Xenocrates and Aristotle
Aristotle played a large role when it came to Xenocrates’ view of metaphysics. Like most people who were following Plato during that time, Aristotle believed that there were three main views on the ideal numbers and their connection to ideas and mathematical numbers. The first principle was that Platonists defined a difference between ideal and mathematical numbers. The second principle was that those who followed Xenocrates recognized that there were ideal numbers within mathematical numbers. Speusippus however, determined that there were only mathematical numbers.
Aristotle heavily disagreed with Xenocrates’ theory of numbers. He challenged Xenocrates that with this theory, the ideas would be numbers created from arithmetical units. He determined that it was not only impossible because the principle would no longer exist but that the numbers then would need to become subject to arithmetical operations. Aristotle argued that the number needs to be the conditioning principle of consciousness and of therefore, of knowledge also. He believed then that to prove what was needed in the in the Pythagorean assumption, as Plato had said before him, it is only when the number can mend the opposition between what was the same and what was different, that the number can move towards a self-motivation within the soul.
This theory is very close to Xenocrates’ own theory about indivisible lines. It was within these lines that Xenocrates discovered that only God and those who worshipped God could know the elements or principles of the Platonic triangle. Xenocrates described them firstly as original lines but in a very much the same sense, have spoken of original neutral figures and bodies. However, Xenocrates principle of what it was should not be searched for within materialistic items and not a divisible that attaches itself to a phenomenon but only in the ideal and perfectly exact form.
Xenocrates very well could have seen Aristotle’s theory as an assumption made from a subjective point of view. However, what Xenocrates’ ever thought of Aristotle’s theory or Aristotle himself, may never be known. His writings, along with any documentation provided from his firsthand writings never survived and so most of his theories and beliefs stem from other assumptions or the little that Xenocrates left behind. Aristotle’s opinions on Xenocrates’ work however, were widely known as Aristotle was continuing to challenge Xenocrates with Platonic beliefs. Although Xenocrates himself was a follower of Plato, and studied under him at the Academy, the interpretation varied between these two philosophers.