Non-Classical Logics

Final Project
Spring, 2009

This page contains information on the final project. This will most likely be a paper, but there are a variety of different approaches you could take to the paper.

Format:

10-15 pages typed double-spaced (ten- or twelve-point font, one-inch margins, no really weird fonts, and preferably also not space-eating fonts like Courier New).

The paper should strive for the following virtues: clarity at every level (sentence, paragraph, section, paper as a whole); argumentative rigor.

The paper must be on a topic closely related to our class, and should make use of class readings in addition to outside research.

Due:

Wednesday, April 22. Each student should also do an oral presentation on the topic of the paper prior to the due date.

Content:

Here are some possible general strategies with a few specific suggestions for each.


• The paper could address a primarily philosophical issue about a nonclassical logic. What are the motivations for the logic? Are they adequate or not? More generally, you could address criticisms of the very idea of a "deviant" logic, as found in Quine and Susan Haack. More generally still, you could address the issue of whether logic should be thought of as a highly general empirical discipline, or whether it is entirely a priori. (See e.g. Putnam, "Is Logic Empirical?", which defends "quantum logic" as well as discussing the general issue.)
  
• You could write a paper which considers a philosophical (or other) application of a nonclassical logic. There are several examples on the topics page: using conditional logic to define or discuss causation, temporal direction, etc.; using temporal logic to discuss the nature of time; using epistemic logic to explore epistemological issues; etc. etc.
  
• You could write a more technical paper, in which you explore technical details of a nonclassical logic that go beyond what we have covered in class, for example discussing what happens when the logic is extended to full first-order logic with quantification. If you're feeling really ambitious, you could tinker: propose a revision of some nonclassical logic and explain and defend it, or perhaps combine a couple of different logics to get a composite system.
  
• Or you could develop an alternative logic of your own. This could be an extremely illuminating project, though it would also be extremely challenging. You'd need some motivation for the changes you proposed, give a careful definition of the syntax of your language, and then develop an appropriate semantics and/or a deductive system for it. (If you developed both a semantics and a deductive system, you could also explore issues of the soundness and completeness of your deductive system relative to your semantics.)

Resources:

Good starting points: the online Stanford Encyclopedia of Philosophy has good (but often somewhat difficult) entries on a variety of nonclassical logics. The Routledge Encyclopedia of Philosophy, available in the library, also has entries on most of the main nonclassical logics. Similarly, the Encyclopedia of Philosophy has articles on some of this material, and the most recent edition is available online via the library web site. Articles in both sources also usually have excellent bibliographies that can provide an entry into the literature. Another possible source: Lou Goble, ed., The Blackwell Guide to Philosophical Logic provides a good entry point for a wide variety of nonclassical logics (with chapters on many topics including modal logic, deontic logic, temporal logic, intuitionistic logic, free logics, relevant logics, many-valued logics, nonmonotonic logic, and probability logic).