Semantics, externalism and a priori truths. This project aims to discover more about the logical roots of a priori knowledge. Pure mathematicians and logicians discover truths which are not justified by inference from observations; philosophers traditionally have aspired to do likewise. Yet little is understood about what makes a priori knowledge possible. There is a growing branch of logic which studies what is known as "double indexing" and this promises to throw light on the a priori. Austral ....Semantics, externalism and a priori truths. This project aims to discover more about the logical roots of a priori knowledge. Pure mathematicians and logicians discover truths which are not justified by inference from observations; philosophers traditionally have aspired to do likewise. Yet little is understood about what makes a priori knowledge possible. There is a growing branch of logic which studies what is known as "double indexing" and this promises to throw light on the a priori. Australian philosophers have played a very salient role in the study of double indexing, and this project is well placed to make significant contributions in this area.Read moreRead less
Mathematics, the science of real structure: an Australian realist philosophy of mathematics. The project will strengthen the already strong Australian philosophical tradition of realism, extending it into philosophy of mathematics. It will develop a robust alternative to the nominalism, Platonism and idealism that dominate northern-hemisphere philosophizing about mathematics, an alternative that is in tune with how mathematicians really apply mathematics. Australian philosophy will thus be stren ....Mathematics, the science of real structure: an Australian realist philosophy of mathematics. The project will strengthen the already strong Australian philosophical tradition of realism, extending it into philosophy of mathematics. It will develop a robust alternative to the nominalism, Platonism and idealism that dominate northern-hemisphere philosophizing about mathematics, an alternative that is in tune with how mathematicians really apply mathematics. Australian philosophy will thus be strengthened in general, giving it a greater attractiveness to the many overseas visitors and students who already appreciate its unique strengths. The nature of the project will also lead to closer ties and interdisciplinary work between philosophers and mathematicians.
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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