Using Circuits to Answer Inference Questions
When the LSAT asks you to make an inference, what does that really mean?
A inference is in essence a main conclusion for a set of premises. That’s it!
In the case of “valid inference” or “must be true,” the question is telling you that the inference you are making is a fully valid one that is supported, as our previous ones were, with both facts about its subject and rules that warrant its claim.
Deductive circuits can serve as the model for our inference circuits. The difference is that in the inference circuit the correct answer will sit at the top as our conclusion, and the information from the stimulus will make up the Minor and Major Premises. You job will be to analyze and organize those statements from the stimulus and figure out what the implied conclusion is.
Let's do an example together.
All employees at TechCorp who receive specialized training are eligible for promotions. Some employees at TechCorp are not eligible for a promotion.
As we discussed above, there is no conclusion in this stimulus. Rather it is our job to come up with one. So, let’s put an empty set of purple boxes at the top of our diagram, one for the Subject and one for the Predicate Claim.
We shade it green because it will eventually become our correct answer.
Now, let’s analyze the statements we DO have with the aim of being charitable about what the author of this stimulus was TRYING to communicate to us.
All employees at TechCorp who receive specialized training are eligible for promotions.
This reads like a rule or general principle: a concept that could be applied once we know about that an employee of TechCorp did in fact receive that training. I’m going to assume that this is my Major Premise and put it on the right:
Hopefully our other premise is a fact-based statement that can serve as our Minor Premise. Let’s take a look:
Some employees at TechCorp are not eligible for a promotion.
Whew! This is what we were looking for, some information about the TechCorp employees. So that can go on the left:
So are we all set? Do we have a sense of what the author is trying to tell us?
Not really.
The problem we have is that the Minor Premise doesn’t trigger the Major Premise. Remember, you can only invoke a rule if the antecedent (the “if” clause) is true; otherwise, you don’t really know anything from that rule. And in this case, the rule’s antecedent is “receive special training” and the fact we have doesn’t tell us that.
What recourse do we have? We can do what I call “rule hunting.”
We can only infer based on what we know, and right now all we know is that there are “some employees who are not eligible for a promotion.” So, we look to adapt our rule to fit our needs. And this is where knowing how to take a contrapositive becomes SO handy.
Original Major Premise: All employees at TechCorp who receive specialized training are eligible for promotions.
Contrapositive: Employees at TechCorp who are NOT eligible for promotions HAVE NOT received specialized training.
(notice how we have switched the order of the statements and also negated them in bold)
Since the contrapositive is the logical equivalent of the original Major Premise, we can insert it into the circuit. And since our rule in the contrapositive has an antecedent that matches our fact, we can now connect them!
We are now at the point where we can affirmatively predict what the author has implied. We simply place the subject of our Minor Premise in our Conclusion Subject box and the consequent of our Major Premise and put it in the Conclusion Predicate box:
As in past questions, the correct answer may not look exactly like what we’ve predicted'; the later in the section, the more likely that the item writer has rewritten it to be a synonymous or logically equivalent statement. Some examples of potential correct answers include:
Not all employees at TechCorp have received specialized training
At least one employee at TechCorp has not received specialized training.
It is not the case that all employees at TechCorp have received specialized training.
There exists at least one TechCorp employee who has not undergone specialized training.
Not all Inference questions will be as direct as this one. Sometimes there will be multiple rules to connect together, like this:
All animals with hair are mammals, and any mammal produces milk for its young. The leopard gecko does not nurse its young.
In this stimulus, there are two rules, and they work together, the consequent of one triggering the antecedent of the other. You can see the way they link together below:
There are others in which there are two rules, but only one of them is applicable to the facts. Take this one for example:
If a battery is long-lasting, then it is suitable for use in portable devices. If a battery is suitable for use in portable devices, then it can be used in medical equipment. None of the batteries produced by Zeta Power are suitable for use in portable devices.
In this case, the first rule, in its contrapositive, can be applied to our facts. The second ends up simply being a red herring and leads nowhere. Because we know neither about any batteries that ARE suitable for use in portable devices nor about those that CANNOT be used in medical equipment, the rule does nothing for us. So our circuit looks like this:
You can see that unused rule doesn’t lead to anything, and that’s OK! In questions like these, there is no requirement that every premise will be involved. Your job is to find what MUST be true. In the next lesson, we will talk about other stimuli in which your job will be to determine what is reasonable but not validly deducible.