Indiana and Stanford University—Philosophy and Logic
Searching for ways to help students grasp the subleties of logic, Jon Barwise of Indiana University and John Etchemendy of Stanford University co-developed three Macintosh programs: Turing’s World, Tarski’s World, and Hyperproof for use in their logic classes. With these three programs, students get a concrete view of logic through the use of dynamic, visual representations.
Barwise and Etchemendy developed the courseware using a variety of software for the various aspects of their projects; included were MacApp, Microsoft Excel, HyperCard, Textures, Aldus SuperPaint, QuicKeys, and Aldus PageMaker. Students did the actual programming following specifications set by the two professors and met with them weekly.
Developed in 1984 and used at Stanford in Philosophy 160B, Logic and Computability, Turing’s World is now a supplement to a standard textbook. It comes with its own manual and lets students build Turing machines (primitive computers) in the form of flow charts. A toolbox allows the students to draw a Turing machine with “state nodes” and “transition arcs” right on the screen. The machine runs dynamically while on the computer. According to Barwise, in the past, students developed Turing machines on paper, limiting them to simple projects and hampering their ability to master and appreciate the concepts involved. With the software, students can design very sophisticated machines in an incremental fashion, check their work, and fix any problems.
Two years after Turing’s World was developed, Tarski’s World evolved to teach students the formal language of logic. Used in introductory logic courses at Indiana University (Philosophy 150), Stanford University (Philosophy 159), and other schools around the world, the program allows students to draw pictures of “worlds” and write logical statements about the worlds. A world consists of a chess board with small-, medium-, and large-sized objects resembling cubes, soccer balls, and pyramids. The computer can check to see if the sentence is true in the world depicted by asking questions about the relation between objects on the board. If a sentence is not true, the computer will play games with students to help them figure out where they made mistakes.
In Tarski’s World, students can learn the language of logic through direct use, instead of translating into and from English. The pictures keep students focused on the meaning of the symbols, not on the symbols themselves. Tarski’s World comes in two packages: one includes a textbook for a complete logic course; the other is designed as a supplement for courses using other texts.
The success of Tarski’s World inspired Barwise and Etchemendy to develop Hyperproof. Developed over a span of three years, Hyperproof is currently used in Philosophy 56, Stanford’s Introduction to Logic class. Each of two 25-student sections starts out using Tarski’s World, then continues into Hyperproof to introduce methods of proof. Hyperproof also combines formal sentences with pictures and allows the student to use both in giving proofs. It does not yet have a supplementary manual or textbook.
For all of their classes, students study either on their own Macintosh computers or in computer labs located throughout both campuses.
Barwise and Etchemendy plan to develop a textbook to go with Hyperproof. They also plan to develop new courseware. Their experience with the programs has convinced them that they need to explore a new area of logic—valid reasoning using diagrams. They want to design the program as a tool for analytical reasoning.
Barwise and Etchemendy envision programs that will help students solve complicated design and reasoning problems with logically valid methods that use both sentences and various kinds of diagrams.
For more information, contact Jon Barwise, Department of Philosophy, Indiana University, Bloomington, IN 47405; (812) 855-4795; Internet:
barwise@phil.indiana.edu; or contact John Etchemendy, Department of Philosophy, Stanford University, Stanford, CA 94305; (415) 723-2062; Internet: etch@russell.stanford.edu.
