Philosophy 3349
Topics in Logic

Final Project
Spring, 2002

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. An alternative to a conventional paper would be to write a well-documented program with a fairly concise discussion of its significance. Possibilities here include theorem-proving programs for either classical logic or an alternative logic. If you are feeling extremely ambitious you could tackle something like a program to translate either from symbolic notation into English or (much more difficult) from English into symbolic notation.

Format:

10-12 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:

Thursday, April 25. Each student should also do an oral presentation on the topic of the paper prior to the due date.

Content:

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


• The paper could address a primarily philosophical issue about logic. Examples: Is logic empirical or a priori? Is it a very general empirical theory, or something completely different? Can there be genuine alternatives or rivals to classical logic, or just extensions and notational variants?


• The paper could address a particular proposed alternative to classical logic, arguing that the motivations for this alternative are (or are not) convincing. The alternative considered could be one of those discussed in class (including many-valued logics, intuitionistic logic, fuzzy logic, quantum logic, nonmonotonic logic) or one we haven't discussed (e.g. relevance logic, dialethic logic, etc.).


• On the other hand, you could write a primarily descriptive paper about one of these alternative logics. Such a paper would still need to consider the philosophical motivation for the alternative, but could focus on a detailed exposition of how it works and what the differences from classical logic are. This might involve the following: developing a set of rules in the style of NK, explaining where the differences from NK lie; developing a semantics for the alternative logic; possibly explaining reasons for thinking the system is or isn't sound and complete given the rules and the semantics.


• 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, and would then need to develop appropriate rules, explain and justify their differences from the rules of NK, discuss differences between the theorems of NK and the theorems of your proposed alternative, etc. You might also want to develop a semantics and consider issues of soundness and completeness.


• Or you could discuss a metalogical result, e.g. compactness, the Lowenheim-Skolem theorem, or one of Godel's incompleteness theorems. A paper on one of these topics could be primarily expository. You would need to describe the result, offer a proof or at least a detailed sketch of a proof, and say something about the significance of the result.


• Or you could write a primarily philosophical paper about one of these metalogical results. The most likely choices here would be a paper on the bearing of the Lowenheim-Skolem theorem on issues of reference and metaphysics, a la Putnam's "Models and Reality," or a paper on whether Godel's incompleteness theorems show the impossibility of artificial intelligence, as Lucas and Penrose have argued.

Have fun with it!