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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 Philosophers need theories to answer their questions. Thus they need to distinguish between true and false theories to find the right answers to their questions. The process of theory comparison in philosophy is much closer to theory comparison in natural science than is usually realized. Theories are assessed for their consistency with the evidence and for their ability to explain it, but also for their simplicity and strength (informativeness), their elegance, and their unifying power. The method of inferring to the theory with the best combination of these virtues is known (following C.S. Peirce) as abduction. Perhaps surprisingly, abduction is also used in mathematics, as Bertrand Russell argued, to select appropriate axioms or first principles. For mathematics, the most relevant evidence is not experimental but simply less basic well-established mathematical facts. Thus the precedent of mathematics shows that the abductive nature of philosophy does not force it to become an experimental science, in order to have an evidence base for the abductive inference to start from. Instead, any previous knowledge can be used as evidence for abduction in philosophy. That knowledge may include the results of natural science, where relevant, but it can also include any knowledge gained from non-experimental inquiry. RESPONDENTS Prof. Arthur Schipper (Peking University) Prof. Xu Zhu (East China Normal University) SECTIONS 0:00 Lecture 1:30:28 Comments I 1:44:00 Comments II 1:49:47 Replies