How much was Boole influenced by Indian logic?

Question

In some of her writings Mary Everest Boole (in particular "Indian Thought and Western Science in the 19 Century") makes references to how ideas brought back by George Everest from India influenced the writing of "An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities" which George Boole wrote and Mary edited.

In particular the following quote.

Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of 1830–65. What share had it in generating the Vector Analysis and the mathematics by which investigations in physical science are now conducted?

What were these ideas?

Answer 1

The Indian influence is explored in Kak, George Boole’s Laws of Thought and Indian Logic. It was more philosophical than mathematical because Indian logic is more focused on the cognitive side of reasoning rather that its formal aspects, as in the West, and because Boole's familiarity did not extend to specifics. Unlike de Morgan, he did not explicitly credit Indian sources either.

However, Boole arguably attempted to merge the idea of describing cognitive "laws of thought" with the then popular in Europe conception of 'generalized arithmetic', a precursor of abstract algebra. Some peculiarities of Boole's algebraic treatment are consistent with this interpretation, for example, his use of division by zero with additional rules to eliminate infinities.

"Boole does not mention Indian logic texts or the larger tradition in his book. We must ascribe this to the fact that while according to his wife’s claim, George Boole and others knew of Indian logic, they were apparently not knowledgeable of its details since only a few of the Sanskrit logic texts had by then been translated into English.

[...] Although scholars agree that Indian logic had reached full elaboration, it was expressed in a special technical language that is not easily converted into modern symbolic form. One can assume that Boole most definitely was aware of the general scope of Indian logic and knew that its focus was the cognition underlying the logical operation, and this is something he aimed in his own work. He was trying to mathematize the role of cognition and he believed that algebra would be effective for this purpose. To the extent Boole was attempting to go beyond what he knew of Indian logic, he thought he could do so using mathematics.

[...] We argue that Boole’s focus was more than a framework for propositions and that he was trying to mathematize cognitions as in the tradition of Indian logic; this is consistent with his own assertion that laws of thought should not be constrained by finitude. This may explain why he was happy to use operations in his algebra that allowed division by zero, which required further side-rules to eliminate infinities so that the final results were correct."