Frege's Theorem http://plato.stanford.edu/entries/frege-logic/index.html
Article in the Stanford Encylcopaedia of Philosophy, entitled `Frege's Logic, Theorem, and Foundations for Arithmetic'. Discusses the 1980 discovery of Crispin Wright that Frege's work of the Grundgesetze can be carried out in second-order logic with Hume's principle.

Why Aristotelian Logic does not Work http://www.abelard.org/category/category.htm
An essay at Abelard.org outlining an argument against Aristotelian syllogistic. The argument focusses upon the relationship between Aristotle's categories and his conception of being, attacking them from an idealist position drawing upon Brouwerian intuitionism and some Zen philosophy.

The Troublesome Paradox http://www.yesgoyes.com/
Online version of book seeking publication by Per Lundgren. Author attempts to argue that a consequence of Goedel's incompleteness theorem is that we should overturn our current approach to scientific method.

Logic http://www.philosophypages.com/lg/
An online textbook by Garth Kemerling, explaining the basic elements of elementary logic at an undergraduate level.