Predicate logic is a subdiscipline of logic that had its roots in the last quarter of the nineteenth century, though it had to wait until the second decade of the twentieth century for a solid foundation. Like any other logic, it is concerned with the validity of arguments, though not of any kind: its interest lies in reasoning about what is universally true. As such, predicate logic is especially suited to reason about mathematical statements and can be considered a generalization of Aristotelian syllogisms. Predicate logic goes beyond syllogisms by introducing predicates with arbitrary numbers of arguments and quantifiers that allow to refer either to all or to some of the elements in the universe that is under consideration. It has a proof theory, which consists of a set of rules that describe how to mechanically derive sentences from a given set of premises (and such derivations are called “proofs”), as well as a model theory that...
- Ebbinghaus, H.- D., Flum, J., & Thomas, W. (1996). Mathematical logic (2nd ed.). New York: Springer.Google Scholar
- Enderton, H. B. (2001). A mathematical introduction to logic (2nd ed.). San Diego: Academic.Google Scholar
- Gabbay, D. M., & Guenthner, F. (Eds.). Handbook of philosophical logic (2nd ed.). In eighteen volumes, the first published in 2001. Dordrecht, The Netherlands: Kluwer Academic Press.Google Scholar
- Gödel, K. Collected works. Oxford University Press. In five volumes, the first published in 1986.Google Scholar
- Simpson, G. (2000). Logic and mathematics. In S. Rosen (Ed.), The examined life: Readings from Western philosophers from Plato to Kant. New York: Random House Reference.Google Scholar
- Tarski, A. (1983). Logic, semantics, metamathematics, papers from 1923 to 1938. Indianapolis: Hackett Publishing Company.Google Scholar
- van Dalen, D. (2004). Logic and structure (4th ed.). Berlin: Springer.Google Scholar