There are four pieces on Kurt Gödel in Parsons’s Philosophy of Mathematics in the Twentieth Century. The first is just ten pages long, and is an encyclopaedia-style entry on Gödel from the 2005 Dictionary of Modern American Philosophers. It seems to me an entirely admirable piece of its kind, though surely rather misplaced in a book whose other chapters are addressed to a significantly more knowledgeable and sophisticated reader.
The second piece is a reprint of Parsons’s introduction to the paper ‘Russell’s Mathematical Logic’ in Gödel’s Collected Works, Vol. II. Again, but for different reasons, this perhaps doesn’t sit entirely comfortably in this collection, for to get the most out of it, you really need to have Gödel’s paper in front of you — in which case you probably already have Parsons’s introduction to hand too. And I do wonder if Parsons has missed a trick here. His introduction in its originally published version very likely had to conform to quite severe space-constraints, and the most interesting sections are hard going because rather compressed. I suspect Parsons had a fair bit more to say, so a more expansive re-presentation of some of the most interesting material would have been a very welcome bonus. In particular, it would have been good if the section on the theory of types — the toughest bit of the paper — could have been reworked at a more leisurely pace.
The topic of one interesting part of the paper — the last main section, on Gödel’s views on whether the axioms of Principia are “analytic” in some sense — does, however, get revisited at much greater length in the third of Parsons’s discussions of Gödel. So I’ll say no more here about Parsons’s first two Gödel essays (this is indeed an insubstantial blogpost!) and instead turn speedily to the essay “Quine and Gödel on Analyticity”.