The aim of this chapter is to criticize the view that it is never rational to attempt the impossible; which is not, however, to advocate all impossible aims. The ideal of positivism, which positivists deem obviously attainable, namely the unity of science in rationality and the rational unity of mankind, is here viewed as very worthwhile, but quite possibly impossible and certainly not obviously possible. Yet, to repeat, not all impossible aims or unattainable goals are reasonable to pursue.