 Aside from the Rule of 0 and 1 and the Elimination Theorem, the 1854 presentation is mainly interesting for Boole’s attempts to justify his algebra of logic. He argued that in symbolical algebra it was quite acceptable to carry out equational deductions with partial operations, just as one would when the operations were total, as long as the terms in the premises and the conclusion were interpretable. He said this was the way ordinary algebra worked with the uninterpretable \(\sqrt{-1}\), the square root of −1. (The geometric interpretation of complex numbers was recognized early on by Wessel, Argand, and Gauss, but it was only with the publications of Gauss and Hamilton in the 1830s that doubts about the acceptability of complex numbers in the larger mathematical community were overcome. It is curious that in 1854 Boole regarded \(\sqrt{-1}\) as uninterpretable.)