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Kurt Gödel is one of the "best" logicians of the 20th century.

Here, the user "Jeffrey Kegler" states that:

Kurt Gödel considered himself a philosopher who did mathematics, rather than as a mathematician who did philosophy.

Are there any sources where Gödel said this? Did Gödel really consider himself primarily a philosopher who is interested in mathematics (instead of the other way round)?

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Kurt Gödel enrolled in the University of Vienna, attending lectures on physics, his initial field of interest, lectures on philosophy given by Heinrich Gomperz, and lectures on mathematics. [...] eventually graduating under [the mathematician Hans] Hahn with a Dr.phil. in mathematics in 1929. The main theorem of his dissertation was the completeness theorem for first order logic.

Gödel's university years also marked the beginning of his attendance at meetings of the Vienna Circle, a group around Moritz Schlick that quickly became known as “logical positivists”.

the decade [1940s] saw the beginning of Gödel's intensive study of Leibniz, which, Gödel reports, occupied the period from 1943 to 1946.

Gödel's philosophical views can be broadly characterized by two points of focus, or, in modern parlance, commitments. These are: realism, namely the belief that mathematics is a descriptive science in the way that the empirical sciences are. The second commitment is to a form of Leibnizian rationalism in philosophy; and in fact Gödel's principal philosophical influences, in this regard particularly but also many others, were Leibniz, Kant and Husserl.

By the decade [1950s]'s close Gödel developed a serious interest in phenomenology.

Having said that, Gödel's main contributions are :

A) mathematical ones:

  • the completeness theorem for the first order predicate calculus,

  • the incompleteness theorems,

  • the results in set theory regarding the consistency of the Continuum Hypothesis and the Axiom of Choice,

  • work in Intuitionistic Logic and Arithmetic;

B) contribution to the "foundational debate" in the field of philosophy of mathematics, with the papers:

  • “Russell's Mathematical Logic” (1944),

  • “What is Cantor's Continuum Hypothesis?” (1947);

C) work on relativity, published in the article: “An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation” (1949);

D) the unpublished ontological proof, dated around 1941, based on modal logic.

Having said that, the long G's involvement with philosophy produced a lot of discussion and manuscripits but no completed work, while his contributions to mathematical logic and set theory :

are among the handful of landmark theorems in twentieth century mathematics.

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Since there is no record of Gödel's view, any response to this question is a matter of opinion.

One of the few philosophers who has published opinions on the merits of Gödel's philosophical views, as well as biographical details on role of philosophy in Gödel's professional life, is Palle Yourgrau of Brandeis University. It is his opinion, expressed in this book The Disappearance of Time: Kurt Gödel and the Idealistic Tradition in Philosophy, that Gödel did indeed consider himself to be primarily a philosopher. I've skimmed the text a number of times but I am unable to locate the paragraph where Yourgrau explicitly states that he believes this is Gödel's view of his own work, which I am certain is there. The best I can do is the following quote :

To philosophers, then and now, he was simply a logician trying to pass as a philosopher.


TL/DR;

As Yourgrau notes, in general philosophers appear to hold a different view. Quoting Yourgrau:

Gödel, throughout his academic life, was exceptionally anxious to avoid being considered a philosophical dilettante or crank, and a "pious" one at that. In this he failed completely. His "special caution" succeeded only in keeping him from contributing to important fields of research. His refusal to publish his ontological argument for the existence of God fooled no-one. He could not hide the fact that he was a kind of believer and that his argument, like Leibniz's before him, was anything but a mere intellectual exercise. What Bertrand Russell called Gödel's' "unadulterated Platonism" marked him for some as a throwback to "precritical" times, before Kant launched is "critique" of pure reason . . . . . Even Gödel's writings on Einstein succeeded only in convincing cosmologists that strange things happen when a logician pays too much attention to the equations of relativity, while forgetting their physical meaning. His absence, in turn, from the Wittgenstein revolution . . . . . combined with his refusal to pay homage to the preeminent figure in contemporary analytic philosophy, W.V.O. Quine, marked him as a philosophical castaway.

In February of 1995, at Boston University, a symposium was held entitled "Gödel's General Philosophical Significance". The two main speakers, Warren Goldfarb and Burton Dreben, both Harvard philosophers, were unrelenting in their ridicule.

Following Goldfarb's speech, a single question was asked :

"Do I understand you correctly, professor Goldfarb, that in your judgement Gödel, though a great logician, was a philosophical fool?" A polite smile was Goldfarb's only answer.

Dreben appears to have particularly irked that Gödel had the "audacity" to engage in rational theology - no doubt a reference to Gödel's recasting of the ontological argument.

For Dreben, it seemed, this was a kind of scandal. He was moved to deliver a sermon on the harm that is done when people who are good at purely formal thinking get the idea that they are qualified to contribute to philosophy. That Dreben's own position in the philosophical world owed much to his reputation in formal logic was an irony that appeared to be lost on him.

In the years since the Boston symposium, philosophers' assessment of Gödel's philosophical work has been more polite, but no less dismissive. Yourgrau appears to be a lone voice in support of Gödel's philosophical views.

The case for Gödel as philosopher is unassailable. Though he published few essays that could be considered explicit contributions to philosophy, they suffice to establish him as an important philosopher of mathematics and time and space. The posthumous publication of several more of his philosophical studies, including the Gibbs lecture, his contribution to the Schilpp volume on Carnap, and the longer version of his contribution to the Schilpp volume on Einstein, confirm this assessment. The essay he wrote for the Schilpp volume on Russell, which contained new and insightful discussions of Frege as well as Russell on the question of meaning, including an illuminating and prescient comparison of Russell on "denoting" with Frege on "sense and reference", leaves little room for doubt that in the philosophy of language, too, his abilities were striking. He had clearly mastered the writings of most of the seminal figures in twentieth-century analytic philosophy ... His grasp of Hegel astonished the philosopher Georg Kreisel, a man not easy to impress. ( paraphrasing: He also demonstrated extensive knowledge of Kant and Husserl.)

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