In this paper, I argue that the indispensability argument unifies all of Hilary Putnam’s diverse work in the philosophy of mathematics. I also argue that his version of the indispensability argument does not justify knowledge of mathematical objects. I first characterize indispensability arguments in the philosophy of mathematics, distilling them to four essential characteristics. I show that t...

Maximum satissability (MAX-SAT) is an extension of satissability (SAT), in which a partial solution is sought that satisses the maximum number of clauses in a logical formula. Enumerative methods giving guaranteed optimal solutions can be derived from traditional search algorithms used to solve SAT problems, in particular the Davis-Putnam procedure. Algorithms have also been developed for the m...