Yesterday I attended an interesting conference on the history of logic in China, organized by Fenrong Liu, Jeremy Seligman and Johan van Benthem, which took place in Amsterdam (unfortunately, I had to miss the second day today, due to a workshop in Vienna, where I am right now). At the conference I met some prominent researchers in the field of ancient Chinese logic such as Chad Hansen, Chris Fraser and Christoph Harbsmeier. I knew virtually nothing about ancient Chinese logic, but as a historian of so-called ‘western logic’ (as usual, a terrible label), I was very interested in finding out more about differences and commonalities between the two traditions.
One of the reasons why I am interested in such comparisons is that they should offer a privileged vantage point on the historical sources of the axiomatic-deductive method in ancient Greek philosophy and mathematics. The Chinese and the Indian traditions are arguably two ancient traditions having attained a level of intellectual sophistication similar to that of the Greek, but in these traditions scientific investigation developed in quite different ways. In particular, the axiomatic-deductive method in its specific details is (originally) unique to ancient Greek philosophy and mathematics. Now, if we are able to isolate specific elements of significant dissimilarity between the Greek tradition and these other traditions, then we might be able to attain a better grasp of some of the crucial factors for the development of the deductive method.
One compelling hypothesis that has been put forward by the eminent scholar G.E.R. Lloyd and further developed by R. Netz in his The Shaping of Deduction is that the social background of public debates in ancient Greece played a crucial role in the development of the axiomatic-deductive method. The idea would be that the deductive mode of argumentation emerged as an alternative to other approaches to argumentation and debate current at the time, in particular that of the sophists. From this point of view, a deductive proof can be seen as a form of dialogue in which one of the participants seeks to compel the other participants to grant some conclusion if they have granted some premises; every step in a deductive proof would actually be a dialogical move, which must thus be compelling and immune to counterexamples. The moves of the other participants are no longer explicit in the regimented formulation of a proof, but presumably at each point they agree with the moves proposed by the person leading the dialogue (any resemblance with Socratic dialogues is not a coincidence!).
Now, Lloyd argues that, while public debates were pervasive in ancient Greece, this was not the case in ancient China, where the Emperor represented the ultimate, uncontested authority. This would (at least partially) explain, he claims, why the axiomatic-deductive method emerged in ancient Greece but not in ancient China. This is a very appealing hypothesis, and I for one have mentioned it approvingly at several occasions. But there is a problem, as I discovered yesterday: it is simply not true that in the Chinese tradition debates and dialogical situations played no significant role. What I have learned about the Mohist tradition yesterday, which developed in China roughly a century before the golden age in ancient Greece, is that it is also profoundly marked by investigations into patterns of correct argumentation, and explicitly against the background of dialogical situations. The model for this background is provided by legal contexts (information provided by Chris Fraser). In fact, while hearing about the Mohist tradition, I often caught myself thinking of Aristotle’s Topics and Sophistical Refutations, and some of the later (medieval) discussions formulated against the background of these two books.
I still think that the dialogical component is very important to understand the very concept of deduction, as I intend to show in the coming years (next year I will start a five-year research project called ‘The Roots of Deduction’). But what I’ve learned yesterday is that the presence or absence of a strong dialogical tradition by itself does not explain the isolated emergence of the notion of deduction in Greek mathematics and philosophy, as Lloyd seems to suggest, given that a similar setting can be found in the Chinese case. Cleary, we need to dig deeper, and that's what long-term research projects are for.
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