For one thing, Hilbert was very clear (especially in his unpublished lectures on geometry: see Hallett and Majer 2004) that, although a domain is asserted to ‘exist’, all that is known about the objects in the domain is what is given to us by the axioms and what can be derived from these through ‘finite proof’. In other words, while a domain is postulated, nothing is taken to be known about the things in it independently of the axioms laid down and what they entail. The basic example was given by geometrical systems of points, lines and planes; although the geometrical domain is made up of these things, nothing can be assumed known about them (in particular no ‘intuitive’ geometrical knowledge from whatever source) other than what is given in the axioms or which can be derived from them by legitimate inference. (The axioms themselves might sum up, or be derived from, ‘intuitive’ knowledge, but that is a different matter. And even here it is important that we can detach the axioms from their intuitive meanings.)