The dimension problem. Not much attention has been paid to this problem although it is fundamental. If the plane consists of a discrete set of elements, hodons or atoms, then this set must have dimension zero. For, in order to determine the dimension, this set must be equipped with a topology and the only possible candidate is the discrete topology. This entails that the dimension is zero. Either one takes the option to simply drop the notion of dimension on the basis of the argument that the concept of dimension presupposes a concept of continuity and topology and hence has no finitist meaning. Or one searches for an analog, but it is not clear at all what that could be.  Something one should not try to do is to derive a notion of dimension from an ordering relation. Suppose that the hodons are labeled by integers \((i, j)\) in some appropriate coordinate system, such that \(-L\le i\), \(j\le L\), where \(L\) is some upper bound. Then quite different ordering relations are possible. One possibility is to define \((i, j) \lt(k, l)\) if and only if \(i + j \lt k + l\). But another possibility is to define \((i, j) \lt(k, l)\) if and only if either \(i \lt k\) or, if \(i = k\), then \(j \lt l\). It therefore requires additional arguments to claim that among all possible order relations on a given set, one and only one has a special status. However in section 3 we will see that, using the tools of graph theory, a definition of dimension can indeed be given.