None of the philosophers I've dealt with so far can be called a philosophical celebrity – I'll hit that milestone when I reach Kant – and even from the viewpoint of the circle of German philosophy scholars, several of these philosophers have been rather obscure. Even among these unknown figures, Adolph Friedrich Hoffmann shines with his apparent anonymity. Hoffmann's fate was to be placed between two more philosophers with more fame, as a mere mediating point of their philosophical development.
Hoffmann's teacher, Rüdiger, was known in his time through his medical writings and was also famous as a counterforce against Christian Wolff. Hoffmann's pupil, Crucius, was to be known as yet another critic of Wolffians, but also as an influence on Kant's thinking. Hidden between these two, it is not unsurprising that Hoffmann's writings never really circulated that much – and indeed, when Lewis White Beck, in his study of early German philosophy, notes that he had the opportunity to see one of the copies of Hoffman's major writings, he also points out that this was one of only three copies of the book.
Hoffmann esteemed his mentor highly, and when Rüdiger's book criticising Wolffian psychology received no answer from Wolff himself, Hoffmann became incredibly displeased. Now, Wolff probably felt that he had adequately answered his critics in his earlier works, and in any case, he was engaged with writing the Latin versions of his works. Still, Hoffmann thought that Wolff could have spared some time after completing his Latin logic for consideration of Rüdiger's text. As the situation was what it was, Hoffmann rebuked Wolff by attacking the just published Latin logic in a writing aptly called Gedancken über Hn. Christian Wolffens LOGIC, oder sogenannte PHILOSOPHIAM RATIONALEM. As far as I know, this was the first time when someone had made critical remarks on Wolffian logic, whereas Wolff's pietist opponents had just ignored this part of Wolff's philosophy.
Hoffmann closes his article by explaining the purpose of the book and also by invoking the simile of the world of letters as a republic, in which the only crime is bad reasoning and the only judges are learned fellows of Europe. Hoffmann thus considers himself to be engaged in a trial of Wolffian logic. He concentrates his questions mostly on the theoretical part of logic, the only exception being Wolff's notion of truth. Hoffmann's criticism shows how well he truly found the weak points of Latin logic – Hoffmann points out how ridiculous Wolff's definition of truth sounds, and in fact, I noted recently that this definition is truly difficult to interpret.
A considerably large portion of the article deals with Wolff's consideration of demonstrations and especially his attempt to incorporate all sorts of deductions in syllogistic guise. Hoffmann argues that there are actually many types of deduction that do not have syllogistic form, such as the immediate deduction from the sentence ”all As are Bs”, to ”some As are Bs”. Wolff of course knew about these cases, but thought them to be at least implicit syllogisms. Thus, one could add an identical proposition ”some As are As” and from this and ”all As are Bs” one could syllogistically prove ”some As are Bs”.
Hoffmann notes that Wolff's moves for syllogising all deductions are rather unsuccessful. For instance, adding the identical proposition ”some As are As” adds nothing new to deduction in hand. One might think that Hoffmann had an unclear intuition of a deep thought developed later in more detail by Lewis Carroll in his famous dialogue between Achilles and turtle. The point of the dialogue is that adding mere premisses to a deduction is never enough to make it valid – for example, if Achilles says ”A, and if A then B” and turtle asks how Achilles could justify the move to ”B” after this, Achilles cannot just add a new premiss ”if A and (if A then B), then B”, because turtle can just ask for the same question again. What the turtle requires is not new premisses, but rules for what to do with those premisses. Similarly, one could say that the identical proposition above is just a description of a rule stating that one could apply everything applicable to members of a class to members in any part of the original class.
But the true controversial topic is the relationship between mathematics and philosophy. It is clear that Wolff himself thought mathematical method to be suitable even in philosophy – this will be argued for in more detail in his Latin ontology. Now, Wolff himself had suggested that philosophy was essential for knowing causes of things, and mathematics would then be of use by revealing dependency relations through correlations of quantities. Hoffmann makes the correct remark that mere quantitative relation does not always mean a causal relationship. For instance, people who frequent most doctors usually have diseases more than other people. Still, this does not mean that visiting doctors would be bad for your health. On the contrary, people happen to visit doctor, whenever they are ill, which explains the correlation more naturally. Hoffmann has thus uncovered the familiar sophistical move from mere correlation to causation. This simple methodological remark does hurt Wolff's credibility more than all the criticism about his Spinozism.
So much for this critical book, next time we shall return to Wolff and his ontology.