 In the late nineteenth century, certain individuals—most notably Kronecker and Poincaré—had expressed doubts about, or even disapproval of, the idealistic, nonconstructive methods used by some of their contemporaries; but it is in the polemical writings of  L.E.J. Brouwer  (1881–1966), beginning with his Amsterdam doctoral thesis, Brouwer [1907], and continuing over the next forty-seven years, that the foundations of a precise, systematic approach to constructive mathematics were laid. In Brouwer’s philosophy, known as  intuitionism,  mathematics is a free creation of the human mind, and an object exists if and only if it can be (mentally) constructed. If one takes that philosophical stance, then one is inexorably drawn to the foregoing constructive interpretation of the logical connectives and quantifiers: for how could a proof of the impossibility of the non-existence of a certain object \(x\) describe a mental construction of \(x\)?