I-reading: Arguments: Induction vs. Deduction
(Guttenplan, 1-10; Johnson, 1-7)
You probably found that finding arguments and putting them into standard form is much easier than paraphrasing the structure of passages in the earlier sections. Now comes the hard part: discriminating the different kinds of arguments and evaluating them. We will begin the work of distinguishing the two main types of arguments in this section and will discuss how to evaluate them in subsequent sections.
Among other things, Jeff knows the following: He and his next-door neighbor live a few blocks from the campus of State University. The next-door neighbor looks about twenty years old, and the neighbor often wears State University T-shirts and sweatshirts.
On the basis of this information, it is quite reasonable for Jeff to generate this new piece of information, although he does not have any direct evidence for it:
his next-door neighbor attends State University. ...
Together, all of the information in the above example is an argument. The term argument has a technical meaning, and, of course, it has a colloquial meaning as well. Here the technical meaning is what matters. In its technical sense, all arguments have two parts: a premise or set of premises, and a conclusion. The premises are that first set of information-the information that is used as a basis for generating the new piece of information. The conclusion is the new piece of information.
To clearly identify each premise and the conclusion, we can write the above argument this way:
1. Jeff and his next-door neighbor live a few blocks from the campus of State University.
2. Jeff's next-door neighbor looks about twenty years old.
3. Jeff's next-door neighbor often wears State University T-shirts and sweatshirts.
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Therefore, Jeff's next-door neighbor attends State University
… [L]eaving aside whether they actually are true or false, if the three premises are true, then they provide reasons for thinking that this sentence is also true: Jeff's next-door neighbor attends State University. In other words, the three premises support the conclusion. Preserving truth is the core notion behind support, but a more intuitive definition will also work, something like the premises back up the conclusion or the premises provide justification for believing the conclusion. In short, that's what an argument is.
An argument is a set of statements, one or more of which are intended to support another in the set. The statements providing support are the premises, and the statement receiving support is the conclusion.
And an inference is just the process by which an argument is created: generating a conclusion on the basis of a premise or set of premises. ...
The main division in arguments is between formal (deductive) and informal (inductive) inference styles. This means that there are different ways that premises support a conclusion. And, yes, unfortunately, “styles” is the appropriate term. The difference between a deductive and inductive argument will not be apparent in their content, so do not think that deductive arguments are more factual than inductive ones. In fact, the very same content can often be treated as deductive or inductive with only slight differences in presentation. Explaining this will be much easier if we can look at some examples:
Inez finds that her car won't start. She remembers that when Jones's car failed to start, it was because the distributor was wet. She also recalls reading that distributor problems are common in the sort of car she has. She is aware of how damp it is today. She concludes, therefore, that a wet distributor is the cause of the trouble.
Dennis is planning his summer holiday. He knows that he can go by airplane or car. If he goes by airplane, he will get there faster, but will be unable to take much luggage. If he goes by car, he can take much more. He recognizes that the success of his holiday depends on his having the right sort of clothing for the unpredictable weather. He could not take the needed clothing on the airplane. He concludes that if the holiday is to be successful, he will have to go by car.
Inez’s Thoughts
- My car doesn't start.
- When Jones's car didn't start, the trouble was a wet distributor.
- Cars like mine have this as a common problem.
- It is very damp today.
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Therefore, she concludes, the cause of my car trouble is a wet distributor.
Dennis’ Thoughts
- I can go on holiday by airplane or car.
- If I go on holiday by airplane, then I shall get there faster, but cannot take much luggage.
- If I go by car, I can take more luggage.
- A successful holiday requires that I take the right clothing.
- I couldn't take the right clothing on the airplane.
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Therefore, he concludes, if my holiday is to be a success, I must go by car.
The transition from the premises to the conclusion is what I want you to focus on. A first thing one might say is this: Inez’s conclusion followed from her premises in a way that made sense, but Dennis’ conclusion followed with more precision. We want to say that there is a logical relation between Dennis’ premises and his conclusion, whereas the relation between Inez’s premises and conclusion is closer to what one would call smart or reasonable as opposed to precise. Inez made a wise summation from her thoughts, but Dennis’ conclusion was produced by his prior thoughts.
