Conditional Logic = Rules (Part 1)

Understanding Conditional Statements and Their Structure

At its core, an “if-then” statement is a type of logical proposition that connects two ideas.  A simple way of thinking about these statements is to think of them as rules that are made up of two primary components: the ‘if’ part and the ‘then’ part.  The “if” part of the statement is called the ‘antecedent’ or the ‘sufficient condition’. The ‘then’ part is known as the ‘consequent’, or the ‘necessary condition’.  For example, consider the statement: “If it rains, then the ground will be wet.” Here, “it rains” is the antecedent, and “the ground will be wet” is the consequent.

A sufficient condition is one that, when met, ensures the consequent will follow. Think of it as a trigger that activates the result. In the example above, if you know that it rained then you also know that the ground is wet.  When you’re dealing with a true rule then if the rule applies to a specific situation then you know what else is true.  In other words, if we know that the rule is true and we know that the antecedent is true then that is SUFFICIENT for us to know that the consequent has to be true. 

A necessary condition is one that must be true if the antecedent leads to the consequent. So we know that the ground being wet NECESSARILY has to be true if that conditional statement above is true (if it’s a true rule) and the sufficient condition is true (the rule has been activated). But by itself, it doesn’t guarantee the consequent.  If all we know is that the necessary condition is true (the ground’s wet) but we don’t know if the sufficient is true, then we can’t say anything about the sufficient.  In other words, it’s a requirement but not a trigger.     But, it’s really important to be aware of the one-way flow of logic from the antecedent to the consequent. If it rains, the ground will definitely be wet. However, the reverse isn’t necessarily true; a wet ground doesn’t always mean it has rained.

Logical Connection Between Conditions

Ok, so we’ve got the structure of a conditional statement; but we also need to be clear on what we’ll be doing with them on the test.  Essentially, like I said above, a conditional statement is a rule – and that makes sense because the law is all about rules.  Laws themselves are rules, but in addition to that you also have rules about how to make rules, rules about how to make inferences from precedents, etc.  In other words, rule-based reasoning is really important for the legal profession, and the LSAT tests your understanding of it.  There are two fundamental dimensions of rule-based reasoning that this test will test you on: the ability to evaluate a rule to determine if it’s a good rule and the ability to make valid inferences/spot invalid inferences on the basis of a good rule plus additional information.

Determining the validity of a conditional statement is crucial. A statement is logically valid if its structure ensures that the consequent follows from the antecedent. In other words, and more simply, you can’t have the ‘if’ part without having the ‘then’ part.  For example, if we are trying to evaluate the statement ‘if you study for the LSAT then you will do well on the LSAT’ we need to see if we can come up with a situation where we apply that rule (so we find someone who studied) but the consequence doesn’t hold (they didn’t do well).  If you can do that then it’s not a valid conditional statement, if you can’t then it’s valid.  There will be certain question types on the test such as the weaken, strengthen, etc questions where your goal is to evaluate the conditional statements.

But there will be plenty of situations where the validity of the statement is not in question – so, for example, the rules in a game, or a Must Be True question in the arguments.  In those situations your job is to make an inference or evaluate the inference made from a conditional statement plus additional information.  There are two ways in which you can make a valid inference from a conditional statement plus additional information: if you’re told that the ‘if’ part is true then you know that the ‘then’ part is also true, and if you’re told that that the ‘then’ part is not true then you know that the ‘if’ part also isn’t true.

If we accept our conditional statement above as true (so we’re now in LSAT-land where everyone who studies does well) and we also know that our buddy John is studying for the LSAT, then since that makes the ‘if’ part true we can also conclude that the ‘then’ part is true as well – John is going to do well on the LSAT.  Likewise, if John tells us that he didn’t do well then we additionally know that he couldn’t have possibly studied.

However, keep in mind the directionality – ‘if’ leads to ‘then’ but not vice-versa.  The difficulty with most students is that in everyday speech we tend to use it so that you can go in both directions.  But not on the LSAT!  That’s how they’ll try and trick you.  So, if you see the conditional above and it’s given as valid, and then they say that John did well on the LSAT – YOU CAN’T SAY ANYTHING!  Keep in mind that this is just different from everyday usage.  Likewise, if you don’t have the ‘if’ part then you don’t know anything about the ‘then’ part.  If we’re told that John didn’t study for the LSAT – YOU CAN’T SAY ANYTHING!  Once again, this is different from everyday usage.  A good way to remember it is to think about where you live.  If you’re in Manhattan then you’re in NYC.  But someone that’s in NYC isn’t necessarily in Manhattan and someone not in Manhattan isn’t necessarily not in NYC.  It’s this more restricted usage that is the technically correct usage that you’ll find on the test.

Identifying Common Conditional Indicators

Understanding how “if-then” reasoning works is part of the equation. You also need to be able to identify conditional statements since they can appear in various ways.  To identify them, you’ll need to identify certain key words that usually signal their presence.

If

• “If” is the primary indicator of the sufficient condition in an “if-then” statement. When you encounter this word on the LSAT, pay close attention to the conditions being set.
• “Whenever” and “when” serve the same function as “if,” setting up a condition for the consequent to follow. For example, “When it rains, the grass gets wet.”
• The word “any” can indicate an inclusive condition. “Any person caught stealing will be prosecuted.”
• “In order to” also signals a sufficient condition, and sometimes you’ll find it shortened to ‘to’.

Then

• “Then” is often used to indicate the consequent, though it’s not always explicitly stated.
• “Only” is also often used to indicate the necessary condition.
• “Only if/when” is also common and most students are confused by it because of the ‘if’ but keep in mind that it’s NOT a sufficiency-indicator but a necessity-indicator.

Unless

“Unless” is another word to watch for. It complicates the conditional logic by introducing an exception to the sufficient condition. For example, “You will fail unless you study,” translates to “If you do not study, then you will fail.”  Whenever you see “unless” replace it with “if not”.

Conclusion

Keep in mind that the easiest way to understand what a conditional is, is to think of it as a rule. The antecedent, or sufficient condition, tells you when the rule is activated and the consequent, or necessary condition, tells you what the outcome is. But keep in mind that the directionality only goes from sufficient to necessary.

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