§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical observations of the first importance.

Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.

1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are (still) philosophers who seriously underestimate and even consciously reject these techniques.

The journal of symbolic logic began publishing in 1936. From the outset, the Journal included a Reviews Section, edited by Alonzo Church. The very first issue carried three pages of reviews, written by Bernays, Church, Rosser, and Quine.

As the first issue stated, “It is intended that this section of the Journal shall serve as a complete bibliography of current literature in the field of symbolic logic, from January 1, 1936. To this end an effort will be made to include in it, at least by title, all publications in this field, both books and articles in journals, and as far as possible these will be accompanied by signed reviews.” Thus the purpose of the Reviews Section was two-fold. For one, there was its bibliographical function: to provide a complete, suitably indexed, listing of all the publications—both books and journal articles—in symbolic logic, wherever and in whatever language published. And secondly, the reviews were to provide critical, analytical commentary on these publications, whenever possible.

The Reviews Section should be viewed as a continuation and expansion of Church's A bibliography of symbolic logic. The Bibliography was a listing, with some annotations, of the publications in symbolic logic prior to 1936. It was published as volume 1, number 4 of the Journal. Church made the listing as complete as he could, of course.

In a lecture manuscript written around 1961 (Gödel *1961/?), Gödel describes a philosophical path from the incompleteness theorems to Husserl's phenomenology. It is known that Gödel began to study Husserl's work in 1959 and that he continued to do so for many years. During the 1960s, for example, he recommended the sixth investigation of Husserl's Logical Investigations to several logicians for its treatment of categorial intuition (Wang 1997, p. 164). While Gödel may not have been satisfied with what he was able to obtain from philosophy and Husserl's phenomenology, he nonetheless continued to recommend Husserl's work to logicians as late as the 1970s. In this paper I present and discuss the kinds of arguments that led Gödel to the work of Husserl. Among other things, this should help to shed additional light on Gödel's philosophical and scientific ideas and to show to what extent these ideas can be viewed as part of a unified philosophical outlook. Some of the arguments that led Gödel to Husserl's work are only hinted at in Gödel's 1961 paper, but they are developed in much more detail in Gödel's earlier philosophical papers (see especially 1934, *193?, 1944, 1947, *1951, *1953/59). In particular, I focus on arguments concerning Hilbert's program and an early version of Carnap's program.

§1. Some ideas from phenomenology. Since Husserl's work is not generally known to mathematical logicians, it may be helpful to mention briefly a few details about his background.

We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M.