A posteriori and a priori

Wolff is interested not just of truth and probability, but of different methods for discovering true and probable statements, that is, scientific and philosophical methodology. Now, as we have seen, Wolff has made the bold statement that logic is all that one requires for methodology, and at least when it comes to truth, logic is essentially based on demonstrations. This rather stringent description is easier to understand, once we remember that Wolff would accept also empirical statements as premisses of demonstration.

What I find remarkable is that Wolff mentions two different methodologies: a posteriori and a priori. In all external appearances, we are moving towards Kant, yet, there are still crucial differences. While for Kant a posteriori would mean all knowledge based on experience, Wolff limits the range of a posteriori to mere experiences. Thus, when Kant says that a posteriori knowledge cannot be universal, his statement is far stronger than Wolff's. Indeed, Wolff would verbally accept Kant's statement, but it would mean something less than with Kant – it would be just tautology because individual experiences are always singular.

Now, if a posteriori has no other meaning for Wolff, but individual experiences, a priori must then get everything else, that is, the class of a priori contains all bits of knowledge requiring demonstration. Now, demonstrations as meant by Wolff here can be either direct or indirect, while a priori can be either intuitive or discursive. Intuitive a priori has a nice paradoxical feeling to it, somewhat reminiscent of later and more famous synthetic a priori, yet, is not completely identical with it. Intuitive apriority characterises all those truths that can be directly intuited as true, just by carefully reflecting on the elements of the supposed truth. The class of such truths contains analytic axioms of logic, but also immediate truths about causes and effects, which Kant would have classified as synthetic a priori.

The final class of knowledge statements contains then discursive apriorities, that is, demonstrated truths. As one should remember, these demonstrations could have reliable experiences as premises. Furthermore, Wolff also included inductions as just one modification of syllogistic reasoning. Wolff's class of discursive apriorities contains then a lot that Kant would have classified as a posteriori, and in fact is probably the largest of the three classes.

Within this threefold classification Wolff places his main methodological considerations: when is experience to be relied upon, when can we say that something is a cause, when can we use experiences to draw general conclusions etc. I shall refrain from going into intricate details, and instead, I shall next time look at how Wolff thinks scientific conclusions should be presented.

Rational philosophy or logic (1728)

I recently had the distinct displeasure of reading a rant of a would-be philosopher who disparaged a logician, because modern logical texts are like circuit diagrams – useful perhaps, but meant only for people with no literary taste and ultimately unphilosophical. Personally, I find logical texts of all sorts – whether they be ancient, modern, formal, informal, transcendental or even Hegelian – to be aesthetically pleasing in a way that a beautiful calculation or a brilliant game of chess is also: as delightful in their very existence as brightest of poems, no matter how useful they otherwise might be. And if someone complains about non-existent philosophical import of logic, I am always reminded of Hegel's clever quip about enthusiastic youth who are enamored by Plato's more vivid and lively dialogues and who later become very disappointed when they hit the abstract heights of Plato's Parmenides and its study of dry concepts like one and many. Thus, I am not afraid of the supposed dryness of next book in line, Wolff's Philosophia rationalis sive logica.

Is this all there is to logic?

As someone might remember, Wolff had already published a book on logic, the first in his famous series of reasonable thoughts. The current book, on the other hand, begins Wolff's philosophy anew, except this time in Latin. While the German series was meant mostly for domestic markets and especially his students, the publication of Latin versions of different parts of his philosophy served the purpose of making Wolff's work more known throughout Europe. Because of their more scholarly ambitions, Wolff's Latin books contain also more material than their German equivalents. Thus, while I first thought that Wolff's Latin logic would contain only about 300 pages and not be much longer than its German counterpart, I noticed quickly I had actually picked up a separately published compendium for Latin logic, containing just the table of contents for the actual book, which happened to be over 800 pages long.

Just like its German counterpart, Wolff's Latin logic contains much that would not be dealt in a logic course these days: it is more of a book of methodology. Thus, it is also meant to be the first book of Wolff's Latin philosophical works in the sense that reader should first grasp how philosophy works before actually reading some philosophy: the true first philosophy is then ontology, because all the other parts of the philosophy depend on it.

As starting points of series, both books begin with an account of what philosophy is all about. But the inflatedness of the Latin logic shows itself in the very start, with Wolff's novel discussion of three forms of cognition – well, it is actually novel only from the perspective of Wolff, because it is quite reminiscent of Bilfinger's disputation with this very topic. What is important in this beginning, is Wolff's clear commitment on empiricism: all cognition begins with a historical phase, where one can just learn facts through observation. The cognition could then develop into mathematical cognition, by quantifying the results of observation, or it could turn philosophical by attempting to find explanations for the facts (note that nothing speaks against cognition that is both philosophical and mathematical, especially if the quantification helps us to discern causal relations).

If philosophical cognition means finding explanations for observed facts, philosopher is then a person who can give such explanations – that is, an expert on some topic. Philosophy, on the other hand, is for Wolff not just any expertise. Just like in his German logic, Wolff defines philosophy as a science of what is possible. I already noted that this definition means actually just what science does: capacity to demonstrate assertions from indubitable premisses.

Whereas German logic left a rather rationalistic impression, in Latin logic Wolff admits that experiences and experiments can well give science its required premises, provided that they just are reliable. Indeed, although Wolff does equate philosophical and mathematical method, he does accept also the construction of hypotheses or reasonable, but unproved assumptions as an incentive to scientific development. Thus, completely axiomatic-deductive system is admitted to be a mere ideal that we can perhaps approach, but never completely satisfy. The ideal also instigates philosophers to remain moderately skeptical in dilemmas where none of the options can be proven indubitably.

Wolff also notes that philosophy might be cognized only historically, that is, we could just e.g. read Wolffian system and learn all its propositions. Such a historical knowledge of philosophy might be useful, but true philosophical cognition of philosophy is achieved only when we try to understand what philosophers say, for instance, by repeating the experiments described in a text book.

Just like in German logic, in Latin logic Wolff also presents a general division of philosophy. What is remarkable is that the new division is more detailed, especially as it comes to more empirical parts of Wolffian system. This no doubt reflects the fact that Wolff has now actually worked out his system in more detail and has especially realized how important empirical observations are to the development of science. In addition, Wolff also helpfully indicates how each part of his system depends on some parts and serves as a foundation for others.

I’ll be continuing for a while with my account of Latin logic, and next time I shall take a look at the difference between natural and artificial logic.

Christian Wolff: Reasonable thoughts on the capacities of the human understanding and their correct use in knowing truth - Levels of certainty

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.