Principia

Remco Bloemen

2015-08-26

“It is to be regretted that this first comprehensive and thorough-going presentation of a mathematical logic and the derivation of mathematics from it [is] so greatly lacking in formal precision in the foundations (contained in ✸1–✸21 of Principia [i.e., sections ✸1–✸5 (propositional logic), ✸8–14 (predicate logic with identity/equality), ✸20(introduction to set theory), and ✸21 (introduction to relations theory)]) that it represents in this respect a considerable step backwards as compared with Frege. What is missing, above all, is a precise statement of the syntax of the formalism. Syntactical considerations are omitted even in cases where they are necessary for the cogency of the proofs”.[

✸1·01. p ⊃ q .=. ~ p ∨ q. Df.