The first notebooks contain plans for his studies and lists of books he intends to read as well as notes of lectures he attended. "Besides that there are philosophical
questions and problems he is dealing with and especially maxims for his conduct of private and academic life. And he is also reflecting on strategies to build up an academic career." More precisely,
Gödel started the philosophical notebooks as a realization of an ethical approach. Self-perfection and self-admonition are part of this approach. They seem very much to be in the tradition of Meditations by Marcus Aurelius or Goethe’s Maxims and Reflections. At the same time Gödel discusses philosophical problems from the viewpoint of different academic disciplines and has a kind of 17th century metaphysics as an outline in mind. The scientific disciplines contribute to answering the question of why the world is as it is insofar as they identify and construct objects, isolate phenomena and find laws that are generalizations from observations and constructions. Gödel tries to show the contribution of each academic and scientific discipline and puts them in relation to each other and the classical problems of traditional philosophy concerning freedom, good and evil, death and the significance of our lives. Generalization, idealization and analogy are essential philosophical methods linking up science and philosophy which cannot be set apart.Apparently, their style style, and, in particular, "the way in which one remark on a certain question follows another and is then taken up again later on to think it through from a different perspective reminds one very much of the form Ludwig Wittgenstein chose for his notebooks and his Philosophical Investigations." But "Gödel is much more engaged in dialogues with thinkers of the past. Among them are classical authors like Plato, Aristotle, Augustine of Hippo, Thomas of Aquinas, René Descartes, Gottfried Wilhelm Leibniz, Immanuel Kant and Georg Wilhelm Hegel, as well as contemporaries like Gottlob Frege, Giuseppe Peano, Bertrand Russell, Luitzen Brouwer, and Rudolf Carnap. But there are also nearly forgotten ones that he mentions like his teacher Heinrich Gomperz", who was also very important to Karl Popper.
It would be good, if these notebooks were published soon. While some people tend to disparage Gödel, the philosopher, at the expense of Gödel, the mathematician, and therefore might argue that nothing of philosophical importance will be found in them, I would find them interesting simply from the point of view intellectual methodology. It should be interesting to find out how someone of Gödel's stature used the notebook method
1. These are not the only notebooks. There are also sixteen notebooks he called "Arbeitshefte" (or mathematical workbooks) and six on "logic and foundation," as well as four on "results on foundation." See here.
2. For more see here.