## Lively Logician 1 & 2 - Logic Courses at The Lukeion Project

Logic is the foundation of the certainty of all the knowledge we acquire.” Leonhard Euler

Pure mathematics is, in its way, the poetry of logical ideas.” Albert Einstein

Logic is the basis for all clear thinking and writing. The ability to think logically about terms, statements and arguments underpins all of science and mathematics as well as philosophy. It important in all academic subjects. It is also essential for participation in civic life. There is no substitute for being able to understand arguments, refute them, and build better arguments. A firm foundation in the basic principles of Logic prepares students to build on this foundation throughout their lives.

Why study Logic at the Lukeion Project

The formal principles of the logic date to Aristotle, who systematized and made formal much of the work of his predecessors including Plato and the Sophists. Logic has typically been a foundation of the liberal arts education and as such, is a natural addition to Lukeion’s curriculum.

Logic is a natural addition to the middle school collection at the Lukeion project. Rigorous thinking complements the analysis in Barbarian Diagrammarian and Witty Wordsmith, as well as the reading in Muse and the construction of papers in Skillful Scribbler. Logic is useful for more advanced students as well. As students progress, logical thinking is essential for translation in classical languages as well as the study of history and philosophy.

Categorical logic begins with Aristotle’s “Three acts of the mind.” The first act, understanding, relates to how we define terms, and whether the definitions are vague or precise. The second act relates terms in propositions which can be true or false. We discuss how statements are related to each other through equivalence, implication, or consistency. Finally, we discuss the third act of the mind, arguments. We discuss how to analyze syllogisms for validity and soundness, as well as how to create our own valid arguments. We end with a chance to evaluate three pieces of logic from real life---literature, news, popular culture, rental agreements, and so on---using the techniques we have studied all semester.

Propositional logic, although developed in antiquity, was rediscovered in the 1800s by philosophers and mathematicians who desired to put mathematical discovery on a firmer foundation. It gained new importance with the advent of computers which integrated logical operators with electricity to create circuits and programs. Propositional logic and its methods form the basis for all modern mathematics and computing. We begin with exploring basic propositions and how they can be combined to form complex propositions and arguments. We then discuss how to find the truth values of these propositions using truth tables (longer and shorter), formal logical proofs (similar to the two-column proofs from geometry) and truth trees. At the end of the semester students have a final and a final project where they will use three of the methods introduced to analyze a single argument from literature or popular culture.

Through the exercises and efforts (even the difficulties) that are taken in the pre-teen and early teen ages, one's personal reasoning develops. An introduction of first order logic into one's education can ensure lifelong logical skills. Entry into the cognitive stage known as the "logic stage" is the time to learn how to think logically. Age 14 is a good average age for the development. Some will be ready earlier, others should wait. Your student is ready to start building his or her logic skills when he or she first develops interests in games that require logic (chess, for example) and shows interest in discussions that follow logical progressions. A student currently enrolled in pre-algebra or algebra 1 should do just fine in these classes.

Essential to logic is the ability to read closely for meaning. For example, although they sound similar, these two propositions have very dissimilar meanings: “The study of logic is necessary for success in academic pursuits,” or “The study of logic is sufficient for success in academic pursuits.”

A familiarity with symbols and abstract reasoning is key for these classes. We will be using generic symbols such as “All S are M” rather than specific terms as we evaluate propositions and arguments. For this reason, a good start in algebra or at least pre-algebra is useful.

Students should be able to organize their time and studies for learning a reasonable amount of vocabulary and techniques each week. Younger students may need help with keeping up with deadlines and their studies each week: this course builds on each week, and falling behind can snowball into significant difficulties.

As with mathematics, the only way to learn logic is to practice the techniques, strategies and definitions in logic. Every week we have guided class sessions where the instructor introduces new ideas and allows students time to practice and make mistakes. The instructor provides guided notes instead of a textbook, so students can actively follow along and complete the instructive exercises during class. There are plenty of samples with answers for practice, as well as weekly homework exercises and bi-weekly quizzes. The course finishes with a comprehensive final and a “Logic in Real Life” project where students apply their knowledge of logical principles to arguments and statements found “in the wild,” so to speak.

