The intuitionist conception of mathematics was developed by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966). According to Brouwer mathematics is not a system of formulas and rules but a fundamental form of human activity, an activity that has its basis in our ability to abstract a conception of "twoness" from successive phases of human experience and to see how this operation may be indefinitely repeated to generate the infinitely proceeding sequence of the natural numbers. In the system of mathematics based on this primordial intuition, language serves merely as an aid to memory and communication and cannot of itself create a new mathematical system; our words and formulas have significance only insofar as they are backed by an essentially languageless activity of the mind. In particular, the wording of a theorem is meaningful only if it indicates the mental construction of some mathematical entity...