What is the nature of the evidence provided by thinking about hypothetical cases, such as those presented in the thought experiments (TE)? Is it psychological, as those who speak about intuitions seem to think, or not? This problem is closely related to that of the nature of the subject matter of philosophy, that most philosophers tend to conceive as non-psychological. Williamson’s position on the matter (Williamson 2007) consists in rejecting the psychological view on intuitions: if we want this method—the armchair method—to provide us with evidence in favour or contra theses or theories concerning the non-psychological subject matter of our inquiry, then we must understand the evidence, collected “by thinking about the cases”, as non-psychological as well. Unlike Williamson, Brown (Brown 2011) thinks that the psychological view on intuitions can be maintained: an indirect approach to the object of our inquiry is feasible; the gap between these data and the non-psychological object they are supposed to provide evidence for can be closed. The main aim of this paper is to argue (against Williamson and with Brown) that a revision of the classical view on intuitions is not required. My strategy consists in adopting a Wittgensteinian perspective on the nature of the aims and results of the philosophical inquiry; in showing how this can help us provide an easy solution to the gap problem; and in arguing —against Williamson—that conceiving the subject matter of philosophy as conceptual does not necessarily amount to conceive it as psychological.