Those of you who have been following some of my blog posts will recall my current research project ‘Roots of Deduction’, which aims at unearthing (hopefully without damaging!) the conceptual and historical origins of the very concept of a deductive argument as one where the truth of the premises necessitates the truth of the conclusion. In particular, this past year we’ve been reading the Prior Analytics in a reading group, which has been a fantastic experience (highly recommended!). For next year, the plan is to switch from logic to mathematics, and look more closely into the development of deductive arguments in Greek mathematics.
But here’s the catch: the members of the project are all much more versed in the history of logic than in the history of mathematics, so we can’t count on as much previous expertise for mathematics as we could in the case of (Aristotelian) logic. Moreover, the history of ancient Greek mathematics is a rather intimidating topic, with an enormous amount of secondary literature and a notorious scarcity of primary sources (at least for the earlier pre-Euclid period, which is what we would be interested in). So it seems prudent to focus on a few specific aspects of the topic, and for now I have in mind specifically the connections between mathematics and logic (and philosophy) in ancient Greece. More generally, our main interest is not on the ‘contentual’ part of mathematical theories, but rather on the ‘structural’ part, in particular the general structure of arguments and the emergence of necessarily truth-preserving arguments.
So here is a question to the very knowledgeable readership of this blog: what can you recommend in terms of literature on these issues? For now I am familiar with the work of Mueller, Fowler, Knorr, Mendell, and of course Netz (whose work has been in the background of the project from the start), but we would welcome further suggestions accompanied by a brief explanation. More generally, what is the latest news on the connections between logic and mathematics in ancient Greece? Is Mueller’s work still the main reference? Ideally, I would like to discover connections between mathematics and dialectic specifically, but I’ve been told by some knowledgeable colleagues that these will be hard to come by – either because there are no such connections, or simply because they are not registered in the scarce extant sources. But I haven’t given up hope yet!
Many thanks in advance for whatever pointers readers may be able to provide.
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