The famous mathematical intuitionist L. E. J. Brouwer believed that the basic intuition of time is the only intuition mathematics needs, while rejecting the intuition of space. The author vindicates the intuitions of space and argues that some of them are essential and cannot be reduced to the intuition of time. With the example of the intuition of ‘betweenness’ which gives rise to ordered geometry, an example of a type of geometry in which no coordinates can be introduced is given. The conclusion of the author is that the intuition of the space in mathematics cannot so easily be discarded as Brouwer attempted to do.
For the entire collection see [Zbl 1519.57002].