*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.*

Sean FeeneyStephen Read says that four of five of the 1320s Oxford (or Merton) calculators had a main focus on mathematical physics (does that count?) but also made “significant contributions to logic”. So you might ask him.

(Brandywine, Richard Kilvington, William Heytesbury, John Dumbarton are the listed logician calculators.)

I can’t help but feel the question would have been considered by the Oxford logician and mathematician Charles Lutwidge Dodgson given how astute a reader he was; but I don’t have his nonfiction to hand to check. You might profitably ask a mathematical Carrollian.

He was astute at identifying Coleridge’s AIds to Reflection for special study (see the Journals) and his philosophy of law as a naked power struggle, presented satirically, was drawn from the Greeks but I forget who.

See page 148 of Novaes and Read’s The Cambridge Companion to Medieval Logic.

Sean FeeneyThe discussion on mathematical physics and the Oxford calculators picks up again a p. 275ff in Chapter 11 by Yrhonsuuri and Coppock. A volume of this school by Heytesbury – Rules on Solving Sophisms – sounds methodological. See page 277.

Sorry if all this vague hand waving turns out to be a red herring!

Ramon GrajoI’ve been told by Peter King, who did his doctorate in Abelard, that one real issue is that many manuscripts are still unexamined. The difficulty with Medieval mathematics is that it’s in Medieval Latin plus you have to deal with palaeographical issues, and it was before modern symbols made math much easier to read.

Justin VlasitsI don’t think you will find much in the Greek/Roman contexts. While there were *fans* of geometry who were also interested in logic, such as Galen, the technical mathematical treatises tend to be relatively independent from the logical innovations.

More promising is the Arabic tradition. Al-Kindi made significant contributions to both mathematics and logic (and, judging by lists of his works, probably wrote at least as much on math as philosophy). If we had more of his mathematical writings, we may well have examples of what you are looking for. Al-Farabi wrote technical treatises on music theory in addition to some of the most impressive work on logic in the early Aristotelian tradition.

Michael ToppelI see where this question is coming from. But it is also very…. strange. Why should one develop a technical system for reasoning for a practice that already has a rather technical system for reasoning, e.g. geometrical constructions? It is on the contrary rather striking that it must be and was in fact the other way around.

The question somehow reflects distinctions, which we must make today, back onto history.

Peter SmithBut you might ask in the same way (of Frege, for example?!) “why should one develop a technical system for reasoning for a practice that already has a rather technical system for reasoning, e.g. arithmetical computations?” I take it that David Makinson’s question was about whether early mathemticians had anything explicit to say about the general logical principles that they were implicitly working with.

David MakinsonYes, in a nutshell, that’s my question.