A Third Type of Argument
Before moving on, it is worth looking at two qualities that, although not desirable, do not prohibit a set of statements from being an argument. First, sometimes premises are meant to support a conclusion, but they fail to do so. For whatever reason, they provide little or no justification for believing the conclusion. Nevertheless, as long as the premises are intended to support the conclusion, the collection of statements is still an argument.
Let’s look at Jeff’s nightly thought process:
There are leftovers in the frig. I forgot to eat lunch again. I really shouldn’t eat a lot right before bed. Aw, heck, who am I kidding, I can’t control myself, hand me an extra large fork...
It is clear that the movement of thought in Jeff’s case is different from that in Inez’s case and radically different from that in Dennis’ case. There are many times when our thoughts move from one to another in a connected way, but we often see no need to justify our reasoning because it seems so obviously logical. It cannot be said that Jeff’s reasoning was logical, that is, we would not say that his conclusion was produced by his prior thoughts. This difference between Jeff’s argument and the other two is simply a matter of Jeff’s being illogical and the others being logical.
Here are a couple more examples:
1. Jeff slept with his chemistry textbook under his pillow last night.
2. He slept for seven hours.
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Therefore, he will do well on his chemistry exam today.
1. Denver is the largest city in Colorado.
2. Colorado is the twenty-fourth-largest state in the United States.
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Therefore, Denver is the twenty-fourth-largest city in the United States.
These are both arguments, but they are not very good ones, because the premises provide little or no support for the conclusions. …
While ideally, all - or at least most - of the information that is needed to support the conclusion will be explicitly stated in the premises, sometimes it may be assumed that an argument will be understandable without all of the details, and so some of the information that could be in the premises might not be included.
Whatever the case may be, to identify an argument the important thing to look for is this relationship of support. If there is a statement or series of statements that are supporting (or at least trying to support) another statement, then it is an argument.
Both Inez's and Dennis' thoughts involved transitions which could be defended. Yet there is a very important difference between these two cases: Dennis’ argument is easier to justify than Inez’s, that is, the movement from Dennis’ assumptions to his conclusion is more certain than Inez’s. This is the key distinction between deductive, or formal, arguments and inductive, or informal, ones: in a deductive argument the goal is to produce an argument in which it is impossible for the premises to be true and the conclusion false. In other words, the truth of the premises would guarantee the truth of the conclusion because the logical movement between them is so precise.
Inez employed her thinking to discover why her car didn't start. At the end of her thought episode, she held the view that a wet distributor was the fault. Moreover, she came to this view by a route that she would defend as justified. What would you say of all this if it turned out that the fault in the car was not a wet distributor? Would Inez be forced to admit that some item in her inventory was false? The answer to this last question is surely “No”. Does this mean that there was something wrong with the way in which she arrived at her final thought? The answer here is again “No”. Inez's method of getting to her conclusion was perfectly reasonable, given what she believed in the first place. It is simply a feature of this sort of movement of thought that, on the one hand, we think it justifiable or reasonable, and, on the other hand, we are prepared to admit that the truth of the initial thoughts does not guarantee the truth of the concluding thought. In short, there can be movements of thought which are defensible but which do not lead to their conclusion with necessity.
This is in contrast to the case of Dennis. Suppose it turned out that Dennis took the airplane, and had a successful holiday. Here we would say that he must have been mistaken about one of the thoughts in his assumptions. If they were all true, then this would have guaranteed the truth of his final thought. Both sorts of thinking are defensible, but Dennis can offer a special ground for his defense. He can say: anyone's thoughts ought to move in the way that mine did because such movement guarantees the truth of the final thought given that the initial thoughts are true. Inez cannot say this - though, in contrast to Jeff, she can insist that the movement of her thought was defensible in some other way. The difference between the arguments of Inez and Dennis is crucial to understanding the subject matter of this section. Inez's argument has these features: the reasoning from premises to conclusion can be defended, yet, it could happen that her premises were all true, and her conclusion turned out to be false. This sort of argument is called inductive or probabilistic. We very often employ such arguments in our thinking. Dennis' argument can be defended too, but its defense has this feature: if all the premises are true, then the conclusion is bound to be true. It could not turn out that the premises were true and the conclusion was false. Arguments that are intended to have this feature are called deductive. But why did I say arguments that are intended to have this feature?
