Conditional reasoning – argumentation based on “if…then” statements – is a prominent feature of the LSAT. While the numbers vary from test to test and year to year, you can expect something in the neighborhood of 10 questions in the Logical Reasoning sections that involve conditional reasoning, and at least half of the Logic Games will employ it as well. Some games (typically undefined or partially defined grouping games) will be entirely conditional, with every single rule setting up an if…then statement (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.). In short, while conditional reasoning is not the be-all and end-all of the LSAT, it is a subject that should be mastered if you want to do well on the test, and it therefore deserves attention and practice.

The good news is that, at its core, conditional reasoning is as simple as falling off a log!

Imagine you are a lumberjack, and it’s time for the annual lumberjack games. There will be contests for chainsaw carving, pole climbing, speed trials for cutting down trees, beard contests, plaid wool shirt contests, etc. I have no idea, really, what happens at lumberjack games, if such things even exist, but go with me on this, will you? One of the events at my imaginary lumberjack festival would be log rolling. Contestants go out into the middle of a lake, and they stand on a floating log, and they try to remain standing the longest. Of course, the log won’t stay still, so it starts to roll in the water, and the lumberjack (that’s you!) walks on the log as it rolls in a way that he stays 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!

(Those words – 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, and we won’t go 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.)

There are two conditions in this claim about you and your precarious situation on the log. One condition is “fall off”, which 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? Maybe the guy who came in second swims over and pushes you off (which, for our purposes, is not the same as you falling off)? 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. 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 I 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.

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.

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

That, my friends, demonstrates the basic rules of conditional reasoning, and it’s as easy as falling off a log! 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. For more advanced help, keep an eye on this blog for my next post, and of course check out the Logical Reasoning Bible and our course materials.

Photo “Midwest Log-Rolling Championship 06-29-2013 075-2” courtesy of Richard Hurd.

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