Xenocrates and Epistemology and Mathematics
Although Speusippus before him had made general divisions between the three different types of philosophy, Xenocrates made the same three types of divisions but made the lines between them much more distinct. To do so, he was required to veer from Plato’s method of working through doubts and take on his own method of creating doctrine that was written authoritatively.
The three types of thinking that Xenocrates identified as being distinct in their own right were knowledge, sensation, and opinion. He believed that knowledge could be narrowed down to that which was the object of pure thought but does not exist in the phenomenal world. Sensation is that which comes into the world through phenomenon. Opinion however, is sensuous perception and mathematically, which is pure reason. Xenocrates showed how opinion could be taken to a higher level and bridge the gap between knowledge and sensuous perception. Plato had also done this before him but Xenocrates took it to a higher level and made it much more definitive. All three types of thinking hold some truth but how scientific perception proved it has never been found out. Xenocrates love of defining things however was seen even in naming these three types of thinking. He named them after the Fates: Atropos, Clotho, and Lachesis.
Xenocrates is also credited for writing two books which pertain to mathematics particularly. He wrote On Numbers and A Theory on Numbers. He also wrote many books on geometry. Xenocrates also was the first to determine how many syllables could be created from all the different letters of the alphabet. The reported number that Xenocrates came up with is 1,002,000,000,000. This speaks to the fact that it was the first combination problem to be solved using an altering method. However, little is known about this as well.
Although it would seem that it may have never been attempted before or that it had and no one had ever been able to do it, one must ask how he did this. Xenocrates referred to is as “invisible lines,” but the variables are many. No one knows exactly what alphabet he was using and how he did count to such a large number without the use of any technical instruments. If he were in fact using “invisible lines” how is one to tell that the counting was accurate? It’s a question that constantly brings much debate and discussion.
