Senior Researcher at CSLI who directs the lab. The theory is based on an idea of Ernst Mally (b. 1879, d. 1944), an Austrian philosopher who worked at the University of Graz (our computer is named after him). In 1912, Mally informally introduced an interesting logical distinction and this distinction is formalized in the axiomatic theory of abstract objects. The abstract objects mentioned above can be precisely defined in terms of the theory and their properties can be derived as consequences of the theory. Our results are collated in the document Principia Metaphysica, which is linked into the button The Theory of Abstract Objects. By examining the other buttons, you may find that the theory unifies some of the ideas of Plato, Meinong, Frege, and Leibniz, as well as other philosophers. In published work, the theory has been applied to problems in the philosophy of language, intensional logic, the philosophy of mathematics, and the history of philosophy.
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Theory of Abstract Objects (Summary and Tutorial)
Gottlob Frege
Gottfried Wilhelm Leibniz
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Ernst Mally
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