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Part of Prof. Timothy Williamson's ten-lecture series 'Methods of Philosophy', organised by Prof. Chen Bo of Peking University, which sponsored and hosted the lectures. ABSTRACT Many philosophers regard the central method of argument in philosophy as deduction, where the premises are logically inconsistent with the denial of the conclusion. Of course, this immediately raises the question of what supports the argument’s premises. Typically, the answer is that they are supported by abduction, a non-deductive form of argument. But this does not mean that philosophy does not need deduction, for it is often the means by which the consequences of a philosophical theory are drawn out, as they must be for the theory to be abductively assessed. Another challenge to the role of deduction in philosophy is that many principles of logic are philosophically controversial, contrary to the assumption that logic is a sort of neutral referee for substantive disagreements. In fact, virtually every proposed principle of logic has been challenged on metaphysical, epistemological, or scientific grounds—for example, concerning infinity, the open future, vagueness, semantic and set-theoretic paradoxes, and even quantum mechanics. Indeed, broadly logical principles constitute a central core of metaphysical theory. The best approach is to make the logic part of the theoretical package to be abductively assessed. RESPONDENTS Prof. Zhang Liuhua (East China Normal University) Prof. Xu Min (Huazhong University of Science and Technology) SECTIONS 0:00 Lecture 1:30:54 Comments I 1:44:16 Comments II 1:48:31 Replies