FALLIBLE FOX

Kinds of Arguments (Arguments & Claims Part 3)

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Distinguishing two basic types of argument is foundational to your ability to evaluate arguments. The two types are referred to as deductive and inductive arguments. Note that there is a lot of confusing information out there about the nature of deductive and inductive reasoning, how the two differ from each other, and how they're used in science. While you're getting acquainted with types of arguments, I suggest avoiding internet searches for information on deductive and inductive reasoning—instead, as your introduction to the topic, stick to this section and the links to outside resources that can be found in this section. Specifically, I recommend the link found here—it will give you another good introduction to deductive and inductive arguments.

 

Spend some time with this topic—it's won't be easy at first! In particular, there's some difficult terminology here, so it'll take time to get things straight.

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To foreshadow where we're going here, we'll start with deductive arguments and break down what makes for valid (vs. invalid) and sound (vs. unsound) deductive arguments. We'll then move on to inductive arguments and develop an understanding of what makes for strong (vs. weak) and cogent (vs. uncogent) inductive arguments. See—lots of terms!

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Deductive arguments

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In deductive arguments the author intends to prove their conclusion using inescapable logic. That is, it's the author's intention for the conclusion to follow by necessity from the premises. The intention part is key here—there is a such thing as poor deductive arguments, in which, even though the author intends for the conclusion to follow from true premises, either the logic doesn't quite work and/or the there are flaws in the premises. We'll get there shortly, but first let's pin down the basic nature of the deductive argument. Here are some examples of deductive arguments:

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All people are mortal (premise 1)

Kanye West is a person (premise 2)

Therefore, Kanye West is mortal (conclusion)

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Halifax is in Canada. (premise 1)

I am in Halifax. (premise 2)

Therefore, I am in Canada (conclusion)
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In the above examples, you can see that if we accept the premises as true (regardless of whether they are true), the logic is—and is intended by the author to be—inescapable. In other words, in the above arguments, if the premises are true, the conclusion must follow. There's no way around it. 

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The two above arguments take the form of a syllogism, which is generally represented in three lines, with two premises and a conclusion. However, deductive arguments need not be in this form. You can learn more about different types of syllogisms, with several examples, here.

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Try this: based on the basic description above, are the following deductive arguments?

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When Jim goes to bed late, he has time to watch a full movie.

Last night, Jim went to bed late.

Therefore, last night Jim had time to watch a full movie.

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This year, 95% of the Halloween candy in my neighbourhood is chocolate.

My son and daughter collected their candy exclusively in my neighbourhood.

Therefore, most of of the candy my kids collected is chocolate.

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Both of the above arguments have two premises and one conclusion. They also both have an indicator word—"therefore"—showing you where the conclusion is (although this indicator word is helpful, it need not be present). However, only one of these is a deductive argument. It's the first one. Why? In the first one, if the premises are true, we have no choice but to accept the conclusion. There's no way around it—Jim had time to watch a movie last night! That doesn't mean he did watch a movie, but if the premises are true he definitely had time. 

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By contrast, we shouldn't take the second of the two arguments to be deductive. The premises render the conclusion likely, but not certain. There's a good chance that the conclusion is true (and I'd definitely bet on it being true!), but it's not certain. Even if the kids went to random houses throughout the neighbourhood, there's a small chance that they visited the houses in the 5% without chocolate at a greater frequency than the 95% that do have chocolate. For instance, it's possible that, despite collecting only in my neighbourhood, the kids went to only three houses before they got cold and those three houses happened to be among the 5% without chocolate. 

 

In short, the conclusion in the second argument is probable, not certain. It can't be deductive. It's an inductive argument, which we'll get to later. For now we'll stick to deductive arguments. Let's have a look at what it means for a deductive argument to be valid. 

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Valid and invalid deductive arguments

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Here's a deductive argument:

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All people are mortal (premise 1)

Mitsy is a person (premise 2)

Therefore, Mitsy is mortal (conclusion)

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In the argument above, if we accept both premises to be true, we also have to accept the conclusion. There's no way around it. You can see that the premises are logically tied to the conclusion—it's impossible to have true premises and a false conclusion. That means this is a valid deductive argument. We can say a deductive argument is valid when, given true premises, it would be impossible for the conclusion to be false.

