This one-to-one correspondence of “likeness” is only supposed to be definite in the limit when the relations are very close together in the structure. Thus we avoid any kind of comparison at a distance which is as objectionable as action at a distance. Let me confess at once that I do not know what I mean here by “very close together”. As yet space and time have not been built. Perhaps we might say that only a few of the relata possess relations whose comparability to the first [Pg 233] is definite, and take the definiteness of the comparability as the criterion of contiguity. I hardly know. The building at this point shows some cracks, but I think it should not be beyond the resources of the mathematical logician to cement them up. We should also arrange at this stage that the monomarks are so assigned as to give an indication of contiguity. Fig. 7 Let us start with a relatum and a relation radiating from it. Now step to a contiguous relatum and pick out the “like” relation . Go on to another contiguous relatum and pick out the relation which is like . (Note that since is farther from than from , the relation at which is like is not so definite as the relation which is like .) Step by step we may make the comparison round a route which returns to the starting-point. There is nothing to ensure that the final relation which has, so to speak, been carried round the [Pg 234] circuit will be the relation with which we originally started. We have now two relations , radiating from the first relatum, their difference being connected with a certain circuit in the world . The loose ends of the relations and have their monomarks, and we can take the difference of the monomarks (i.e. the difference of the identification numbers comprised in them) as the code expression for the change introduced by carrying round the circuit. As we vary the circuit and the original relation, so the change varies; and the next step is to find a mathematical formula expressing this dependence. There are virtually four things to connect, the circuit counting double since, for example, a rectangular circuit would be described by specifying two sides. Each of them has to be specified by four identification numbers (either monomarks or derived from monomarks); consequently, to allow for all combinations, the required mathematical formula contains or 256 numerical coefficients. These coefficients give a numerical measure of the structure surrounding the initial relatum.