 Intuitionism originates in the work of the mathematician L.E.J. Brouwer (van Atten 2004), and it is inspired by Kantian views of what objects are (Parsons 2008, chapter 1). According to intuitionism, mathematics is essentially an activity of construction. The natural numbers are mental constructions, the real numbers are mental constructions, proofs and theorems are mental constructions, mathematical meaning is a mental construction… Mathematical constructions are produced by the ideal mathematician, i.e., abstraction is made from contingent, physical limitations of the real life mathematician. But even the ideal mathematician remains a finite being. She can never complete an infinite construction, even though she can complete arbitrarily large finite initial parts of it. This entails that intuitionism resolutely rejects the existence of the actual (or completed) infinite; only potentially infinite collections are given in the activity of construction. A basic example is the successive construction in time of the individual natural numbers.