 

Validity in the context of deductive arguments is only about the relationship between premises and conclusions. Validity means the conclusion logically and inescapably follows from the premises. Put aside whether the premises are true or false—validity has nothing to do with truth or falsity of premises. That is, a deductive argument can still be valid when one or more of the premises is false. For instance, if it turns out that Mitsy is a cat, not a person, the above argument is still a valid deductive argument. Again, that's simply because the argument's internal logic works.

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Here's an alteration that renders the argument invalid:

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All people are mortal (premise 1)

Mitsy is in Argentina (premise 2)

Therefore, Mitsy is mortal (conclusion)

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The above example is an invalid deductive argument. This occurs when there's an error in the logic linking the premises and conclusion. In this example, although the author seems to be intending to prove Mitsy is mortal, the relationship between the premises and conclusion of the argument doesn't make sense. From the argument alone, premise 1 is not useful evidence in favour of the conclusion (we need to know whether Mitsy is a person, and we don't!). Furthermore, premise 2 is totally irrelevant to the conclusion—there's no connection there at all. It's possible that Mitsy is a mountain range or a city in Argentina. There's nothing in the argument suggesting otherwise. Therefore, we cannot conclude that Mitsy is mortal. Obviously, an invalid argument like this is a very bad argument.

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Here's another example of an invalid deductive argument (the reason it's invalid may be slightly harder to grasp, so take a minute with it):

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All living things need water. (premise 1)

Roses need water. (premise 2)

Therefore, roses are living things. (conclusion)

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In the above argument, even if we accept the premises as true, they do not provide evidence for the conclusion. That roses need water is not a sufficient condition for the conclusion that roses are alive. For instance, there are non-living things that need water, such as swimming pools and lemonade. If we replace the word "roses" with "swimming pools", but keep the argument the same, we can see the problem: .

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All living things need water. (premise 1)

Swimming pools need water. (premise 2)

Therefore, swimming pools are living things. (conclusion)

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Simply replacing the roses with pools renders the argument ridiculous, but the logic is exactly the same. You can't say swimming pools are alive just because they need water, and the same goes for roses! If you're still stuck on this one, don't just skip forward—give it a think until you see the problem with the logic.

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By the way, upon first reading the roses argument above, many university students think it makes logical sense and is a valid argument. It shouldn't bother you if you, too, find this one tough! It should, however, suggest to you how difficult it can be to evaluate even simple arguments. Why is it so hard to see the problem with the roses argument? To help us, let's bring back some of the content from the metacognition module. It might be because we're processing the argument in "type 1" thinking mode, relying too much on our intuition and, therefore, missing critical information. Specifically, we may intuitively and automatically do only half the required work, evaluating the truth of the statements alone (they're all true!) but ignoring the logic in the links between the statements. When we ponder arguments, we have to both consider truth of premises and the logic of argument. This often requires that we slow down our thinking.

 

Again, validity of arguments hinges only on the connections between premises and the conclusion. When you're assessing validity, forget about truth! Below, we'll get to soundness, which adds truth of premises to the mix.

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Sound and unsound deductive arguments

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Let's return to an example from above:

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All people are mortal (premise 1)

Kanye West is a person (premise 2)

Therefore, Kanye West is mortal (conclusion)

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Here, again, the premises together work to make the conclusion certain (if the premises happen to be true). What's important here is that we know the premises are true: it's correct to say that (1) all people are mortal (i.e., all people will one day die) and (2) Kanye is a person. These statements are true. Now, because (a) the conclusion is logically tied to the premises and (b) the premises are true, there's no way around accepting the conclusion.

 

When both of those conditions are met in a deductive argument, we refer to it as a sound deductive argument. That is, a sound deductive argument is valid (there's a logical connection between premises and conclusion) and the premises are true. A sound argument is a good deductive argument.   

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To summarize, an argument is valid when the premises are logically linked to the conclusion. This validity is a precondition for soundness—an argument cannot be sound without being valid. Furthermore, an argument is sound when (a) the premises are true and the link between the premises and conclusion is logical (the connection between the premises and conclusion makes sense).

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Let's revisit another argument from above:

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Halifax is in Canada. (premise 1)

I am in Halifax. (premise 2)

Therefore, I am in Canada (conclusion)

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In this argument, again, there is a clear logical connection between the premises and conclusion. Therefore, it counts as a valid deductive argument. That is, if we can accept the premises as true, we must also accept the conclusion. However, it happens to be the case that one of the premises is not true: I am not in Halifax. If one or more of the premises is false, the argument is not sound—we'll call it an unsound deductive argument. So, this one is valid but unsound.

