Short Little Lessons in Logic: Statements




Lesson 3: Statements

What you’ll learn in this lesson:

  • The semantic and syntactic structure of premises and conclusions
  • What a declarative statement is
  • How declarative statements are used in logic

In a previous lesson, we learned that arguments form the basis of logical analysis and they’re what we use to convince others that something is true. We also learned that logical arguments are made up of premises (the reasons given), a conclusion (the idea you want to show is true), and a logical relation. In this lesson and the next lesson, we’re going to look at two important concepts that will help us better understand the syntactic and semantic nature of the parts of an argument. By ‘syntactic’ I mean how the grammar or the structure or form of the argument functions. By ‘semantic’ I’m referring to how the elements of the argument function in the understanding of the person making and hearing the argument. This may sound a bit technical but I’ll explain these ideas more clearly in this and the following lessons.

Statements and Logic

As we’ve seen, in formal logic, the person making the argument uses the premises and the conclusion to make truth claims. That is, the person intends to state things that are true or probably are true (arguments present facts that represent the way the world is or might be). As we’ll see in a later lesson, it’s not always important that you know up front whether the claims are actually true only that the intention of the person presenting the argument is to make truth claims. Because of this, all claims in logic take the grammatical form of declarative statements or just statements.

The examples we use in these lessons are in English but the principles apply to any language that can declare or state that something is true in the mind of the person hearing the language. Since language is symbolic—it points to something else as we’ll see in the next few lessons—the language could be something as simple as Morse code.

The Oxford English Dictionary defines ‘declare’ as a type of action: "to assert, proclaim, announce or pronounce by formal statement or in solemn terms". In other words, a statement is just making an assertion that the world is a specific way at a specific time. We’ll define a logical statement then as:

a claim made in some language (a sentence) that asserts that something is true or possibly true.

Here are some examples:

  • The total land area of Australia is approximately 2.97 million square miles
  • Objects fall to the earth in a vacuum at 9.8 meters per second squared
  • Sigmund Freud was born in London
  • The coffee has been on the counter for 15 minutes so it probably is cold

Each of these statements declares that something is true. The first two statements actually are true and the third statement is false (Freud was born in the town of Freiberg in the Czech Republic). The fourth statement declares that something most likely is true but could be false.

Other Types of Sentences

When constructing arguments in logic only declarative sentences can be used. The way to test whether you can use a particular sentence in logic is to ask whether it possibly could be true or false. If your answer is ‘no’ then it can’t be used for your premises or conclusion. If it can be true or false, then it’s permitted in your premises and your conclusion. Here are some examples of other types of English sentences that can’t be used for premises or conclusions in logic:

  1. Questions or interrogatives: "What day of the week is this?"
  2. Commands or imperatives: "Bring me some water!"
  3. Exclamations or exclamatory: "Wow!"
  4. Performatives: "I solemnly vow"

We now have a better understanding of the syntactic nature of premises and conclusions in logical arguments. Later on in the course, we’ll study more about syntax and how it relates to constructing arguments. Next, we’ll need to look at the semantics of premises and conclusions. The semantics or "meaning" of a declarative statement is essential to understanding how the logical relation works and will help us analyze arguments. But first, we need to spend some time on this concept of ‘truth value.’ We’ll turn to that in the next lesson and then move on to learning about semantics.

Try this quick review to test your understanding.

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