David Makinson: A historical question about mathematicians and logic

David Makinson raises a very interesting issue, originally in a comment on my recent post on Jonathan Barnes’s book. It seems a pity to leave his question buried there, where it is likely to be overlooked, so I’m making it a guest post! He writes:

We know that many philosophers, theologians and polymaths (such as Aristotle) have written on formal logic, and some of their writings have survived, whether in whole or in fragments, quoted or distorted. Question: Were there any figures who were primarily mathematicians — from Greek antiquity through the Roman, mediaeval and renaissance periods but before, say, Leibniz — who investigated and wrote on the logic that they were actually using in their own work?

The question is particularly acute for Euclid and his school, since they were devoting immense attention to perfecting deductions from basic principles, but it arises for all those who carried out mathematical reasoning.

From my memory of reading in histories of logic, none are mentioned! Even so late a figure as Descartes, who wrote important guides to methodology and heuristics, does not seem to have ventured into formal logic, so far as I know. If, indeed, there is a big gap in the historical literature, how far is it really a gap in what was actually written, or merely in accidents of which texts have survived the tyranny of time, or even in the attention that has been accorded by historians of logic?

An interesting question indeed.

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