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Spinoza's  Ethics  self-consciously follows the example of Euclid and other geometers in its use of axioms and definitions as the basis for derivations of hundreds of propositions of philosophical significance. The choices about what to define and what to leave as an undemonstrated axiom are clearly essential in such a project and were made by Spinoza with great care. Usually, when coming up with first principles in this sort of system, one aspires to have a list of axioms and definitions, each of which is necessary for at least one of the theorems to be proven. Spinoza's  Ethics  fails in this regard with EIa2. In this brief note, I show how Spinoza intended to and should have appealed to this axiom in his proof of EIp4 by appealing to parallels between the first four propositions of the  Ethics  and the correspondence with Henry Oldenburg.

Everything is conceivable: a note on an unused axiom in Spinoza's Ethics