Gödel left in his papers a fourteen-point outline of his philosophical beliefs,that are dated around 1960. They show his deep belief in the rational structure of the world. Here are his 14 points:
1.The world is rational.
2.Human reason can, in principle, be developed more highly (through certain techniques).
3.There are systematic methods for the solution of all problems (also art, etc.).
4.There are other worlds and rational beings of a different and higher kind.
5.The world in which we live is not the only one in which we shall live or have lived.
6.There is incomparably more knowable a priori than is currently known.
7.The development of human thought since the Renaissance is thoroughly intelligible (durchaus einsichtige).
8.Reason in mankind will be developed in every direction.
9.Formal rights comprise a real science.
10.Materialism is false.
11.The higher beings are connected to the others by analogy, not by composition.
12.Concepts have an objective existence.
13.There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.
14.Religions are, for the most part, bad– but religion is not.
Source: http://braungardt.trialectics.com/mathematics/mathematicians/kurt-godel/existence-of-god/