Welcome to part one of our lesson on necessary assumption questions. In this video we'll talk about how we identify a necessary assumption question and how we distinguish it from a sufficient assumption question. We'll also examine in detail exactly what a necessary assumption is. And we'll talk about a technique that we can use to help identify necessary assumptions. Read full transcript
In part two of the lesson, we'll work through some real examples of necessary assumption questions on the onset. Let's start with how we identify a necessary assumption question. Go ahead and take a look at these question steps. Notice that the words highlighted in red here all mean the same thing as needs. The argument depends on assuming that the argument relies on something.
This language is the tell-tale sign of a necessary assumption question, because these prompts are all asking us for something that the argument needs to assume, for something that the argument needs to be true in order for the argument to work. Now it's important to distinguish this kind of question from another kind of assumption question called a sufficient assumption, and that's something that we will cover in a separate video.
In a sufficient assumption question, we're looking for an answer that if true, would guarantee the conclusion, but in a necessary assumption question, we're just looking for an answer that needs to be true in order for the argument to work. So for example, if the argument is premise, I'm about to eat a dish with broccoli conclusion, therefore I'm not going to like the taste. A sufficient assumption would be something like I dislike the taste of all vegetables or I dislike the taste of any vegetable.
That would be something that would be enough to prove that I'm not gonna like this dish with broccoli. But it's not necessary because the argument was just about broccoli. I just have to dislike the taste of broccoli, I don't need to dislike the taste of all vegetables. That's why it can be important to distinguish between necessary assumption questions and sufficient assumption questions.
And to that end, let's take a look at some sufficient assumption question stems. These stems are examples of sufficient assumption questions. And notice that they don't use the same language of requires needs, depends on that you saw in necessary assumption questions stem. So if you're having trouble distinguishing between necessary assumptions and sufficient assumptions, keep this idea in mind.
Necessary assumption question stems will never have the phrase, if which one of the following is assumed. Now that we know how to identify one of these questions, let's talk about exactly what a necessary assumption is. On the onset, a necessary assumption of an argument is a statement that must be true in order for the conclusion to follow logically from its premises.
Another way to think about it is a necessary assumption of an argument is something that the author of the argument, the person who is giving you the argument had to be thinking on the way towards reaching their conclusion. It's something that they believed was true but just forgot to explicitly say it. Here's an example argument to help us understand what a necessary assumption is. The premise is this candy bar costs only $5 and the conclusion is therefore Timmy can afford to purchase it.
Let's examine whether the following ideas are statements that must be true in order for this argument to make sense. The first one is Timmy has at least $5, is that something that his argument must assume? It does seem like the argument has to assume that because, if Timmy didn't have at least $5, then how can we say that he can afford to purchase it?
So in order to say that he can afford to purchase it, it must be true that he has at least $5. This is a necessary assumption. What about this statement? Timmy has at least $1, is it something that the argument needs to assume in order for its conclusion to follow?
The answer is yes, because if he didn't have at least $1 then there's no way that he'd be able to afford this $5 candy bar. So when the author of this argument was trying to conclude that Timmy can afford this candy bar., the author must have been thinking that Timmy had at least $1. So this statement is also a necessary assumption. Now notice that the statement that Timmy has at least $1 is not enough to actually prove that he can, afford to purchase the candy bar.
That's because he would need at least 5, not just at least 1. But even though it's not sufficient to make the conclusion follow, it is still something that the argument had to believe was true. Another way to think about it is it's not the complete assumption. The complete assumption is that Timmy has at least $5 but it is part of what the argument is assuming, which is why it's necessary for the argument to assume it.
What about this statement Timmy has $10, does this have to be true in order for the conclusion to follow from the premise? No, it doesn't have to be true at all because even if he didn't have $10, he could have $9, or $8, or 7, or 6. He just needs to have at least $5 in order for this argument to work, he doesn't need to have $10.
So this is not a necessary assumption. How about this statement. Timmy has exactly $5, does this have to be true in order for the conclusion to follow from the premise? Not exactly, it doesn't have to be true, because Timmy doesn't need to have exactly $5.
