I suggest that there exists an interesting and little known relationship between Neuroscience, Consciousness and Spirituality. To illustrate this, I first outline the paradoxical relation between the subjectivity of mind (i.e. consciousness) and its objective material correlate (i.e. neuroscience). I then give support to the notion that this paradox is rationally unsolvable by showing that it is isomorphic to the wave-particle paradox in quantum physics, where the impossibility to rationally resolve it has eventually been accepted as a fundamental property of reality, called the complementarity principle. Next, I point out that spiritual (mystical) traditions have also arrived at very similar paradoxical descriptions of reality, which lends additional plausibility to the insights from quantum physics and philosophy of mind (and vice versa!). Finally, and most importantly, I suggest that since mystical practices offer ways to individually transcend logical paradoxa by developing non-dual, transrational states of consciousness, they may provide a solution to fundamental theoretical problems such as those outlined above and should thus be regarded as an indispensible part of any advanced research methodology.