I can’t imagine why anyone would bother with Peirce’s logic if it’s just Frege and Russell in a different syntax, which has been the opinion I usually get from FOL fans. But the fact is Peirce’s 1870 “Logic of Relatives” is already far in advance of anything we’d see again for a century, in principle in most places, in practice in many others, chock full of revolutionary ideas, not all of which he developed fully in subsequent work. Although I studied the 1870 Logic from early on I did not realize how far ahead of its time it was until I began reading approaches to logic from category-theoretic and computation-theoretic angles in the 1970s and 1980s. An indication of Peirce’s innovations can be found in the series of selections and commentary I started on the 1870 Logic of Relatives.
Here’s the work in progress so far on the OEIS Wiki.
Here’s the overview for a parallel series of blog posts.
- Logical Graphs
- Proof Animations
- Survey of Theme One Program
- Survey of Animated Logical Graphs
- Propositional Equation Reasoning Systems