Conditional Reasoning 101: As Easy as Falling Off a Log

Conditional reasoning is argumentation based on “if…then” statements and it is a prominent feature of the LSAT. While the numbers vary from test to test, year to year, you can expect around 10 questions in a single LR section that involve conditional reasoning. You’ll also see that at least half of the Logic Games will employ it as well. Some games will be entirely conditional, with every single rule setting up an if/then statement. For example, if R is on the committee, X is also on the committee; if W is not on the committee, S is on the committee, etc. Typically these will be the undefined or partially defined grouping games.

In short, while conditional reasoning is not the be-all and end-all of the LSAT, you need to master it in order to do well on the test. So, it goes without saying that it deserves attention and practice.

As Simple As Falling Off a Log

Imagine you are a lumberjack and it’s time for the annual lumberjack games. There will be chain saw carving contests, speed trials for cutting down trees, beard beauty contests, etc. Does this actually exist? Who knows, but stick with us on this. One of the events at this imaginary lumberjack festival is be log rolling. Contestants go out into the middle of a lake and stand on a floating log. They then try to remain on that log as long as they can. Of course, the log won’t stay still, so it starts to roll in the water. You walk on the log as it rolls in a way that allows you to stay on top instead of being rolled off into the lake. If you fall off your log, then you end up in the water.

IF you fall off your log, THEN you end up in the water.

There it is, folks! Conditional reasoning! As a note, if and then are not the only ones that indicate conditional reasoning. Other words like when, only, any, all, unless, must, and many more will clue you in to its presence. We aren’t going into all of those here. You can find more about the classic indicators in a lot of our published materials like our course books and the Logical Reasoning Bible. For now, we’ll stick with the basic ones used here.

Examine the Conditions

There are two conditions in this claim about you and your precarious situation on the log. One condition is “fall off” and is introduced by the word “if”. We call that condition a Sufficient Condition. The presence of a Sufficient Condition indicates that another condition, the Necessary Condition, must also be present. In our claim, the Necessary Condition is “end up in the water”. In other words, falling of the log guarantees (is sufficient for proving) that you will end up in the water. Falling in the water is necessary. We can diagram that claim this way:

FOL (Fall Off Log) → IW (In Water)

Now, let’s think about a few things you might do at the lumberjack games. We already know what happens if you fall off the log in the log rolling contest. But what happens if you do not fall off that log? What if you win the contest? Do we know whether you end up in the water or not? Actually, no, we don’t know anything about that.

Maybe after you are declared the winner, you jump off the log and splash around in celebration?
Perhaps the guy who came in second swims over and pushes you off! For our purposes, is not the same as you falling off.
Or, maybe you decide to dive in and swim back to shore?

Any of these things could happen. NOT falling off the log proves nothing about you ending up in the water. The absence of the Sufficient Condition tells us nothing about the absence or presence of the Necessary Condition.

Mistake Negation

If you jumped to the conclusion that if you did not fall off the log, you did not end up in the water, you made what we call a Mistaken Negation. The absence of the Sufficient Condition proves nothing about the absence of presence of the Necessary Condition. We can diagram that error like this:

FOL → IW

This is always bad logic. As we just demonstrated, you cannot prove this to be true. Could it be true? Sure! It’s entirely possible that you did not fall of the log and you did not end up in the water. The point is that we can’t prove that you didn’t end up in the water just because you didn’t fall off the log.

Mistake Reversal

So what if you end up in the water? That’s the Necessary Condition occurring. What do we know about whether you fell off the log? Again, nothing that we can prove. Maybe you fell (the Sufficient Condition occurred), but maybe you jumped, or dove, or were pushed, etc. If you know that you ended up in the water and you conclude that you must have fallen off the log, you made a Mistaken Reversal. You assumed that the presence of the Necessary Condition guaranteed the presence of the Sufficient Condition. That flaw has a diagram that looks like this:

IW → FOL

That’s always bad logic, too. It’s possible, but not provable.

The Contrapositive

Finally, what if you do not end up in the water, but remain high and dry? That is, what if the Necessary Condition never happens? Then there is something we can prove! We know, absolutely, that you did not fall off the log. The absence of the Necessary Condition proves the absence of the Sufficient Condition. That’s what we call the Contrapositive of the original claim, and we diagram it by reversing the order of the terms and negating them both, as follows:

IW → FOL

There You Have It!

And that demonstrates the basic rules of conditional reasoning. Things can get more complex when you add more conditions, and when some of the terms are negative and some are positive, and there are plenty of ways that the authors of the test can cloud the issue, but with this as your starting point you are well on the way to mastering this crucial type of reasoning and increasing your score on the LSAT. If you want to continue with some Conditional Reasoning 101, check out these blogs: