A Computational Solution to the Problem of Reference. This project will attack the core problem of philosophy of language by developing and applying tools from the theory of algorithmic complexity. Groundbreaking pure research at the intersection of logic, language, information and computation is the lifeblood of commercial research and development in information technology and telecommunications. The project will foster a cross-fertilisation of ideas between philosophy, computer science, math ....A Computational Solution to the Problem of Reference. This project will attack the core problem of philosophy of language by developing and applying tools from the theory of algorithmic complexity. Groundbreaking pure research at the intersection of logic, language, information and computation is the lifeblood of commercial research and development in information technology and telecommunications. The project will foster a cross-fertilisation of ideas between philosophy, computer science, mathematics, linguistics and psychology, and will provide students with skills and analytic techniques that will be valuable in future pure and applied research.Read moreRead less
A Paraconsistent Approach to Vagueness. This project will utilise logical techniques that have been developed largely by Australian logicians. This techniques will be brought to bear on the problem of vagueness, one of the most important problems in the philosophy of logic. The project will thus greatly enhance Australia's already strong international reputation in logic and philosophical logic.
Analysis in the idealist tradition: the development of Leibniz's analytic method by Kant and Hegel and its implications for contemporary philosophy. This project investigates the development of the 'analytic' method in the idealist philosophies of Leibniz, Kant and Hegel, and compares it to 'analysis' as used in analytic philosophy. It thereby seeks to find a ground for dialogue between strands within contemporary philosophy that are usually thought to be opposed.
Idealism, Pragmatism, and the Historical Norms of Rationality. This project engages critically with the remarkable "normative pragmatics" of Robert Brandom, essentially the first analytic philosopher in a century to defend Hegel's "logic" from a modern logical perspective. It develops Brandom's suggested "inferentialist" interpretation of Hegel, but shows how a presupposition distorts both Brandom's reading of Hegel and his substantive account of the norms of reason. A corrective is developed on ....Idealism, Pragmatism, and the Historical Norms of Rationality. This project engages critically with the remarkable "normative pragmatics" of Robert Brandom, essentially the first analytic philosopher in a century to defend Hegel's "logic" from a modern logical perspective. It develops Brandom's suggested "inferentialist" interpretation of Hegel, but shows how a presupposition distorts both Brandom's reading of Hegel and his substantive account of the norms of reason. A corrective is developed on the basis of the later work of Brandom's mentor, Wilfrid Sellars. The corrected account shows how the norms of thought need not be eternal to be rational, but rather, are rational because of the way they are historical.Read moreRead less
Rationality and Resource Bounds in Logics for Intentional Attitudes. Formal philosophy is the discipline at the interface between traditional philosophy and modern mathematical logic. It has had a substantial impact in recent years and has benefited neighbouring disciplines, including computer science and artificial intelligence. It is a good example of how philosophical research can interact with more practical disciplines. This project will make substantial contributions to formal philosophy, ....Rationality and Resource Bounds in Logics for Intentional Attitudes. Formal philosophy is the discipline at the interface between traditional philosophy and modern mathematical logic. It has had a substantial impact in recent years and has benefited neighbouring disciplines, including computer science and artificial intelligence. It is a good example of how philosophical research can interact with more practical disciplines. This project will make substantial contributions to formal philosophy, which will in turn provide benefits in computer science and artificial intelligence, by providing a framework for logicians, computer scientists and researchers in artificial intelligence to discuss issues concerning knowledge, belief and rationality.Read moreRead less
The Logical Theories of Robert Kilwardby. The project is to produce a monograph on the logical theories of Robert Kilwardby (d. 1279) as they are expounded in his commentary on Aristotle's Prior Analytics, analyzing them from the perspective of modern logic. Kilwardby's commentary - which has not been critically edited, translated, or extensively studied - is remarkable for its fidelity to Aristotle's text, and its innovations in logical theory. This forms part of a larger project jointly with D ....The Logical Theories of Robert Kilwardby. The project is to produce a monograph on the logical theories of Robert Kilwardby (d. 1279) as they are expounded in his commentary on Aristotle's Prior Analytics, analyzing them from the perspective of modern logic. Kilwardby's commentary - which has not been critically edited, translated, or extensively studied - is remarkable for its fidelity to Aristotle's text, and its innovations in logical theory. This forms part of a larger project jointly with Dr Henrik Lagerlund (Uppsala University), to do a critical edition, historical introduction, and English translation of Kilwardby's commentary, together with the present logical analysis.Read moreRead less
Aristotle's Categories in the Byzantine, Arabic and Latin Traditions. High quality pure research is of national benefit because it adds to the depth of national culture and because it enhances our national profile overseas. When it involves collaboration with leading scholars at leading international universities, the enhancement is even greater. To understand the great religions that form part of our national identity, and their influence on philosophical thought, is of national benefit because ....Aristotle's Categories in the Byzantine, Arabic and Latin Traditions. High quality pure research is of national benefit because it adds to the depth of national culture and because it enhances our national profile overseas. When it involves collaboration with leading scholars at leading international universities, the enhancement is even greater. To understand the great religions that form part of our national identity, and their influence on philosophical thought, is of national benefit because it helps understand our place in today's world.Read moreRead less
Critical edition of Robert Kilwardby's commentary on Aristotle's Prior Analytics, with historical / philosophical introduction and analytical notes. In the Middle Ages, logic was one of the areas of philosophy that could be pursued relatively independently of theology. Great conceptual achievements resulted, many of which have been given new expression using the techniques of modern logic. This project will make Kilwardby's highly original work in logic accessible to contemporary logicians.
Mathematical explanation. The best mathematical proofs tell us why some mathematical fact holds, not simply that it holds. However to understand how one piece of mathematics explains another piece of mathematics is poorly understood. This project will develop a philosophical account of mathematical explanation. In particular, it will show how mathematics can explain further mathematics as well as how it can explain physical phenomena.
Mathematical notation: a philosophical account. This project will explore philosophical issues associated with mathematical notation. In particular, it will provide an account of how mathematical notation is used in mathematical applications and how it facilitates analogical reasoning in science.