Logic in Secondary Education
Michael Genesereth and Vinay Chaudhri
Computer Science Department
Logic is one of the oldest intellectual disciplines in human history. It dates back to Aristotle. It has been studied through the centuries by people like Leibniz, Boole, Russell, Turing, and many others. And it is still a subject of active investigation today.
We use Logic in just about everything we do. We use it in our professional discussions. We use it in our personal conversations. We use the language of Logic to state observations, to define concepts, and to formalize theories. We use logical reasoning to derive conclusions from these bits of information. We use logical proofs to convince others of our conclusions.
Logic is essential for many STEM disciplines, especially computer science. We know that calculus is important to physics, and we teach is at the high school level. Well, logic is the language of computer science and computer science is arguably getting to be as important as physics.
More broadly though, Logic is useful for everyone. It is more relatable than traditional quantitative math for many students, students who see qualitative relationships between people and things but who are uncomfortable making everything quantitative, i.e. reducing everything to numbers. And it is useful in everyday life. Advertisers, politicians, companies, organizations, friends, family, and experts want us to buy their products, vote for them, or support what they believe and want to do. Logic helps us spot the hype, the nonsense, who is wrong and who is right.
And we are not alone! Logic is increasingly being used by computers - to prove mathematical theorems, to validate engineering designs, to diagnose failures, to encode and analyze laws and regulations and business rules. Logic is also becoming more common at the interface between man and machine, in "logic-enabled" computer systems, where users can view and edit logical sentences. And Logic is sometimes used not just by users in communicating with computer systems but by software engineers in building those systems (using a programming methodology known as logic programming).
The importance of Logic in our lives raises the question of how we come by the ability to use Logic. To some extent, it is innate, like our ability to recognize faces. However, some elements of Logic need to be taught explicitly, in the same way that we teach algebra. And this raises the question of how and when this education should take place.
The ancient Greeks thought it sufficiently important that Logic was one of the three subjects in the Greek Trivium, along with Grammar and Rhetoric. Oddly, this is not the case in the American educational system. Logic occupies a relatively small place in the modern curriculum.
Admittedly, some elements of logic do appear in secondary school courses today, e.g. elementary proofs in geometry, discussions of fallacies in writing courses, and of course tips and techniques for using search engines and other computer systems. However, Logic is not taught as a standalone topic in most secondary schools today. Imagine saying we do not need to teach arithmetic because some of the elements are covered in chemistry and history.
It is our belief that logic is important enough to deserve treatment as a standalone topic There is easily enough material for a standalone course. Topics in Boolean Logic include logical connectives (e.g. and, or, not), contrapositives, converses, inverses, de Morgan's Laws, counterfactual statements, truth tables, and propositional proofs. Topics in Relational Logic include variables and quantifiers, model checking, and relational proofs. More general topics include negation as failure (knowing not versus not knowing), the differences between consistency and entailment and equivalence, and fallacies and paradoxes.
In summary, we believe that whether to teach logic high school is not really a point of debate, and we need to make this education available in high schools all across America. Logic has to be and must be taught to all students if we want to prepare responsible citizens. A logically literate populace will know how to ask the right questions of their leaders, how to spot fallacies, and most importantly, how to make decisions that truly align with their values. Logically fluent citizenry is not really an option for any functional democracy, and there is so much at stake in thinking systematically, that training for it must be included in the curriculum and cannot be left to chance. With a background in logic, the students will be well-prepared for careers in STEM that are so critical for any country to be competitive in the modern day world. The goal of making logic education available across the country may sound formidable, but is achievable, by mobilizing the students and parents to demand for it, and empowering our high school teachers to teach it.