Meeting times both semesters: Wed 11:30 am ET

Instructor: Dr. Kim Johnson

Why study Logic at the Lukeion Project

The formal principles of the logic date to Aristotle, who systematized and made formal much of the work of his predecessors including Plato and the Sophists. Logic has typically been a foundation of the liberal arts education and as such, is a natural addition to Lukeion’s curriculum.

Logic is a natural addition to the middle school collection at the Lukeion project. Rigorous thinking complements the analysis in Barbarian Diagrammarian and Witty Wordsmith, as well as the reading in Muse and the construction of papers in Skillful Scribbler. Logic is useful for more advanced students as well. As students progress, logical thinking is essential for translation in classical languages as well as the study of history and philosophy.

**Lively Logician 1: Categorical Logic**Categorical logic begins with Aristotle’s “Three acts of the mind.” The first act, understanding, relates to how we define terms, and whether the definitions are vague or precise. The second act relates terms in propositions which can be true or false. We discuss how statements are related to each other through equivalence, implication, or consistency. Finally, we discuss the third act of the mind, arguments. We discuss how to analyze syllogisms for validity and soundness, as well as how to create our own valid arguments. We end with a chance to evaluate three pieces of logic from real life---literature, news, popular culture, rental agreements, and so on---using the techniques we have studied all semester.

**Lively Logician 2: Propositional Logic**Propositional logic, although developed in antiquity, was rediscovered in the 1800s by philosophers and mathematicians who desired to put mathematical discovery on a firmer foundation. It gained new importance with the advent of computers which integrated logical operators with electricity to create circuits and programs. Propositional logic and its methods form the basis for all modern mathematics and computing. We begin with exploring basic propositions and how they can be combined to form complex propositions and arguments. We then discuss how to find the truth values of these propositions using truth tables (longer and shorter), formal logical proofs (similar to the two-column proofs from geometry) and truth trees. At the end of the semester students have a final and a final project where they will use three of the methods introduced to analyze a single argument from literature or popular culture.

When to take Logic at the Lukeion Project?When to take Logic at the Lukeion Project?

Through the exercises and efforts (even the difficulties) that are taken in the pre-teen and early teen ages, one's personal reasoning develops. An introduction of first order logic into one's education can ensure lifelong logical skills. Entry into the cognitive stage known as the "logic stage" is the time to learn how to think logically. Age 14 is a good average age for the development. Some will be ready earlier, others should wait. Your student is ready to start building his or her logic skills when he or she first develops interests in games that require logic (chess, for example) and shows interest in discussions that follow logical progressions. A student currently enrolled in pre-algebra or algebra 1 should do just fine in these classes.

Essential to logic is the ability to read closely for meaning. For example, although they sound similar, these two propositions have very dissimilar meanings: “The study of logic is necessary for success in academic pursuits,” or “The study of logic is sufficient for success in academic pursuits.”

A familiarity with symbols and abstract reasoning is key for these classes. We will be using generic symbols such as “All S are M” rather than specific terms as we evaluate propositions and arguments. For this reason, a good start in algebra or at least pre-algebra is useful.

Students should be able to organize their time and studies for learning a reasonable amount of vocabulary and techniques each week. Younger students may need help with keeping up with deadlines and their studies each week: this course builds on each week, and falling behind can snowball into significant difficulties.

What to expect when studying logic at the Lukeion Project?What to expect when studying logic at the Lukeion Project?

As with mathematics, the only way to learn logic is to practice the techniques, strategies and definitions in logic. Every week we have guided class sessions where the instructor introduces new ideas and allows students time to practice and make mistakes. The instructor provides guided notes instead of a textbook, so students can actively follow along and complete the instructive exercises during class. There are plenty of samples with answers for practice, as well as weekly homework exercises and bi-weekly quizzes. The course finishes with a comprehensive final and a “Logic in Real Life” project where students apply their knowledge of logical principles to arguments and statements found “in the wild,” so to speak.

Meeting times both semesters: Wed 11:30 am ET

Instructor: Dr. Kim Johnson

Logic is the beginning of wisdom, not the end.” Leonard Nimoy

Logic is the anatomy of thought.” John Locke