FALLIBLE FOX

​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 these, 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 are to 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. Stated differently, from the premises, there's no way around arriving at the conclusion—if we're being logical, we're forced to accept it. 

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Try this: based on the basic description of deductive arguments two paragraphs 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 our neighbourhood.

Therefore, most 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 (remember from a previous section that, although this indicator word is helpful, it need not be present). Only one of these two arguments, however, is a deductive argument.

 

It's the first one. Why? In the first one, if we accept the premises as 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 certainly bet on it being true!), but it's not certain. Even if the kids went to random houses throughout the neighbourhood, there's a very 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 at least two of those three houses happened to be among the 5% without chocolate.

 

In short, if it's possible that the conclusion is false, .

 

In short, the conclusion in the second argument is probable, not certain. It 's not deductive—we're not logically compelled to certainty about the conclusion, but that conclusion remains likely to be true. Rather, 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 are to assume both premises to be true, we must accept the conclusion. There's no way around it. You can see that the premises are logically tied to the conclusion. In this case, 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 logic in the relationship between premises and conclusions. Validity means the conclusion logically and inescapably follows from the premises. Importantly, to assess validity, put aside whether the premises are in fact true or false—validity has nothing to do with actual 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 perfectly well—the conclusion follows logically from the premises.

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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.

 

To accept the conclusion, we need to know whether Mitsy is a person and we don't. Premise 2 is totally irrelevant to the conclusion—there's no connection there at all. It's possible that Mitsy is a mountain range, city in Argentina, or the sound ketchup makes when it comes out of the bottle. There's nothing in the argument suggesting otherwise. Therefore, we cannot conclude that Mitsy is mortal. Obviously, an invalid argument like this is a poor argument.

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The following is another example of an invalid deductive argument. The reason it's invalid may be quite a bit 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 assume the premises are true, they do not provide evidence for the conclusion. Specifically, the premises do not say anything about whether roses are living things. Roses may indeed need water, but that doesn't tell us whether they belong to the category of living things. 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 as for the first of the two arguments. 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 be a huge concern if you, too, find this one tough! It should, however, suggest to you how difficult it can be to evaluate the logic of 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, jumping to conclusions. For example, a person might 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.

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Another way your intuition might lead you astray is if you're relying too much on what you already know instead of thinking solely about the internal logic of the argument itself. That is, you already know that the conclusion is true: "roses are living things". But I was not asking if the conclusion is true. I asked if the conclusion that roses are living things follows from the premises alone.   

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Again, validity of arguments hinges only on the connections between premises and the conclusion. When you're assessing validity, forget about what you know or think you know about the premises or the conclusion. Focus on the logic alone.

 

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: we know that 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 logically follows from 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 (the conclusion logically follows from the premises) and the premises are true. A sound argument is a good deductive argument.   

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To summarize, a deductive argument is valid when the conclusion logically follows from the premises. This validity is a precondition for soundness—an argument cannot be sound without being valid.

 

Furthermore, a deductive argument is sound when (a) the premises are true and the link between the premises and conclusion is logical (the conclusion logically follows from the premises).

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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. It is, therefore, 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 currently 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. 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 take this form—they may, for example contain more than two premises, for example. I just use these so-called syllogisms here to keep things simple (Although not essential for moving forward with this section, you can learn more about the specific nature of syllogisms here and different types of syllogisms, with several examples, here).

 

Anyway, keep in mind that deductive arguments need not appear in this 3-line 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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While deductive arguments aim to provide proof for a conclusion, other arguments instead offer evidence in support of a conclusion (i.e., they render the conclusions likely or probable). These are inductive arguments. In a good inductive argument, the conclusion is likely rather than certain to follow from a set of true premises.

 

85% of St. Joseph's students complete their homework on time. (premise 1)

Dave is a student at  St. Joseph's school. (premise 1)

Dave probably completes his homework on time. (conclusion)

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This sort of argument is inductive because the statistical information found in the premises render the conclusion that Dave completed his homework on time probable but not certain. Dave may well be among that 15% of students that do not complete their homework on time, but it's more likely that he's among the other 85%.