 

Get it? It might be a good idea to draw yourself a diagram of valid vs. invalid and sound vs. unsound deductive arguments. We're starting to juggle a lot of new concepts!

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Before we leave this basic look at deductive arguments, note that the above arguments we've considered are all of the same 3-line structure, with two premises and a conclusion. These arguments are called syllogisms. Deductive arguments can look different from these—with more than two premises, for example. I just use syllogisms here to keep things simple. For our purposes, keep in mind that deductive arguments need not appear in this form. What makes an argument deductive is simply that the author is trying to prove that a conclusion is true with what they intend to be inescapable logic.

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Inductive arguments

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Often, premises are not intended to provide proof for a conclusion as in the case of deductive arguments, but are instead offered as evidence in support of the conclusion. These are inductive arguments. In a good inductive argument, the conclusion is likely rather than certain to follow from a set of true premises. For example:

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Mike just unexpectedly broke off his engagement with Julie. (premise 1)

Julie was in love with Mike. (premise 2)

Julie is probably upset. (conclusion)

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Here, assuming the premises are true, although it might seem very likely that Julie is upset, it doesn't necessarily follow that Julie is upset. As unlikely as it might be, perhaps Julie found out other news that kept her afloat. Maybe Julie somehow misheard or misinterpreted what Mike said. It's also possible that Julie has a condition that renders it impossible to experience negative emotions. In short, we don't have enough information here to know that she would be upset (and indeed can never know for certain). The argument is inductive rather than deductive because the premises render it probable or likely, rather than certain or definite, that Julie is upset.

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In the Julie example above, the word, "probably" is suggestive of an inductive argument; however, even if that word were absent we'd generally still be better off taking it as inductive. If there is even one possible reason we can find suggesting a that Julie might not be upset, we cannot be certain about Julie's state given the premises. In short, indicator words like "probably", "likely", and "odds are" can be useful clues that you're seeing an inductive argument, but they don't always appear in the argument so it's best to not depend on them alone to tip you off. 

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As you can see, then, it's not always easy to judge whether and argument is inductive vs. deductive. This is because we have to depend in part on (1) what we believe the author's intentions to be (which can be extremely difficult) and (2) what we can extract from the wording and subject matter (e.g., does the wording suggest an attempt to prove something or the expression likelihood?).

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Knowing inductive from deductive arguments is a useful foundation for our ability to evaluate what the author is truly claiming. Here's a good rule of thumb: if you can reasonably make the case that an argument is inductive rather than deductive, it's better to take it as inductive. Use the principle of charity. The principle of charity, in this context, asks us to interpreting the argument in the best possible light within the bounds of reason. By angling toward interpreting the argument as inductive, you're giving the author the benefit of the doubt, assuming if possible that they're dealing with likelihoods rather than certainties.

 

For instance, we should generally angle toward assuming an argument is inductive when a competent author is talking about conclusions they're drawing from scientific research. This is because science doesn't generally deal with certainties but, rather, probabilities. An author who's scientifically competent knows this. So, if they seem to be saying something like the following, even though it sounds deductive, it would be more charitable to take it as inductive when evaluating its merits. That is, it's a much better inductive argument than it is a deductive argument.

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Learning in person is better for students' learning (conclusion). Most research studies support the idea that students learn more from learning in person rather than online (premise).

 

The author seems to be saying with certainty that this body of research proves that learning in person is better. However, we know that this research cannot prove but, rather, may serve as a source of evidence for the likelihood that in person learning is better. All else being equal, assume that this is intended to be an inductive argument, despite the wording choice (which may be sloppy or an attempt to persuade the audience). In practice, when evaluating arguments, there's more to consider than just wording choices.  

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Similarly, it's more charitable to assume an argument is inductive when the conclusion is referring to something future events, such as the outcome of an upcoming election. No one knows what the future might hold. Presumably the writer or speaker knows this—in general that can be assumed. In any case, if it's important to get it right, do some digging into the source of the argument (e.g., the author) to see what evidence you can find about the author's reasoning competency. 

