First, let’s take a little test. Is the following true or false:
All Toyotas are cars.
Some cars are Porsches.
Therefore, some Toyotas are Porsches.
If you answered “false,” you’re right, though you might have trouble explaining exactly why you know it is wrong. This deliberately illogical example appears in the first chapter of a new electronic textbook for a course in logic created by Stanford computer science professor Michael Genesereth.
“There’s a clear need for people to think more clearly in modern life and they need the tools to do that,” Genesereth says. “Logic is one of those tools. And the need for it grows more important as these kids move on to college.”
To help students get prepared earlier in their academic careers, Genesereth is helping to introduce logic at select high schools in the Bay Area, including Palo Alto High School and Monta Vista High in Cupertino.
A fully fledged logic curriculum was once thought out of reach for high schoolers, but Genesereth has developed a different approach to teaching that makes logic much more accessible than traditional techniques.
People rarely have to prove things in real life, Genesereth says, but we use logic anyway. We use it in our work. We use it informally when we discuss politics, or solve a sudoku, or play a whodunit game like Clue.
“We all use logic, but we make up the techniques, and often, we get things wrong. As a result, we get incorrect results,” Genesereth says. “Logic can help us think more clearly.”
Genesereth’s approach begins with a new formulation of logic known as Herbrand semantics. Herbrand semantics is simpler and, therefore, easier to teach and to learn. Herbrand semantics makes the material more accessible and more relevant to everyone.
The traditional approach to teaching semantics is so complex that it is often not taught at all, and when it is introduced, it is usually in college or later. Contrary to past thinking, Genesereth believes that Herbrand semantics makes it possible to teach the fundamentals of logic in high schools.
The difference is twofold, says Chris Kuszmaul, a computer science teacher at Palo Alto High School, who offers a course based on Genesereth’s materials. The first is Genesereth has removed a layer of complexity designed for more advanced logics that is both confusing and unnecessary for high schoolers.
“I know Michael’s materials are easier because we are actually teaching high school kids, which no one has done before, because it was thought out of reach for these kids,” Kuszmaul says. “I feel a little like Neil Armstrong. We are on the frontier here.”
The second advantage, Kuszmaul says, is Genesereth himself: “Michael is a force. He’s one of the world’s great logicians and really passionate about helping people learn.”
Genesereth knows a trick or two about teaching logic. He has been teaching it to computer science students for 30 years. For the last decade he has been developing online course materials and, about four years ago, he began offering his course via massive open online courses – the so-called MOOCs – in which he might have 100,000 students at a time, ranging from teenagers to octogenarians.
“We’ve learned that they all seem to be able to learn logic. Our approaches work, so we have developed course materials aimed at high schoolers,” he says.
In dispensing with the complexity, Genesereth can explain the differences between various forms of reasoning and introduce the fundamental rules of reasoning, and teach this mental discipline to students who would not traditionally have had access to these thinking tools.
Ann Greyson teaches digital circuits at Castilleja School, an independent school for girls grades 6–12 in Palo Alto. She incorporated the first chapter of Genesereth’s textbook into her course. She sees potential for it as either a math or humanities elective for advanced students. Meanwhile, Debbie Frazier at Monta Vista, a public high school in Cupertino, has developed two new course outlines incorporating Genesereth’s logic material. The first is aimed at ninth-grade students as a way to analyze programs and algorithms. The second course, for advanced students, introduces logic to debug circuits and verify programs.
The study of logic goes back to Aristotle. It is among the oldest intellectual disciplines. The Greeks included logic as part of the trivium – literally, “the place where three roads meet” – that includes grammar, the study of the structure of language, and rhetoric, the study of persuasiveness. When combined, language, persuasiveness and logic converge at the place otherwise known as truth.
Over the centuries logic has been marginalized, but Genesereth argues that it is far from esoteric. It is quite useful – perhaps even fundamental – in our everyday lives. Hence, the effort to infuse the subject earlier in students’ educational careers. Stanford is among just a handful of schools to teach it as a fundamental of computer programming, Genesereth says. Logic at most colleges is more likely in philosophy or mathematics departments.
While the language of computer science is logic, logic’s usefulness reaches from STEM disciplines to the liberal arts, such as English, where students can use logic to recognize fallacies in written material.
Logic has gotten short shrift, Genesereth insists, compared to calculus, which is commonly taught in high schools. Calculus is great and necessary if you’re a physicist, he says, but it’s not so useful for computer science.
“Calculus is the language and the mathematics of physics, and we teach that to a lot of high schoolers. But logic is the language and mathematics of computer science, and so far we haven’t tried to teach logic to young people who may be future computer programmers.”
“Logic is a lot more accessible than calculus, and is more broadly valuable, yet we don’t teach it,” he says. “Why is that?”
Though Genesereth’s new course is being test driven at just a handful of local high schools today, there are plans to add more in the near future. Long term, Genesereth has big plans.
“We’d like to make this available to every school in the country in the next decade,” he says. “I think it’s doable, but more importantly, I think it’s necessary.”
This work was supported by Infosys Foundation USA.