Inference: A Logical-Philosophical Perspective
In this talk, Professor Paseau will describe some of his work on inference within mathematics and more generally. Inferences can be usefully divided into deductive or non-deductive. Formal logic studies deductive inference, the obvious question here being: which formal logic correctly captures it? His view, defended in his recent monograph One True Logic (Oxford UP, co-authored with Owen Griffiths), is that any such logic must be highly infinite. In this Inference Project event, he shall explain what this means and sketch some arguments for it.
The other side of the coin is non-deductive inference. This is much harder to capture precisely, but many interesting and important things can still be said about it. Professor Paseau will present some of his ideas about non-deductive reasoning in mathematics and explain why, contrary to current and traditional thinking, it can be a source not just of justified belief but also knowledge.
What links the two halves of the talk? The idea that inference, both deductive and non-deductive, is more permissive than often imagined.
Professor Gila Sher of the University of California, San Diego will be the conversant for this event. As a philosophy professor, her research interests center on foundational issues in epistemology, the philosophy of logic, and the theory of truth. Her books include: The Bounds of Logic: A Generalized Viewpoint (MIT, 1991), Epistemic Friction: An Essay on Knowledge, Truth, and Logic (Oxford, 2016), and Logical Consequence (Cambridge, 2022). She is currently working on a book tentatively titled Truth as a Human Value, which offers a reconception of the philosophy of truth in light of the post-truth crisis.
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Alexander Paseau
Alexander Paseau read Mathematics (BA 1996) followed by a year of Philosophy (Part II) at Trinity College, Cambridge. After taking the BPhil in Philosophy at Oxford (1999), he returned to Cambridge for his PhD, supervised by Alex Oliver. He spent 2001 as a visiting graduate student at Princeton, working with Paul Benacerraf and David Lewis. After three years of a Research Fellowship at Jesus College, Cambridge, he came to Oxford in 2005, where he is now a professor and a fellow of Wadham College. He has been an Associate Editor of the journal Mind and has held Research Fellowships from the Mind Association and the Leverhulme Trust, as well as visiting appointments at the Sydney Centre for the Foundations of Science, King’s College London, and the Institut d’histoire et de philosophie des sciences et des techniques in Paris.
