Universal Education and the University
The graduates of such a collegium or university could then become professors, that is, people who had thrashed out their ideas, threshed out the chaff from their ideas, and trashed the bad ideas, so as to be able to profess something worth professing. The whole idea was to go through the process first and then go out into the world to make it a better place (or not).
This was why most universities of old grew up as relatively cloistered environments akin to monasteries. The word 'edifice' from Latin aedificium (what they called libraries, mostly) reflects that. Sadly, many modern buildings are edifices that do not edify (much as many sacrifices these days do not make sacred).
In the early days only people who valued education went into such institutions. This changed when education was seen as imparting economic value to graduates. Then getting the degree became more important to the majority of the world than actually going to a college or university. And, as with watches, clothing and the luxury versions of all such consumer goods, labels also became worth something.
However, there are many simple tests of educational quality. Some come with counter-tests.
For example, ask a student whether there is such a thing as absolute truth. If that student replies in the negative, then ask whether this negative is absolutely true. On the other hand, an educated mind can juggle n+1 contradictory ideas in n sections of the brain while working out how to verify and hold on to n-1 of them for further analysis.
A good institution will have made students who, formerly unable to survive a battery of these simple tests, can do so by the time they graduate. For students who could already survive such a battery, the institution will have made them able to design and deploy such tests themselves.
All this, of course, leads to a society where ideas are thrashed, threshed and trashed more accurately and usefully. Or in theory, that's what should happen. Universally.