(from a joint work with G. Sundholm) Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. We will discuss a number of these issues, both from an historical, as well as a systematic point of view. We will argue that Brouwer's demonstration is a transcendental argument.