Every Proof is (and isn't) a Dialogue
Lecture organized by the Dept of The History of Philosophy
Every proof is (and isn’t) a dialogue: by Dr Catarina Dutilh Novaes (University of Amsterdam)
In this talk, I present the outlines of my forthcoming VIDI project, ‘The Roots of Deduction’, in particular its conceptual starting point: a reconceptualization of the very notion of deduction based on its multi-agent, dialogical origins. I argue that it is a mistake to think of logic and deduction as pertaining to the mono-agent level of thinking; rather, they belong essentially to the multi-agent level of arguing.
I draw on the historical development of the deductive method (as documented in Netz’s The Shaping of Deduction) to argue that a deductive argument is originally a discourse aimed at compelling the audience to accept (the truth of) the conclusion, if they accept (the truth of) the premises. It is only in the modern period, in particular with Descartes and Kant, that logic became predominantly associated with inner thinking processes rather than with public situations of dialogical interaction.
Crucially, proofs would correspond to a specific kind of dialogues, namely adversarial dialogues, as the participants have opposite goals: proponent seeks to establish the conclusion; opponent seeks to block the establishment of the conclusion. But proofs are no longer dialogues properly speaking; they have a hybrid status in between orality and writing. In effect, the two main transformations leading from actual dialogues to proofs seem to be the move from oral to written contexts, and the fact that the deductive method has internalized the opponent in the sense that it is now built into the framework: every inferential step must be immune to counterexamples. I refer to this conception as the built-in opponent (BIO) conception of proofs, which thus differs from earlier dialogical conceptualizations of logic, and I argue that it is a particularly compelling account of the nature of deductive proofs.
Catarina Dutilh Novaes studied philosophy (major) and mathematics (minor) at the University of Sao Paulo (Brazil), and obtained a MSc degree in logic at the ILLC in Amsterdam. She obtained her PhD degree in Leiden, focusing predominantly on the Latin medieval logical tradition. In 2007 she started working on a VENI project on uses of formal languages in logic at the ILLC, in which she combined historical and conceptual analysis with an empirically-informed approach, relying on data from the empirical sciences of the mind. In 2010 she was awarded a VIDI grant for the project ‘The Roots of Deduction’, which will commence in July 2011, and will deploy an integrative approach combining history, philosophy and empirical data. Her publications include Formalizing Medieval Logical Theories (Springer, 2007), “14th century logic after Ockham” (chapter in The Handbook of the History of Logic vol 2., 2008), “‘He doesn’t want to prove this or that’ – On the very young Wittgenstein ” (Philosophical Books, 2010), “ Lessons on truth from medieval solutions to the Liar paradox” (Philosophical Quarterly, 2011), “ Reassessing logical hylomorphism and the demarcation of logical constants” (forthcoming in Synthese).
|Laatst gewijzigd:||11 januari 2013 18:49|