According to Sergio Galvan, some of the arguments offered by Lucas and Penrose are somewhat obscure or even logically invalid, but he accepts their fundamental idea that a human mind does notwork as a computational machine. His main point is that there is a qualitative difference between the principles of the logic of provability and those of the logic of evidence and belief. To evaluate this suggestion, I shall first compare it with Searle’s concept of “intentionality”, and then introduce a distinction between two different senses of intentionality: a reflexive-transcendental sense and a positive (that is, historical empirical or formal logical) one. In the first of these senses, the nature of human reason is such that we have no idea how a real material system - or the corresponding formal one - could instantiate it. However, although this will turn out to be an important element of truth in Searle’s and Galvan’s conception, it does not exclude the opposite truth of Turing’s functionalism: because intentionality, intuition, vision or insight - taken in their reflexive-transcendental sense - are simply invisible to the scientific eye, a man and a machine (or a robot) that is and one that is not endowed with intentionality are de facto indistinguishable from a strictly scientific point of view. For this reason, we might eventually be entitled, or even - by the practical precautionary principle - morally obliged, to attribute minds to machines.