Welcome! My name is Gary Curtis, and this course is an introduction to the basic concepts and terminology of logic. What is logic? Logic is the science of reasoning. It is the science that studies how one reasons correctly and incorrectly.
True and False
Let’s start by learning how to identify statements, which are the building blocks of logic.
The primary purpose of reasoning is to determine what is true and false. Sentences that are true and false are called “statements.” A statement is a whole sentence or a clause within a sentence that is either true or false.
Example: “It is raining.”
This is a sentence that is either true or false—that is, either it’s raining now or it’s not. Therefore, this is a statement. If it is raining, then the statement is true. If it’s not raining, then it’s false.
Statements contrast with other types of sentences, such as questions and commands. The distinguishing feature is whether the sentence is true or false, as neither questions nor commands are true or false.
• “Who gave the Gettysburg Address?”
This is a question. It is neither true nor false, so it is not a statement.
• “Don’t touch me!”
This is a command. It is not true or false, so it is not a statement.
Reasoning is constructed out of statements, so the first skill you need to learn is how to recognize statements and how to tell them from non-statements. Practice this skill with the following examples, each of which is a sentence taken from Lewis Carroll’s Alice in Wonderland.
• “The first witness was the Hatter.”
Either the first witness was the Hatter or it wasn’t, so this sentence is true or false, which makes it a statement.
• “Do cats eat bats?”
This is a question, so it’s not a statement.
• “One of the jurors had a pencil that squeaked.”
Either the juror’s pencil squeaked or it didn’t, so this is a statement.
• “Off with her head!”
This is a command rather than a statement.
• “‘Take off your hat,’ the King said to the Hatter.”
This example is a little trickier than the previous ones. Either the King said this or he didn’t, so this is true or false, which means it’s a statement. Of course, what the King said—namely, “Take off your hat”—is a command, but the whole sentence is a statement.
• “‘But what did the Dormouse say?’ one of the jury asked.”
Like the previous example, the whole sentence is a statement, but what the juror asked is a question.
• “You’re nothing but a pack of cards!”
This is a tricky example. Don’t let the exclamation point fool you. It’s not a command but an emphatic statement.
• The miserable Hatter dropped his teacup and bread-and-butter, and went down on one knee.
This is another tricky example. It’s a single sentence that makes two statements connected by the word “and.” The two statements are:
1. The miserable Hatter dropped his teacup and bread-and-butter.
2. [The Hatter] went down on one knee.
Don’t assume that every statement must be a complete grammatical sentence ending with a period, because sometimes sentences make two or more statements.
Remember: Ask yourself whether a sentence or clause of a sentence is true or false. If it is, then it’s a statement. If not, then it’s probably a question or command, but it’s not a statement.
By now, you may have noticed that I’ve made many statements in this lesson. I’ve also asked a few questions and issued a few commands. As an exercise, you might want to go back over the lesson and pick out the statements I’ve made—hopefully, I haven’t made any false ones!—as well as the questions and commands. Learning logic requires practice! (That’s an emphatic, true statement.)
Tomorrow, you’ll learn what to do with statements, specifically, how to use them to build the fundamental unit of reasoning: the argument.
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