# Short Little Lessons in Philosophy: Logic

Welcome to Short Little Lessons in Philosophy. We’re happy you’re here and we’re looking forward to learning with you. The Short Little Lessons collection is designed to teach you philosophy in bite-sized lessons that you can do anywhere as you have time. This series covers the very basics of formal logic—the fundamental discipline for sound reasoning that applies not only to doing philosophy but to other areas of study and to living a better life.

For each lesson, you can provide feedback or participate in a discussion about the lesson using the discussion forum at the bottom of each page. You will need to sign up for a free Disqus account in order to do this. Disqus is widely used across the web and is a reliable and rich forum tool so we encourage you to sign up if you don’t have an account and participate in the conversation. Learning is best done by interacting with others and some of the best learning happens when you help others. If you see a question and have a good way of explaining a concept, please participate and offer your ideas.

Below is the outline and description for the course. Lessons without a link have not been published yet so check back regularly for updates.

## Course Outline

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Module 1: Introduction and Foundations

#### 1. The Science of Logic

In this lesson, we introduce formal logic and how it can be used to help us become better thinkers. In it, we claim that there is a right way to organize our thoughts and logic is the tool that helps us do this. You’ll learn the definition of logic and some important terms that will help set you up for success in the rest of the course. Go to the lesson

#### 2. Arguments

Learn what an argument is and how it functions in logic. You’ll learn the three parts of an argument and we’ll introduce you to the building blocks of sound reasoning. We promise we won’t yell at you and say mean things. Go to the lesson

#### 3. Statements

To build arguments, we need to use very specific types of sentences. This helps our arguments to have the right structure so they’re, well, logical. This lesson talks about those sentences and sets the stage for determining what is true and what isn’t. Go to the lesson

#### 4. Truth Value

While logical analysis has a lot to do with the structure of arguments, knowing what is true and false is an important part of a good argument as well. In this lesson, you’ll learn what to do when you don’t know whether a claim is true or false as well as the role truth plays in logic. Go to the lesson

#### 5. Propositions

What is the difference between a numeral 7 and a number 7? What about the difference between syntax and semantics? Do you know what a symbol really does? Find out in this lesson and learn what these topics have to do with logical analysis. Go to the lesson

#### 6. More on Propositions

In the previous lesson, we learned a little metaphysics as a foundation for understanding how propositions work. In this lesson, we apply those concepts to better understand how propositions relate to statements in logic. We also refine our concept of truth value. Go to the lesson

#### 7. More on Statements

To close out this module, we’ll revisit the idea of statements and you’ll start to learn how to construct arguments. We’ll take the foundational idea of a statement and specify it a bit more so we can use statements to build the premises and conclusion of an argument. With the lessons you’ve learned in this module, you’ll be ready to start building arguments which we’ll cover in Module 2! Go to the lesson

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Module 2: Symbolizing Arguments and Using Operators

#### 8. Symbolization

With the background we built in Module 1, we begin Module 2 by looking how to replace simple statements with variables to isolate the form of an argument and separate form from truth value. This provides a foundation for the two-step process we’ll use to both analyze and construct deductive arguments. Go to the lesson

#### 9. Operators

In previous lessons we learned that simple statements are joined by operators to construct compound statements. In this lesson, you’ll learn more about how operators work and why using them properly is essential for building the correct logical relations between the terms in an argument. Go to the lesson

#### 10. The Conjunction and Disjunction Operators

The first two of our four operators. Each operator has an impact on the truth value of a compound statement and in this lesson, you’ll learn how to use these operators and how to understand the truth value of the whole compound statement relative to the truth value of the individual simple statements that make them up. Go to the lesson

#### 11. Negation and Conditional Operators

The negation operator is the only ‘monadic’ operator in the bunch. You’ll learn what that means and how to use negation with other operators. The conditional is a special operator that is both a little more complicated to understand but also very powerful. You’ll learn how to construct conditionals and what each part of the conditional communicates about truth value. Go to the lesson

#### 12. Truth Function

The type of logic we’ve been studying is called “truth-functional” logic. In this lesson, we’ll learn more about what that term means and how understanding truth function can help us better analyze truth value. Go to the lesson

#### 13. Operator of the Largest Scope

Before we leave this module, we need to look at one final concept involving operators. We’ll use the concept of ‘operator of the largest scope’ when we study truth tables in a future module and it will help us as we study deductive arguments in the next module. Go to the lesson

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Module 3: Deductive Arguments

Coming soon!

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Module 4: Inductive Arguments

Coming soon!

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Module 5: Truth Tables

Coming soon!

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Module 6: Categorical Logic

Coming soon!

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Module 7: Informal Logic

Coming soon!