Short Little Lessons in Logic: More on Statements




Lesson 7: More on Statements

What you’ll learn in this lesson:

  • How to write statements
  • More on the relationship between statements and propositions
  • An introduction to operators

When constructing arguments, we’ve learned that premises and the conclusion should be declarative statements (if you haven’t studied the previous lesson on statements, it may help to review that lesson before studying this one). In this lesson, we’ll get more specific about how to write those statements so they function properly in a formal argument. We want to make sure the terms in each of the statements we make relates to other terms in the right way; our statements need to have a specific structure so this relationship is easier to analyze.

Simple statements

Remembering that a statement declares that something is true, a simple statement is one which makes a single truth claim. Simple statements are simple grammatically as well. They typically have one subject, a verb, and an object (in English grammar). Consider these examples:

  • Joe is at the office
  • Philippa is driving
  • Megan eats lunch

Each statement declares something, and only one thing, is true. In the real world, things tend not to be so simple and we generally make claims about a lot of things all at once or combine our truth claims into longer sentences. When writing and analyzing logical arguments, it’s good practice to break complex ideas down into simple ones so you can sort out how many truth claims are being made. For example:

Statement A: When I was at the store, I saw Aidan and he was buying soup. So I walked over and picked up some soup and we chatting for about five minutes.

How many truth claims are in this sentence? Let’s take a look:

  1. I was at the store
  2. I saw Aidan
  3. Aidan was buying soup
  4. I walked over to Aidan
  5. I picked up some soup
  6. We chatted for five minutes

A sentence like statement A can be fairly common in regular conversation and you may not be aware of all the things you’re claiming to be true when you make such a statement but there is a lot going on in that sentence! The person who writes or speaks that sentence has made six truth claims and when analyzing an argument, it’s necessary to break longer statements down into separate, simple statements so it’s clearer how many truth claims are being made. While this may need to be a conscious effort when you’re first starting out, with practice, you’ll learn to pick out truth claims almost automatically—they start "jumping out" at you.

In a complex statement like Statement A above, some of the individual simple statements may be true and some may be false. The truth value of the whole statement will be a function of the truth value of the individual simple statements (we’ll learn more about this in future lessons). This is why it’s important to find all the simple statements. If we don’t know the truth value of the individual statements, we can’t determine the value of the complex statement as a whole. Complex statements like Statement A are called compound statements in logic and there are ways to write compound statements so the simple statements are easier to see. In logic, writing compound statements in a particular way is essential for being able to analyze them for truth value.

Compound Statements

Compound statements are simple statements joined together using statement operators. When you see a statement like Statement A, you want to identify the simple statements similar to the way we did it above: write them out as simple, complete sentences. Once you have the simple statements identified, you can rewrite the compound statement using the simple statements and the operators you need to retain the original meaning of the statement. Two operators we use in logic are AND and OR. There are others and we’ll look more closely at operators in a future lesson. For now, it’s important to note that in logical statements, all compound statements need to be simple statements joined by operators. The reason for this will be more clear as we progress.

Let’s take another look at Statement A. Since this statement is made up multiple simple statements, we can be assured it’s a compound statement. But as it’s written, it needs some work to "prepare it" for use in a logical argument. Even though it’s a compound statement, it’s missing some operators so we’d have to rewrite it to include those operators. For this example, we can use a single operator to join each of the simple statements—the AND operator. Here’s how it would look re-written with our operators:

Statement B: I was at the store AND I saw Aidan AND he was buying soup AND I walked over to Aidan AND I picked up some soup AND we chatting for about five minutes.

This statement doesn’t read as well as Statement A but it is formatted properly for use in an argument (notice too that I called this Statement B as a matter of convention to distinguish it from Statement A since it’s a different statement though both point to or symbolize the same proposition ). We removed all the punctuation and made sure all the simple statements were joined to other simple statements using an operator. Since there are six simple statements, we should have five operators and that’s what we see in Statement B: there are five "and" operators.

So here’s a quick review of the relationships between all the components of a logical argument that we’ve studied so far:

  • A statement expresses a proposition in some symbolic language. If I wanted to declare that a person named Bob is at home, I could use the sentence "Bob is home" to state that truth. But I also could use the statement "Bob is at his place of residence" or "Bob is at 123 Maple Lane where he lives" or "The house where Bob lives is where his is right now". All three communicate the same proposition but use a different sentence or statement to do it (and one communicates it more clearly and simply than the others).
  • Statements can be simple or compound.
  • Premises and conclusions are made up of these specific declarative statements.
  • Arguments are premises and conclusions in a specific structure.

In the next few lessons, we’ll learn more about argument structure, how to symbolize arguments to see their structure more clearly, and what operators we can use to create compound statements.

Here’s a short video that explains the concepts from this lesson and walks through how to create a compound statement from simple statements.

Module quiz

Test your knowledge of the concepts in lessons 1-6 by taking this quiz. This is just an opportunity to evaluate your knowledge and how you’re learning. You can take the quiz as many times as you’d like by refreshing the page. Try to take the entire quiz without hints or showing the answers first. Once you get your score, take the quiz again and show the hints or answers on the questions you missed so you can review the material.

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