Good and Bad Arguments
It would be wonderful if all the deductive arguments that we used in our thinking were like Dennis': given that the premises of the argument are true, its conclusion is bound to be true. Unfortunately, this is not the case. It can, and often does, happen that we employ arguments which are intended to have this feature even though they don't. Here’s a tragically common example:
- I am a person with rights and I have human DNA.
- A fetus has human DNA.
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Therefore, a fetus is a person with rights.
We can see the mistake if we plug in another placeholder:
- I am a person with rights and I have human DNA.
- My fingernail clippings have human DNA.
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Therefore, my fingernail clippings are humans with rights.
It might not be obvious at first, but you can get a sense that the author has argued in the wrong direction. Using a bad deductive argument in one’s thinking should be distinguished from the case of using an inductive argument. Inez’s argument seemed justifiable, even though she would have readily admitted that her premises could be true and her conclusion false. She didn't expect the sort of argument she used to guaranteethe truth of the conclusion. We would say that her intention was to produce a conclusion that was highly likely based on her evidence. On the other hand, the abortion argument seems quite clearly to be of the deductive sort - only faulty. It's just that genuine inductive arguments do not even pretend to meet those standards.
Inductively Strong
An argument is inductively strong when it is the case that (1) the argument is not deductively valid, and (2) if the premises are true, then they make it probable that the conclusion is true. (Or, an inductively strong argument is an argument in which the truth of the premises supports the truth of the conclusion, but does not guarantee the truth of the conclusion.)
If an argument does not satisfy the definition of deductively valid, then it is deductively invalid. There is no in-between; every argument is either deductively valid or deductively invalid. …
With respect to being inductively strong, the situation is somewhat different. ..
The issue here is this: How probable is it that the conclusion will be true if the premises are true? The more probable the conclusion, the higher the argument's degree of inductive strength.
1. Paul is twenty years old.
2. Paul is on his university's cross country team.
3. Paul runs six days a week.
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Therefore, Paul will complete the race, consisting of 1,576 stairs, up the Empire State Building.
As it is, this has a pretty high degree of inductive strength; if the premises are true, then they (the true premises) make it very likely that the conclusion will be true. The same cannot quite be said for this next argument, however.
1. Tom is forty years old.
2. Tom runs four to five miles twice a week.
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Therefore, Tom will complete the race, consisting of 1,576 stairs, up the Empire State Building.
This is a decent argument. The race up the Empire State Building is challenging, but not impossible, and, according to premise 2, Tom is not a couch potato. But the information in those two premises cannot support the conclusion as well as the premises in in the Paul argument support that argument's conclusion. Hence, anyone would be - or at least should be - less confident about the truth of the conclusion in the Tom argument than in the Paul one. This next argument, meanwhile, has the lowest degree of inductive strength of the three.
1. George is sixty years old.
2. George walks two miles twice a week.
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Therefore, George will complete the race, consisting of 1,576 stairs, up the Empire State Building.
Based on the information in the premises, there is a chance that the conclusion will be true, but that chance is not especially high.
Finally, let's consider what makes some inductive arguments stronger, that is, more probable, than others. First, the evidence contained in the premises must be relevant to the conclusion.
1. George owns a pair of running shorts.
2. George loves the Empire State Building.
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Therefore, George will complete the race, consisting of 1,576 stairs, up the Empire State Building.
Obviously, these two premises don't increase the likelihood of the conclusion. These two claims do not directly support George's running ability.
Second, the evidence needs to be truthful.
1. George is an immortal God.
2. George can run faster than the speed of sound.
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Therefore, George will complete the race, consisting of 1,576 stairs, up the Empire State Building.
Finally, there needs to be sufficient evidence. This means that there needs to be enough evidence, depending on the initial likelihood of the conclusion. For instance, it would not take much evidence to make it likely that George could complete a three mile race. Walking two miles twice a week might be enough evidence to make it likely that he could walk three miles. But, we are going to need much more evidence to make it likely that he could complete the Empire State Building race. Oh, wait, we haven't made fun of Jeff in several pages… we need one more example.
1. Jeff has become interested in economics.
2. Jeff has read a few books on economic theory.
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Therefore, Jeff will win the Nobel prize in economics this year.