It's okay if Timmy has $6 or $7 or 550. Any number that's 5 or above would be enough for him to afford the candy bar. So he doesn't need to have exactly $5 and that's why this statement is not necessary. Let's go a little bit deeper into necessary assumptions. So we know that a necessary assumption is something that must be true in order for the conclusion to follow from the premise, but it can help on the onset to think about necessary assumptions as falling into two different categories.
There are some necessary assumptions that bridge a gap between the premise and the conclusion. And they are others that block an objection to an argument. Here's another example to help us explore this idea. The premises, everyone I see outside is using an umbrella, and the conclusion is thus, it must be raining.
Do you notice that there's a gap here between the idea of using an umbrella and seeing people use an umbrella, and the claim that it must be raining. It doesn't necessarily have to be true that it's raining just because you see people using an umbrella. So here's an assumption that bridges the gap between the premise and the conclusion.
If everyone I see outside is using an umbrella, then it must be raining. This is something that the author must be thinking is true because they offered you this premise in support of the conclusion. They are thinking that if that premise is true, that's going to be enough to prove the conclusion. Here's another assumption that you can think of as involving a bridge between the premise and the conclusion.
Whether people are using an umbrella is a sign that it is raining. That's something that must be true in order for this argument to make sense, because the premise is about seeing people use an umbrella. And the author clearly believes that that is something that proves it must be raining. Or in other words, that is something that is a sure sign that it is raining.
These two statements are examples of ideas that seem to link the premise to the conclusion, or in other words to make the premise more relevant to the conclusion. And it's a common form of necessary assumption on the outset. But there's another kind of assumption that this argument is making and it's one that blocks a potential objection.
Consider this statement, the people using umbrellas are not using them for protection from the sun. This is something that must be true in order for the argument to make sense, because the author is assuming that the umbrellas have something to do with the rain, that the umbrellas are assigned that it must be raining. If the umbrellas are actually being used for something else besides rain, then this argument wouldn't make sense.
So this statement is blocking the objection, what if the umbrellas are being used for the sun? It's saying no, the umbrellas are not being used for the sun. Up until now in this lesson, we haven't really been using any specific technique to determine whether a statement is actually necessary or not. But I'm about to share with you an awesome technique that can really help us figure out when something is necessary.
The technique is just negate it, negate the answer, negate the statement, that is gonna help us figure out what's necessary. Now by negating an answer, I mean to consider what it means for that statement to be false. If you negate a necessary assumption, or in other words, think about what it means for that necessary assumption to be false, then the arguments won't make sense anymore.
After all, if that idea was actually necessary for the argument, then taking away that idea will mean the argument shouldn't work. Think about necessary assumptions as the legs of a table. If you take one of those legs away, then the table will be unbalanced and it'll fall over. Similarly, if you take away a necessary assumption, or in other words, if you negate it, if you falsify it, then the conclusion won't follow from the premises anymore, the argument will fall apart.
But if a statement is actually not necessary to an argument, then if you negate that statement, the argument can still stand, the conclusion can still follow from the premises. Let's go back to our prior example argument to see how negation actually works in action. So remember the premises, everyone I see outside is using an umbrella.
The conclusion is, thus, it must be raining. Here's our first bridging assumption, if everyone I see outside is using an umbrella, then it must be raining. Let's see why this is necessary. What happens if we negate this idea? What if it was the case that even if everyone outside is using an umbrella, it might not be raining.
Well if it might not be raining despite everyone using an umbrella outside, then how could this conclusion that it must be raining makes sense? It doesn't have to be raining anymore. So because the negation of this statement means that the conclusion doesn't follow from the premise, that's what tells us this statement is a necessary assumption. What about our other bridging example, whether people are using an umbrella is a sign that it is raining.
What if this idea were not true, what would happen to the argument? What if whether people are using an umbrella is actually not a sign that it is raining? Well, in that case, what does the fact that you see people outside using an umbrella have to do with whether it's raining. If it's not a sign of it being raining, then the conclusion doesn't follow anymore.
