Consequences  (IF/THEN)

Consequences (IF/THEN)

No doubt, your parents and grandparents talk to you about consequences.  If you make this decision, this other thing will be the consequence, or result, of your action.  Did you know that you won’t be your best at figuring out the consequences of ideas or actions until you’re 24?  We’re learning so much about the brain, that we’ve found out that the brain’s ability to make inferences does not fully mature until the age of 24.
That means you are just over half way old enough to getting really good at making inferences, but you are faced with figuring out the consequences of actions and ideas all of the time… including on the SHSAT!  On the exam, inferences most often show up in two ways:  questions will ask you to figure out what the consequence of a view will be, and questions will ask you to organize a paragraph’s sentences to make the most sense. (Pro Tip!  Inferences are called logical sequence, because they have a logical structure that’s built around the order of things happening.)  You might be given a passage that includes a lot of data or historical facts, and then you have to figure out the consequence of what would happen if some person responded to those facts in a particular way.  Or, you might be given a passage in which each sentence is numbered, and you’ll have to tell the writers where the best place for sentence 3 is.
We’re going to practice both kinds of logical sequencing.  Right now, we’ll focus on what we mean by IF/THEN statements, and how to figure out the right answers.
SHSAT writers *love* IF/THEN questions!  Here’s one example, from a practice test:  “Which of the following would have been the most likely result if the candidates had not debated on television in 1960?”  Another way to say the question is, “If the candidates had not debated on television in 1960, then FILL IN THE BLANK would have most likely resulted.”  You will see these throughout the ELA part of the exam.  Are there general tips about answering IF/THEN questions?
There are two main things to keep in mind when you do IF/THEN questions:  1. Look at the relationship between what is said in the first part—the if part—and what is suggested as the consequence—the then part. 2. Know that if your if part is true, then the consequence has to occur.  If you find out that the consequence cannot occur, you know that the whole IF/THEN statement or argument is false.  Here’s more.

The IF/THEN Relationship

In an IF/THEN statement (and argument), the “if” statement sets up what can be true later.  When I say, “If you prepare for the SHSAT, you will perform better than if you didn’t,” I’m saying there is a relationship between your prep for the SHSAT and how well you do on the exam.  Whether the relationship is true depends on whether the IF leads to the THEN.
But, IF/THEN statements are actually pretty fun, because you can figure out whether they lead to good arguments if they follow two types of math-like equations.  These equations are super easy.  Learning them will not only help you do better on the exam—they’ll help you win arguments in every day life!  Here’s why:  if an argument follows one of these two types, they will always be a strong argument.  You’ve already looked at ways that arguments can go wrong (see “Big, Ugly, Hairy, Wrong Fallacies”).  It makes sense to do yourself a favor and see how reasoning works well.

Version 1, MP

We’ll call Version 1 of these always strong arguments IF/THEN arguments MP.  (Pro-Tip:  this stands for modus ponens.)  Just like the Pythagorean Theorem works to prove the side of any triangle, any argument that follows an MP form will be a strong argument.  Here’s Version 1’s form:

  1. If this is true, then that must occur.
  2. This is true.
  3. Then, that must occur.

You might not believe this, but any argument that follows an MP form is a strong argument.  You can fill in any content for “this” and “that”, and it will be a strong argument.  Here’s some examples that make complete sense:

  1. If you get good sleep, you will feel rested.
  2. You got 8 solid hours last night.
  3. Of course, you feel great!

And, another:

  1. If Superman touches Kryptonite, he loses his powers.
  2. Lex Luther thrusts Kryptonite onto Superman’s chest.
  3. Superman passes out, completely weak.

How about one last one?

  1. Whenever Beyonce produces her next album, I’m buying it!
  2. The news just reported she is putting out an album in July.
  3. I am going to be buying a Beyonce record in July.

What all of these arguments have in common isn’t that they are in fact true—it’s that all of their conclusions (all given in the #3 sentences) are guaranteed by what comes with their #1 and #2 reasons.  The relationship in #1 says that “IF something happens, THEN another thing will happen”.  And, then #2 says something factual—that something happens!  There is only one thing we can conclude with the #1 and #2, and that is what is listed in the conclusion.
Remember, any argument that has MP’s form is a strong argument.  That means that these arguments are also strong:

  1. If Lucky Charms loses its marshmallows, treble clefs will bottom out.
  2. Sofie ate all of the Lucky Charms marshmallows.
  3. The treble clefs bottomed out.

As well as:

  1. When the cow jumps over the moon, the little dog laughs.
  2. The cow jumps over the moon.
  3. The little dog laughs.

And try:

  1. If Dinglehoppers sniff jumbleweeds, musclekrays snorkel with kresselbums.
  2. Dinglehoppers love to sniff jumbleweeds.
  3. Musclekrays snorkel with kresselbums.

Just as in the original three examples, each of these follow the MP form, and are strong arguments.  What makes them strong?  Their conclusions (#3) are guaranteed by their reasons.  That might seem weird, since they don’t actually make sense.  But, what makes them strong arguments is that they are guaranteed.
This means that even strong arguments might not be the best arguments for IF/THEN statements.  The relationship between the IF and the THEN should be true.  In the first set of arguments, the IF/THEN relationships are true:  it is true that you feel rested if you get good sleep, that Superman loses his powers when there is Kryptonite, and that I will buy the next Beyonce record when it’s cut.  In the second set, there isn’t a true relationship between the IF and the THEN:  it doesn’t make sense to say that treble clefs bottom out, little dogs laugh, and musclekrays snorkel with kresselbums.  So, even guaranteed arguments need truth to be the best arguments.
Make sure that you aren’t duped by a.) arguments that don’t have the right form and b.) arguments that have the right form but aren’t actually true.

Version 2:  MT

When we have IF/THEN statements, there is one more argument form that is always strong, but also require truth to be good arguments.  We’re calling Version 2 MT arguments (Pro-Tip, we call this modus tollens).  MT arguments all have this form:

  1. If this is true, then that must occur.
  2. That does not
  3. Then, that cannot

We only have two things we can say about any IF/THEN statement.  It’s either going to be true that the “if” thing is true, or that the “if” thing is not true. That’s it.  We can’t say more—the thing is either true or not.  In MP arguments, we learn that the thing is true in the #2 sentence, and the result has to be that the consequence stated in #1 is stated.  In MT arguments, we learn that the consequence could not occur, and so our conclusion has to be that the “if” does not occur.  Here’s an example:

  1. If you eat the pizza, you will need the soda.
  2. You don’t need the soda.
  3. You didn’t eat the pizza.

This is a strong argument!  The conclusion (#3) is guaranteed by #1 and #2.  So, for IF/THEN arguments, we can say in #2 either that the thing does occur, or that the consequence didn’t occur.  (Any other option is not a strong argument.)  Just as in MP arguments, we want the best arguments, which require a true relationship between the “IF” and the “THEN” in the argument.  If the relationship in #1 is not true, then we need to steer clear of thinking that the argument will be true.