The Platonic analogy of a broken line is probably familiar to all philosophy enthusiasts. Just like the knowledge of shadows and pictures is to the knowledge of real things, so is the knowledge of the whole world of sense experience to the knowledge of the world of ideas, and how the knowledge of the sense experience is to the knowledge of the ideas, so within the knowledge of the ideas is the doxa to the episteme. I am not doing Plato-study here, so I won't consider more closely how e.g. the doxa is to be differentiated from the episteme. What is interesting here is the idea that certainty of knowledge comes in grades: for instance, that knowledge of sense experiences is unreliable compared to our knowledge of mathematical issues.
This idea was inherited by later philosophers and eventually also reached Germany, where Wolff finally translated the Platonian classification of the levels of certainty to German, although Wolff apparently left out the lowest rang of the Platonic ladder. Comparing to the sense experience Wolff speaks of Glauben, Platonic doxa is replaced by Wolff's Meinung and the highest level of episteme has been transformed into Wissenschaft. The three terms play an important role in the later German philosophy, so let's have a look at them in more detail.
The term Wissenschaft or science is already familiar to us. One might wonder why Greek episteme corresponds with science, when words like ”epistemology” suggest that the Greek original has something to do with knowledge in general. Yet, if we look at how Plato and Aristotle used the word, science or Latin scientia is a very apt translation. For instance, in Aristotle's Posterior analytics episteme refers to a deductive system of knowledge based on indubitable axioms and definitions. As we saw in the previous text, in Wolff this mathematical ideal of science has already been replaced by a more modern notion of science as based on both axioms (in mathematics) and reliable experiences (in experimental sciences).
The meaning of Wolff's Meinung or opinion is also easy to understand, although unlike the Greek original, Wolff appears to evalue opinion as the lowest cognitive state. Opinion is essentially a weaker version of science: ”If we assume definitions that appear to be possible and in inferences assume some axioms, which appear to be correct, although we have not yet demonstrated them, and which we cannot corrobarate through indubitable truths – then we arrive to opinions”. That is, opinions might be argued for, but they still lack the ultimate certainty of science based on incontrovertible truths: if I have an opinion of something, things might still be different than I think. Furthermore, opinions are more subjective than science, because my opinions might known to be false by another person. One might even think that one's opionions are scientifically certain, if one is not aware of how things are demonstrated in science.
It is Glauben that is the most distant from its Platonic predecessor, pistis, but this just reflects the development of the Greek word. While for Plato pistis referred simply to sense experiences, even in Aristotle's Rhetoric pistis meant conviction and trust invoked by a good speaker, while in Pauline letters pistis refers to the first member of the triad ”faith, hope and love”. German Glauben means similarly both belief and faith.
Wolff's use of Glauben reflects Aristotle's rhetorical use of pistis: Wolff understands by Glauben the approval that is given to a statement because of a testimony of someone else. Yet, Wolff extends the role of such a conviction on a testimony from mere judicial matters. While opinion is only a sort of diluted version of science, Glauben is the counterpart of science. Remember that for Wolff science, at least in humans, deals only with possibilities, for instance, with what can be done: these are the things that can be demonstrated. What has actually happened, instead, is beyond scientific proof and we just have to believe the testimony of our own senses and of others, when it comes to such historical questions.
In addition to methodology of mathematican and experimental sciences, Wolff's logical work then also contains the rudiments of a methodology for history. An important element in these rudiments is to recognise how reliable a person describing some events is. Wolff suggests several rules of thumbs how one could decide e.g. whether a witness would have some reasons for lying about what has happened, but does not move further beyond such rules of thumbs.
Although Wolff appears not to use Glauben in the sense of religious faith, we might apply his definition also to faith. Then religion and faith would become intersubjective, communal issues. Having faith on certain religious dogmas would mean being convinced that the people ascribing to those dogmas are reliable witnesses who have no reason for lying on such matters and who are linked through a chain of equally reliable persons to an original witness who was there to actually see what the holy books describe.