What Is an Inference?

The reading sections on both the ACT and SAT and the science section on the ACT require students to draw inferences.  In fact, inference problems often make up some of the hardest problems on the test.  We devote quite a bit of time in our curriculum book to inferences, and we do so for good reason: we believe this is an area where students can see some real improvement.

One thing I’ve noticed, however, is that many students aren’t entirely clear on what an inference actually is.  Many times, students think an inference is simply what they think of when reading or hearing something else.  That isn’t true, and I want to help some students out with this pesky topic in this post.

Inferences and Implications

Before we dive too deeply, let’s get some insight from The Office:

Michael Scott probably isn’t the only one who gets mixed up on the meaning of “inference” and “implication.”  Inferences and implications are two sides of the same coin.  Implications are made by a given piece of information, and an inference is what you draw from that information.  Imagine I told you that Max is the tallest kid in 5th grade, and that Max is 5′ tall.  We could correctly say several things:

• The fact that Max is 5′ tall and is the tallest kid in 5th grade implies that no kid in 5th grade is taller than 5′.
• We can infer that no kid in 5th grade is taller than 5′.

That’s what I mean when I say implications and inferences are two sides of the same coin: the content is the same, but implications deal with what statements or pieces of information provide, whereas inferences deal with what the listener does with that statement or information.

Inferences are Logical

Many students erroneously believe an inference to be anything that pops into their mind after hearing something.  “Mr. Turner is a tough teacher” might imply “Don’t take Mr. Turner” or “Bears can kill people” might imply “Don’t go into the woods.”  Of course, none of these are valid inferences.  Inferences need to be the logical conclusion of a given piece of information.  If a given statement is true, then its implication must be true.  It isn’t simply what we think about when we hear something.  It is instead something that logically must be true if what we hear is true.  There may still be some very good reasons to take Mr. Turner or to go into the woods, even if those two facts about bears and Mr. Turner are true. so those aren’t valid inferences.

Examples

Below are some examples of valid and invalid inferences and their corresponding statement:

Statement: Exercise is an important part of health.

Valid Inference: A good health plan should include exercise.

Invalid Inference: Running a marathon is better for one’s health than running a 5k.

Exercise being an important part of health at least implies that a good health plan should include some form of exercise, but it doesn’t imply anything about which types of exercise are better than others.  To arrive at that conclusion, we are inputting some of our own beliefs about exercise, and that means we are no longer just drawing inferences.

Statement: All mammals have hair.

Valid Inference: Since animal X is a mammal, animal X has hair.

Invalid Inference: Since animal Y has hair, animal Y is a mammal.

This might have seemed a bit tricky, and it’s a common logical error I see students make.  In this example, having hair is a necessary but not sufficient trait for being a mammal.  In other words, all mammals must have hair, but having hair alone isn’t necessarily enough to qualify as a mammal.  Therefore, if we know a given animal is a mammal, we know it must have hair because having hair is a necessary part of being a mammal.  On the other hand, simply knowing that a given animal has hair is not, based on the information here, enough to know it is a mammal.

To clarify that last one, let me change it around a bit:

Statement: All clowns have hair

Valid Inference: Since Bozo is a clown, Bozo must have hair.

Invalid Inference: Since my friend Jeff has hair, Jeff must be a clown.

Summary

Inferences are a big part of both the SAT and ACT, but inferences are more than what we think of when hearing something.  They are logical conclusions that can be drawn based on the information given.  For an inference to be valid, it must be true if the information we are hearing is true.

This is an area we spend a lot of time practicing in with students.  Because a lot of students don’t utilize these sorts of logic skills in school, it’s often an area where big score improvements can happen!