I’ve claimed that all the Five Ways begin with a type of chain relative, i.e. repeatable relations like “being to the left of” or “being fathered”. But what about the Fourth Way? STA seems to mention no chain relatives at all, but simply says right out of the gate that things that are more and less good, true, and dignified, etc. (GTDE) exist relative to something maximal. Nevertheless, we understand the claim better if we take it as a conclusion for a reductio ad absurdum that assumes the GTDE has no maximal but is only relatively greater and less.
[The] bald assertion of a difference between fair and foul things, virtuous and vicious actions, offers no standard whereby to determine their difference no reason for the similarity of all fair things qua fair and for their difference from all that are foul. So long as these are only characteristics of material individuals no standard can be found, for to measure individuals against one another is to seccumb to relativism.
Harold Cherniss, The Philosophical Economy of the Theory of Ideas.
Logically, things are either more or less GTDE only relative to each other or ultimately to something maximal. Said another way, iff we take the more and less GTDE as a chain relative where something less relates to something greater, with the greater in turn being something less relative to some greater, etc; then this either goes on without ever requiring some ultimate, or some ultimate is required. But if the first, then GTDE is arbitrary and consists in nothing more than the irrational prejudice. I stress that it is an irrational prejudice to set it apart from what we are doing when we declare something better by hypothesis, since the whole point in treating something as if it is greater in GTDE is to find out what is in fact greater, i.e. to discover some standard why things are more and less what they are. But to assume that all one ever has are chain relatives is to dogmatically rule out discovering anything that is truly better in fact, and so to deny any point of framing hypotheses about it. But it is reasonable to form hypotheses about what is more or less GTDE, and so these things must exist relative to something maximal.
This throws light on an important difference between what is more and less in mathematical and virtual quantity. Mathematical quantities are given in greater or less on some continuum or set of ordered points, say, the number line. This number line fixes what is greater or less in terms of position or direction: what is to the right is greater than what is to the left. But in order to develop the analogue to position or direction in virtual quantities we need some standard S1 different from the things which we order. If S1 is itself variable in GTDE to S2, then unless S2 is given we cannot be sure even of the “direction” we have set up for the things falling under S1. The difference between the more and less in quantity and the GTDE is that what sets the direction of the greater an less in quantity is not itself a quantity, but what sets the order of, say, goods is itself a good. This is why the order of integers need not have a greatest but the order of virtual quantities must, and why, even though things greater and less in virtual quantity are chain relatives that can have an indefinite order of things merely relatively greater and lesser, it is impossible that all virtual quantities be of this kind.