maanantai 15. elokuuta 2011

Christian Wolff: Albegraical dissertation on infinitesimal differential algorithms (1704)

As promised, I shall begin my blog with Christian Wolff, the major figure in the arena of German philosophy before Kant. I am sure that many of you have heard the phrase Leibniz-Wolffian philosophy, which would indicate that Wolff merely copied Leibniz and had nothing original to say. Furthermore, many critics, like Hegel, have stated also that Wolff is a pedantic and boring writer. Both of these statements are far too critical. Even before this project, I had read German-language versions of Wolff's logic and metaphysics and have nothing to complain about his style: his writings are at least as exciting and engaging as writings of an average analytic philosopher.

In addition, we should not think Wolff as a mere faithful disciple or even imitator of Leibniz. Wolff and Leiniz corresponded mostly about mathematcial questions and Wolff could not even have known Leibniz's philosophy in a deep manner: the majority of the works of Leibniz were published only after his death and after Wolff had begun his own philosophical career. Indeed, we might as well speak of a Wolff-Leibnizian philosophy: Wolff was the true beginner of the philosophical tradition in Germany, while Leibniz's works influenced this tradition only later.

I have chosen to take Wolff's dissertation Dissertatio algebraica de algorithmo infinitesimali differentiali as a suitable beginning for his career, although the work is not philosophically important. In fact, the dissertation is not about philosophy at all, but as the title says, studies mathematics and particularly differential calculus. Wolff began as a mathematician and what we would call a physicist and in a later book he even congratulates himself on having made important innovations in the field of aerometry or the study of measuring air pressure.

The subject matter of the dissertation is from a modern viewpoint rather elementary. Wolff derives some easy formulas of differential calculus, such as how to differentiate a product of two functions – nowadays a clever high school kid could do this. Although differential calculus was still somewhat of a novelty, I can find nothing in Wolff's dissertation that either Leibniz or Newton wouldn't have achieved already – Wolff even himself makes copious references to his predecessors in the thirty-odd pages. If this was a standard dissertation at the time, I must say that the criteria have been tightened from those days.

What I find most interesting in the whole dissertation are the short corollaries at the end of the work. After rather mathematical considerations Wolff merely enumerates certain further consequences such as ”matter is infinitely divisible” and ”God is to creatures as our mind is to entities of reason”, without offering any argument or explanation as to how these rather philosophical sentences related to the question of differential calculus. This might remind one of certain analytic philosophers who do a whole article or presentation full of clever logical tricks and then end up by telling that all of this has rather interesting philosophical consequences, but that this is so evident one hardly needs to spell the argument.

This is undoubtedly all we need to say about Wolff's dissertation, but we are still not yet through with his mathematical writings: the next few texts shall describe Wolff's mathematical masterpiece that purports to go through the elements of all mathematical sciences.

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