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Here's a different sort of example that doesn't deal with statistics:

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

Julie was in love with and wanted to marry 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 Julie would be upset (and indeed cannot know for certain from those premises). However, given this information alone (i.e., the information provided in the premises), it would be reasonable to conclude that Julie is probably upset.

 

The argument is inductive rather than deductive because the premises render the conclusion that Julie is upset probable or likely, rather than certain or definite.

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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 to take this argument as inductive. If there is even one possible reason we can find suggesting 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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​​​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 is a logical connection between the premises and conclusion. One of the following inductive arguments is better than the other—which one is it and why? Make sure to consider the wording carefully.

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1. In a well-executed 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 well-executed 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 the 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 (again, not proof) in support of 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. Remember, this is a strong inductive argument. Here it is again:

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In a well-executed 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 this was a real  study but it was faked! Alternatively, perhaps they misinterpreted the findings of the research (unfortunately, that happens a lot).

 

IN any case, the falsity of this premise would make this 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 an inductive argument is weak. Again, this is because, for an argument to be cogent (a) the premises need to be true and (b) 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 premise of this argument were false—say the research was faked—the argument would still be labeled a strong inductive argument. This is because inductive strength vs. weakness deals solely with the logic of the connection between premises and conclusions. That is, the truth of premises has no bearing on degree of argument strength. When we're interested in evaluating truth of premises and the connection 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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Categorizing Ambiguous Arguments Using the Principle of Charity

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It's not always easy to judge whether and argument is meant to be 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 difficult) and (2) what we can extract from the wording and subject matter. That is, does the wording suggest an attempt to prove a conclusion or an attempt to support the conclusion's likelihood? If it's the former, it's a deductive argument. If the latter, it's inductive.​

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Here's a good rule of thumb about sorting more ambiguous arguments: if (a) the premises don't seem to prove the conclusion and (b) you can reasonably make the case that an argument is inductive rather than deductive, it's better to take the argument 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, imagine an argument put forward by a competent scientist appearing on a podcast. She says:

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Most research studies support the idea that students learn more from learning in person rather than online (premise).

Therefore, learning in person is better for students' learning (conclusion).

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Even if she sounds quite certain, we might be better to assume her argument is inductive. ​​​The speaker might be saying with certainty that this body of research proves that learning in person is better. However, a scientifically literate person would know that this body of research cannot prove the conclusion. This is because science doesn't generally deal with certainties but, rather, probabilities. A series of studies can give evidence in favour of a conclusion but cannot prove it. 

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So, even though it sounds deductive, it would be more charitable to the speaker if we take it as inductive. That is, the argument is much better if taken as an inductive argument (dealing with likelihood) than it is if we assume it's deductive (dealing with certainty). In other words, it's easier to find fault in or knock down this argument if we assume the speaker is truly certain about the conclusion. ​
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Similarly, it's more charitable for us to assume that an argument is inductive when the conclusion is referring to some future event, such as the outcome of an upcoming election.

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The majority of polls tell us that candidate X has a strong lead over candidate Y (premise).

Therefore, candidate X will win the presidency (conclusion).

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No poll and no set of polls can tell us with certainty what the future holds. The speaker should have said "candidate X will probably win the presidency." Although the speaker should have been clearer, it's also your job as a discerning member of the audience to use clues to figure out what they really mean—are they really perfectly certain about that conclusion? If this speaker is a pollster or knowledgeable journalist, they are likely aware that polls deal with probability. In such a case, it's more charitable to assume this person is making a probabilistic argument (inductive), even though it might sound like they think the polls are proof of an upcoming victory.

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Why is it important to treat others' arguments charitably? Gregory Bassham and colleagues (p. 62) write: 

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The principle of charity serves two important goals in critical thinking. First, it fosters civility and mutual understanding in argument by demanding that we treat the arguments of others with the same generous and respectful spirit that we would like others to treat our own arguments. Equally important, it promotes the discovery of truth by insisting that we confront arguments that we ourselves admit to be the strongest and most plausible versions of those arguments.

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In practice, when evaluating real-world arguments, there's more to consider than just the wording. If it's important to get author or speaker's intentions right, do some digging into context and source of the argument as it could reveal important contextual information about things left unsaid such as hidden intentions behind the argument that render it more likely to be inductive than deductive or vice versa. 

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