One will not find the foundation of Socrates' teaching directly in Plato's dialogs, one has to find it from another acquaintance of Socrates, Xenophon
“By the Gods, replied Socrates, the discovery will be most useful! The standard of right and wrong once fixed; all difference of opinion among the judges;—all sedition among the people;—all law-suits between citizens;—all wars and contentions among communities, must be at an end! and truly it would grieve me to leave you, Hippias, without knowing what this inestimable secret may be that you say you have discovered.” Xenophon, Memorabilia, Fielding.
The idea that there is a single standard for information processing, for judgment, is demonstrated today, globally by the computer.
Many simple minded people actually believe, because they cannot distinguish the difference between the perceptible and intelligible, that the perceptible applications of it, multiplies the standard, itself. However, if one comprehended what Plato stated, and reflected sufficiently on it, they know that the perceptible is never intelligible, nor is the intelligible ever perceptible. Now, put into a particular examples, say, for example, Euclid "The point is that which has no part." Or put into semantics, the map is not the territory. Or again, grammatically, the noun is not a verb.
This binary distinction can be traced back at least as far as Genesis in the Bible.
There are two, and only two parts of speech, but they are universally applicable to the perceptible Cosmos.
Now the definition of a thing, that there is a distinction between the noun, or limit, and the verb, i.e. the relative difference, is not an axiom, it is simply a physical fact.