So because the negation of this statement means a conclusion doesn't follow, that's what proves that statement is a necessary assumption. And this technique also works with our blocking assumption. The people using umbrellas are not using them for protection from the sun. Well, let's say this statement were not true, what if the people outside are using umbrellas for protection from the sun.
If that were true, then we can no longer say that it must be raining because the umbrellas could be used for something else, it could be used for the sun. So again because the negation of this statement would make the conclusion no longer follow from the premise, that's what proves this statement is necessary. Let's use this technique on some other statements. Let's figure out whether these are necessary assumptions.
The first statement is the people using an umbrella knew that it would rain today. Go ahead and think about this on your own, is this necessary? Let's go ahead and try negating this idea, what if this were not true? What if the people using an umbrella did not know that it would rain today? Does that mean this argument doesn't work anymore? Not quite because even if they didn't know that it would rain, it still could be the case that once they saw that it was raining, they went ahead and got an umbrella.
So this argument doesn't need to assume that people knew it was gonna rain, just that once they saw it raining, that had something to do with them getting the umbrella. Because the negation of the statement does not make the argument fall apart, it is not a necessary assumption. What about this one, the people outside are wearing clothes that are wet.
Is this necessary for the argument to work? Well, it's negated. What if the people outside are not wearing clothes that are wet? What if their clothes is dry? But that doesn't do anything to the argument because maybe the umbrellas are protecting them from the rain.
Maybe the umbrellas are helping to keep their clothes dry. The argument doesn't need to assume that in order for it to be raining, clothes has to be wet. So because the negation of this idea doesn't ruin the link between the premise and the conclusion, it's not a necessary assumption. And finally, let's consider this statement, umbrellas are the most effective tool for protecting oneself from rain.
Does that have to be true for this argument to work? Again, let's apply the negation test, what if umbrellas are not the most effective tool for protecting oneself from rain? Does that mean that this argument doesn't work? Well, even if umbrellas are the second most effective tool, or the third most effective, or the fourth most effective, people could still be using the umbrella to protect themselves from rain.
Maybe they didn't use the best method, but they are using a method. So because the negation of this idea doesn't make the argument fall apart, it is not a necessary assumption. I hope you can see from these examples how negating a statement is a really powerful technique for determining what an argument actually depends on. And what's not truly irrelevant to the logic of an argument?
If you practice this technique, you'll get a lot better on necessary assumption questions, and it's something that we'll use together on some examples. So that brings us to our strategy for necessary assumption questions. Let's follow these three steps whenever we're faced with this kind of problem. Step 1, identify the conclusion and premises. This is the first step of any argument based question, it is critical for us to understand what the main point of the author is, the conclusion, and what are the supporting statements of the premises.
Step 2, prephrase. And what this means for necessary assumption questions is that we should start by thinking about why the conclusion doesn't have to be true, even if the premises are true. There's always gonna be some kind of gap, something missing between the premises and the conclusion.
And it always helps to think about that gap to identify what's missing to help us identify the assumption. Now one question that we can ask to help us think about that gap is whether there is any concept shift between the premises and the conclusion. If there is some concept in the conclusion that's totally new or in other word, that was not brought up in the premises, then that means there's a clear concept shift going on.
So if you think back to our rain and umbrella example, the conclusion was it must be raining but the idea of rain was nowhere in the premise. So there was a concept shift between seeing people use an umbrella and it being raining outside. Here's another question that can help us figure out what the gap in an argument is. Are there objections to the conclusion that need to be countered?
So again, in that rain and umbrella argument, the conclusion was it must be raining and the premise was, people are using umbrellas. But if you can think about why people might be using an umbrella besides for rain, then that is an objection to the conclusion that would need to be countered. Then that objection was maybe they were using it for the son.
After we prephrased, we'll move on to step 3, evaluate the answer choices. Pick the answer choice that must be true in order for the arguments logic to make sense. Now remember, you can always negate it. If you negate the answer and the argument falls apart, then that means it is a necessary assumption, it actually was required for the argument to work.
But if you negate an answer and it doesn't destroy the argument, it doesn't weaken the link between the premise and the conclusion, and that means that statement was not necessary for the argument to work. We're gonna follow these three steps on some real logical reasoning problems in part two of necessary assumptions.