Logic Seminar: Session 4
With the publication of previously unknown manuscripts, we now know that Leibniz's foundations of the infinitesimal were much more rigorous than previous commentators concluded. One of the Leibniz's innovations is to posit that many of the properties of finite quantities will hold when those quantities are infinitely small. For instance, the square of the hypotenuse of a right triangle will be equal to the sum of the squares of the other two sides, regardless of whether or not the quantities in question are finite or infinitely small (also known as "infinitesimal"). Additionally, Leibniz is incredibly careful in distinguishing between points and infinitesimals. Infinitesimals and finite quantities differ in degree, but infinitesimals and points differ in kind. While Leibniz's thought on this issue has received much attention, less work has been done on Leibniz and the infinitely large. In an interesting footnote to a text outlining the use of infinitesimals, Leibniz identifies two ways something can be infinitely large. The first is terminatus, which is analogous to the infinitesimal, differing only in degree and not kind. The second is interminatus, an infinity that differs in kind from the type of infinity described by terminatus. In this presentation, the groundwork for Leibniz's thoughts on points and infinitesimals will be covered before introducing the terminatus and interminatus in order to show to what extent Leibniz's thoughts on the infinitely large mirror his attitude towards the infinitely small.
Chair for Session: tba