"; conjunction as the negation of incompatibility. But it has been shown by Sheffer[34] that we can be content with one primitive idea for all five, and by Nicod[35] that this enables us to reduce the primitive propositions required in the theory of deduction to two non-formal principles and one formal one. For this purpose, we may take as our one indefinable either incompatibility or joint falsehood. We will choose the former.
[34]Trans. Am. Math. Soc., vol. XIV. pp. 481-488.
[35]Proc. Camb. Phil. Soc., vol. XIX., i., January 1917.
Our primitive idea, now, is a certain truth-function called "incompatibility," which we will denote by
. Negation can be at once defined as the incompatibility of a proposition with itself, i.e. "not-
" is defined as "
." Disjunction is the incompatibility of not-