Conditional Logic = Rules (Part 2)

Causation

Conditional statements often express causal relationships. For instance, “If you expose iron to oxygen and water, it will rust.” Here, the antecedent identifies the cause, and the consequent specifies the effect.  It can also be reversed, “If there’s rust on the piece of iron then it must have been exposed to oxygen and water.” 

Obligations/Proposals/Permissions

“If-then” statements can also express obligations and permissions. “If you are drafted, then you have to join the army.” The antecedent sets a condition, and the consequent establishes an obligation.  A variation is when a proposal is made – the difference is that proposals are generally not an obligation, look for the word ‘should’.  Likewise, conditional statements can establish permissions. “If you have a ticket, then you may enter the theater.” Here, having a ticket is the condition that permits the action described in the consequent.

Constitutive Reasoning

“If-then” statements can also establish when something counts as something else. For instance, “If a person is born in the United States, then they are a U.S. citizen.” Here, the antecedent specifies the conditions that constitute the consequent.  Think of definitions/categorizations/etc.

Hypotheticals

Look out for hypothetical situations or assumptions that set up a conditional relationship.

More broadly, when you come across language that suggests something is either required or a guarantee for something else to happen, you’re likely dealing with conditional reasoning. For example, “A high GPA is necessary for law school admission,” or “Passing the bar exam is sufficient for practicing law.”  Additionally, certain statements may not use the typical conditional indicators but are inherently conditional because they express sufficiency and necessity. For instance, “A leads to B,” or “C is dependent on D.”

Contrapositives

In addition to standard conditional statements, there’s also something called a ‘contrapositive’.  This is an inference that can be made from any conditional statement that you’re given and that can be very useful in situations that come up on the test.  It’s basically the same conditional relationship, the same statement, but looked at from a different perspective.

In the context of conditional statements, a contrapositive is essentially the flipped and negated version of an original “if-then” statement. If the original statement is “If A, then B,” the contrapositive would be “If not B, then not A.”  Every single conditional statement can be made into a contrapositive of itself.  The definition of a conditional statement is that the ‘if’ part can’t happen without the ‘then’ part.  You can look at that from two different perspectives:

1. If you have the ‘if’ then you have to have the ‘then’.
2. If you don’t have the ‘then’ then you can’t have the ‘if’.

To get the contrapositive you simply flip and negate the two conditions. First, negate the antecedent. If the original statement is “If it rains, the grass gets wet,” the antecedent (“it rains”) becomes “it does not rain.” Then, negate the consequent. In our example, “the grass gets wet” turns into “the grass does not get wet.” Finally, switch them around: “If the grass does not get wet then it didn’t rain.”

The benefit of transforming a conditional statement into a contrapositive is that it will be easier to recognize deductions and inferences.  Specifically, if you’re also told that the necessary condition is not true then you can see very simply that the sufficient can’t be true either if you’ve written out the contrapositive.  This is most useful in the games section but also in the arguments, and for specific question types in particular.

Analyzing Conditional Chains and Their Logical Implications

Understanding how multiple conditional statements interact is crucial for complex logical reasoning situations. In many LSAT questions, you’ll find a sequence of “if-then” statements, each dependent on the other, making a conditional chain.

Transitivity

Transitivity is what allows us to infer a direct relationship between the first and last elements in a chain of conditionals. If “If A, then B” and “If B, then C” are true, then it’s also true that “If A, then C.” Chaining multiple conditionals together can often lead to useful insights and for some questions will be the whole point of your analysis. In particular, games rules will often have multiple conditionals in them and if you chain them together you’ll be able to see what follows much more easily. 

Additionally, you will often have to recognize what the missing links in the chain are (this is more common in the arguments section).  Let’s say you have any argument that says: “If you study, you’ll do well on the LSAT, and if you do well on the LSAT you’ll get into a good law school, therefore, if you study you will get a high-paying job when you graduate.”  There’s a missing link, the high-paying job condition comes out of nowhere – but if we add “if you get into a good law school then you’ll get a high-paying job” we now see how the premises get us to the conclusion.  And you can also incorporate contrapositives – “if you didn’t get a high-paying job then you didn’t go to a good law school” works just as well for the argument above.

Common Mistakes and Misconceptions in Conditional Reasoning

One of the most common mistakes is overlooking the language that signals a conditional relationship.  Words like “if,” “unless,” and “when” are often the easiest and quickest way of identifying conditional statements. You need to train yourself to spot them and then immediately establish the appropriate conditional framework to analyze what’s going on.  Similarly to overlooking the indicators, it’s also common for students to mix them up – particularly ‘only if’ for ‘if’.  Make sure to memorize the common indicators and be accurate in identifying what they signal.

Related to overlooking the conditional indicators is when a student doesn’t pay attention to the common situations where you might find conditionals.  Remember to be on the lookout for causality, obligation/permissions/proposals, hypotheticals, and constitutive relationships.

But probably the most common problem students of mine have had is that the direction in which a conditional statement flows is often a source of confusion, leading to frequent mistakes.

Confusing Necessary and Sufficient

False Reversal

A common mistake is reversing the antecedent and the consequent and assuming the statement still holds. For instance, if “if it rains, the ground gets wet,” it’s incorrect to assume “if the ground is wet, it has rained.” This is known as a false reversal.  In other words, just because the necessary is true doesn’t mean that the sufficient is also true.

False Negation

Another error is incorrectly negating both the antecedent and the consequent. For example, from “if it rains, the ground gets wet,” you can’t deduce “if it doesn’t rain, the ground won’t get wet.”  Just because the sufficient is false doesn’t mean that the necessary is false.

As mentioned before, the root of this confusion is that we use conditional reasoning in a more expanded way in real life – when our parents said “if you do your chores you can go play with your friends” they weren’t simply giving us a condition that is sufficient for us to go play with our friends.  They were making an implied threat.  “If you DON’T do your chores then you won’t be allowed to go play with your friends.”  This is incorrect from the point of view of the LSAT, but we’ve heard something like this so often that it’s lays the groundwork for the confusion.  A good way to keep in mind the proper conditional relationship is to remember two things:

1. When you’re trying to make a deduction on the basis of the conditional and additional information, DON’T look at both sides of the conditional.  Most students will look to see if either the sufficient or necessary is true and then whatever is true of one of them is true of the other.  That’s incorrect.  What you should do is train yourself to just look at the left-hand side.  The sufficient is important, don’t look at the necessary.  But you have to remember to write out the contrapositive so that you also see if the negative of the necessary is true (that’s the sufficient in the contrapositive, so just look at the sufficient once again).
2. Remember the example of where you’re from: If you’re from NYC that means you’re from the US, but that doesn’t mean that if you’re from the US then you’re from NYC.  And it also doesn’t mean that if you’re not from NYC then you’re not from the US.

It’s important to be aware of these common conditional reasoning mistakes since they’re exactly how the test will try and trick you.

Conclusion

In addition to having a good understanding of the fundamentals of conditional reasoning it’s also important to be aware of the more complex ways in which it will appear on the test. Contrapositives are key, conditional chains will appear in specific situations, and DON’T BE TRICKED BY FALSE REVERSALS OR NEGATIONS.

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