Classes: Wednesday 19:00-21:00 in UH 112 January-April 2017
Instructor: Richard T. W. Arthur Office: UH 305; ext. 23470 OH: Wednesday 4-5 pm
Although this course presupposes a high level of competence in logic, it develops into something very different from Phil 2B03. Thus on the one side, various alternative logics have been developed that build on those foundations. But on the other, investigations of those foundations have raised some profound and fascinating questions. The following quotation from Nietzsche puts it well: “When the enquirer, having pushed to the [periphery of science], realizes how logic in that place curls about itself and bites its own tail, he is struck with a new type of perception: a tragic perception which requires, to make it tolerable, the remedy of art.” This could serve as the motif for this course: logic biting its own tail. It is implicit in paradoxes such as Zeno’s paradoxes of motion and plurality, which Lewis Carroll extends to modus ponens. But the theme of logic curling about itself is unfolded with a vengeance in developments in modern mathematical logic, particularly with the theory of recursive functions, and the discoveries of Gödel’s Theorem and Skolem’s Paradox. These have profound implications for subjects as diverse as the theory of knowledge and the nature of artificial intelligence, and are imaginatively and artistically explored in Hofstadter’s Gödel, Escher, Bach—as are their implications for artificial intelligence, their connections with Escher's woodcuts, Bach's fugues, molecular genetics, Zen Buddhism and a million other fascinating subjects. Meanwhile Logical Options will serve as our guide for alternative systems of logic.