John Searle and Roger Penrose are two staunch critics of computationalism who nonetheless believe that with the right framework the mind can be naturalized. While they may be successful in showing the shortcomings of computationalism, I argue that their alternative noncomputational frameworks equally fail to carry out the project to naturalize the mind. The main reason is their failure to resolve some fundamental incompatibilities between mind and science. Searle tries to resolve the incompatibility between the subjectivity of consciousness and the objectivity of science by means of conceptual clarification. He, however, fails to deal with the concepts crucial to this incompatibility, namely, the publicness of scientific knowledge and the privacy of psychological knowledge. Penrose tries to resolve the incompatibility between the noncomputationality of psychological process and the computationality of scientific process by expanding the scope of science through some radical changes in quantum physics. His strategy, however, has the danger of trivializing the distinction between science and nonscience thereby putting into question the very value of the project to naturalize the mind. In addition, the feasibility of this strategy remains dubious in light of the mysteries that still surround quantum physics.