Editing Principia Mathematica (section)

===Gödel 1944===
[[Kurt Gödel|Gödel]] offered a "critical but sympathetic discussion of the logicistic order of ideas" in his 1944 article "Russell's Mathematical Logic".{{sfn|Kleene|1952|p=46}} He wrote:
{{blockquote|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 ... The matter is especially doubtful for the rule of substitution and of replacing defined symbols by their ''definiens'' ... it is chiefly the rule of substitution which would have to be proved.<ref name="Gödel 1944">{{harvnb|Gödel|1944|p=126}} (reprinted in {{harvnb|Gödel|1990|p=120}}).</ref>}}