Despite all the bad reputation and hatred to people that have any kind of magical thinking (i.e. believes in magic, any kind), this ideology still very present in society these days, day that seems all about reason and science. What happened to the enlightenment?
All thinking, including the basic phenomenology of science is at root magical thinking. We tie results to causes, and without further study, they remain tied. One of the things we tie to causes most directly is our own wish, since we do things like move our bodies and manipulate conversations so unconsciously that we cannot analyze the process without involving others.
The idea that applying any set of principles make this any less magical is dismissed by Hume's problem of induction. The idea of induction or observation is itself 'magic' and remains so despite our biases. Science itself is an enormous elaboration of metaphors, all derived from more natural magical thinking.
Particles 'vibrate' because mystical substances in ancient India 'vibrated'. The metaphor is entirely dishonest, and springs straight out of religion. But it is a part of basic physics because it helps, somehow.
Science has a point in insisting we should always get around to explaining our beliefs, when we can. But scientific thinking must always be built upon a more basic foundation, and it must always leave space for the facts that are so close to us that we cannot focus on them (what exactly is morality, what is a purpose, etc.)
Magical thinking has entered mathematics with Cantor's set theory.
Aristotle is the first to distinguish potential infinity and actual infinity. He bans actual infinity from philosophy and mathematics. The idea of the infinity of God, created in Hellenism, amalgamates – not later than in the works of Thomas – with the Aristotelian postulate of the pure actuality of God. This yields the Christian perception of God's pure actuality. During the renaissance, in particular with Bruno, the actual infinity is carried over from God to the world. The finite world models of present science show clearly, how the superiority of the idea of actual infinity has ceased with the classical (modern) physics. In contrast the inclusion of the actual infinite appears disconcerting which explicitly began during the end of the last century with G. Cantor. In the intellectual framework of our century – in particular when considering existential philosophy – the actual infinite appears really as an anachronism. [Paul Lorenzen: "Das Aktual-Unendliche in der Mathematik", Philosophia naturalis 4 (1957) p. 3]
Meanwhile Cantor's followers believe in "real" numbers that cannot be defined or used in any way (Cantor himself did not as we must say in his favour). Even uncountable alphabets (i.e., unlistable lists) are accepted. The whole matter has completely pushed out the former precision and definiteness of the "Queen of Sciences".