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​​Strong versus weak inductive arguments

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Like deductive arguments, inductive arguments vary in their quality. Once again, this has to do with whether (a) the premises are true and (b) there are reasonable connections between the premises and conclusions. One of the following inductive arguments is better than the other—which one is it and why? 

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1. In a representative survey of 500 professors across Canada, 80% expressed non-belief in a higher power (premise).

Therefore, if we take a random professor at a Canadian university, it's likely that they will express non-belief in a higher power (conclusion).

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2. In a representative survey of 500 professors across Canada, 80% expressed non-belief in a higher power (premise).

Therefore, if we take a random Canadian, it's likely that they will express non-belief in a higher power (conclusion).

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In the first argument above, the premise and conclusion are fairly tightly linked. Though the survey findings cannot provide proof for a conclusion, we should be able to draw reasonable inferences about the majority of Canadian professors' beliefs from a well-done, representative survey of Canadian professors' beliefs. This is what is referred to as a strong inductive argument—the premise(s) provide good evidence,  but not proof, for the conclusion.

 

In a weak inductive argument the premises don't sufficiently support the conclusion. The premise of the second argument, for example, does not provide good evidence for the argument's conclusion. I would not be convinced by an argument like this and you shouldn't be either—a survey of professors, is not representative of the Canadian population as a whole, and so inferences about the general population cannot reasonably be drawn from such a sample. In short, the premise provides insufficient evidence for acceptance of the conclusion, and so this is a weak deductive argument (to foreshadow a later section of this module, this argument is representative of fallacious reasoning—in particular, it commits the fallacy of hasty generalization).

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Importantly, note that whether or not the premises in the arguments above are true does not matter in the least for determining whether these arguments are strong or weak. Strength of inductive arguments is only concerned with the connection between the premise(s) and conclusion.

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Cogent and uncogent inductive arguments

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We can't forget that the truth of the premises matters in inductive arguments just as it does for deductive arguments. To think about this, we'll stick with argument 1 from above for a moment longer. Here it is again:

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In a representative survey of 500 professors across Canada, 80% expressed non-belief in a higher power (premise).

Therefore, if we take a random professor at a Canadian university, it's likely that they will express non-belief in a higher power (conclusion).

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If the premise is true—that a survey of 500 professors across Canada, did indeed reveal that 80% of professors express non-belief in a higher power—then we can call this a cogent inductive argument. This means that (a) the premise(s) are true and (b) there is a logical connection between the premises and conclusion.

 

Perhaps, however, the premise was revealed to be false. Maybe the arguer lied about the study having been conducted. Maybe the arguer thought the researchers had conducted the study but it was faked! Alternatively, perhaps they misinterpreted the findings of the research (unfortunately, that happens a lot). The falsity of the premise would make it an uncogent inductive argument. An uncogent argument is found where at least one of the premises in an inductive argument is false and/or when a deductive argument is weak. Again, this is because, for an argument to be cogent the premises need to be true and the premises need to provide support for the conclusion.

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It may at first be confusing to note that, even if the premises of the first argument were false—say the research was never actually conducted (the author lied or misinterpreted)—the argument would still be labeled a strong inductive argument. This is because inductive strength vs. weakness refers solely to the link between premises and conclusions. That is truth of premises has no bearing on degree of argument strength. When we're interested in evaluating truth of premises and the links between the premises and conclusion, we must speak of cogency. That's a bit of terminology it may be tough to grasp, so spend some time with it.

 

As I noted in the section above on deduction, it may be useful to draw a figure or a table to help you map these terms out.

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One final point of importance. Recall at the outset of this section that I suggested not to depend on searches for internet resources on deductive and inductive arguments. This is because of a confusing, and I think extremely unhelpful, way others sometimes discuss inductive and deductive arguments: inductive arguments are often discusses as reasoning from specific premises to general conclusions. Deductive arguments, by contrast, are often referred to as reasoning from general premises to specific conclusions.

 

Without getting into the details here, this is a confusing way to frame inductive and deductive arguments and I simply suggest ignoring it. If you have ideas about inductive and deductive arguments that are consistent with general/specific idea, I suggest trying to remove them from your thinking and instead focus on certainty vs. likelihood as the distinguishing characteristics of deductive and inductive arguments, respectively. See the link in the "Additional Resources" section for a good supplemental reading on deduction vs. induction that aligns closely with our intruduction to the topics above.