In a rather lengthy article at Aeon Alexander Englert discusses the argument Gödel makes for his belief in an afterlife. His reasons are found in a series of several letters he wrote to his mother Marianne in 1961.
The crux of his argument is contained in these words to his mother:
If the world is rationally organised and has meaning, then it must be the case [that there's an existence beyond this one]. For what sort of a meaning would it have to bring about a being (the human being) with such a wide field of possibilities for personal development and relationships to others, only then to let him achieve not even 1/1,000th of it?His argument has Kantian resonances, and his basic reasoning makes sense. If the universe is rational then human life is rational. But human life cannot be rational if physical death ends it before it achieves anything meaningful. Thus, if the universe is rational, which he believed it certainly was, then physical death must not be the end of our existence.
Gödel writes this:
What I name a theological Weltanschauung [Worldview] is the view that the world and everything in it has meaning and reason, and indeed a good and indubitable meaning. From this it follows immediately that our earthly existence – since it as such has at most a very doubtful meaning – can be a means to an end for another existence.Englert offers the reader much more insight into Gödel's reasoning, which the great logician elaborates over the course of several letters to Marianne, and there's a lot more analysis by Englert of the argument as well.
It's a fine essay written about one of the towering intellectual figures of the 20th century.
