certain that none of the discoverers of the quantification of the predicate, Bentham, Hamilton, Thomson, De Morgan, and Boole, were in any way assisted by the hints of the principle contained in previous writers. As to my own views of logic, they were originally moulded by a careful study of Boole’s works, as fully stated in my first logical essay.11 As to the process of substitution, it was not learnt from any work on logic, but is simply the process of substitution perfectly familiar to mathematicians, and with which I necessarily became familiar in the course of my long-continued study of mathematics under the late Professor De Morgan.
I find that the Theory of Number, which I explained in the eighth chapter of this work, is also partially anticipated in a single scholium of Leibnitz. He first gives as an axiom the now well-known law of Boole, as follows:—
“Axioma I. Si idem secum ipso sumatur, nihil constituitur novum, seu A + A ∝ A.” Then follows this remarkable scholium: “Equidem in numeris 4 + 4 facit 8, seu bini nummi binis additi faciunt quatuor nummos, sed tunc bini additi sunt alii a prioribus; si iidem essent nihil novi prodiret et perinde esset ac si joco ex tribus ovis facere vellemus sex numerando, primum 3 ova, deinde uno sublato residua 2, ac denique uno rursus sublato residuum.”
Translated this would read as follows:—
“Axiom I. If the same thing is taken together with itself, nothing new arises, or A + A = A.
“Scholium. In numbers, indeed, 4 + 4 makes 8, or two coins added to two coins make four coins, but then the two added are different from the former ones; if they were the same nothing new would be produced, and it would be just as if we tried in joke to make six eggs out of three, by counting firstly the three eggs, then, one being removed, counting the remaining two, and lastly, one being again removed, counting the remaining egg.”