# 19 The Logical Structure of an Argument: Examine the Quality of Deductive & Inductive Arguments

What is inductive reasoning?

You have been employing inductive reasoning for a very long time. Inductive reasoning is based on your ability to recognize meaningful patterns and connections. By taking into account both examples and your understanding of how the world works, induction allows you to conclude that something is likely to be true. By using induction, you move from specific data to a generalization that tries to capture what the data ‘mean’.

Imagine that you ate a dish of strawberries and soon afterward your lips swelled. Now imagine that a few weeks later you ate strawberries and soon afterwards your lips again became swollen. The following month, you ate yet another dish of strawberries, and you had the same reaction as formerly. You are aware that swollen lips can be a sign of an allergy to strawberries. Using induction, you conclude that, more likely than not, you are allergic to strawberries.

Data: After I ate strawberries, my lips swelled (1st time).

Data: After I ate strawberries, my lips swelled (2nd time).

Data: After I ate strawberries, my lips swelled (3rd time).

Warrant*: Swollen lips after eating strawberries may be a sign of an allergy.

Claim**: Likely I am allergic to strawberries.

*A warrant is a concept that, when applied to the data, leads to the claim. It is the “understanding of how the world works” mentioned in the paragraph above.

**Alternately, the claim may be referred to as the conclusion. You may also find that some discussions of induction use the word premises to refer to data.

What are the limitations of inductive reasoning?

Inductive reasoning can never lead to absolute certainty. Instead, induction allows you to say that, given the data and the warrant, the claim more likely than not is true. Because of the limitations of inductive reasoning, a claim will be more credible if multiple lines of reasoning are presented in its support.

When applying inductive reasoning, always keep in mind that the better and more complete the data and the more relevant the warrant, the likelier it is that the claim will be credible. For example, medical researchers report their results with greater confidence if they can say the following about participants in a study: that the participants were a representative sample and that the sample size was a large one. The larger and more representative a sample, the less likely it is that the results arose out of random variation.

Also keep in mind that the results of inductive thinking can be skewed if relevant data or warrants are overlooked. In the previous example, inductive reasoning was used to conclude that I am likely allergic to strawberries after suffering multiple instances of my lips swelling. Would I be as confident in my claim if I was eating strawberry shortcake on each of those occasions? It is reasonable to assume that the allergic reaction might be due to another ingredient besides strawberries?

This example illustrates that inductive reasoning must be used with care. When evaluating an inductive argument, consider:

the amount of the data,

the quality of the data,

the relevance of the warrant, and

What is required for appropriate cause and effect reasoning?

One type of inductive argument involves reasoning about causes and effects. To argue credibly that one event is the cause of another, a speaker or writer must be careful not to confuse correlation with causation.

Humans seek meaning and therefore tend to ‘see’ patterns where none exist. This meaning-seeking phenomenon includes ‘finding’ causal patterns in what is actually nothing more than correlation—the coincidental occurrence of two or more events.

If events regularly occur within the same time frame, an observer may conclude that one event causes another. For example, April has a reputation for rain; during this rainy month, income taxes come due. Still, the rain does not cause taxes to come due; nor is tax season the cause of spring showers.

Confusing correlation with causation may cause great harm, as when parents stop vaccinating children because of a weak correlation between vaccine administration and the age at which children are typically diagnosed with autism. A perceived pattern has been mistaken for causation.

Since humans are prone to see patterns, claims about causation need to meet a scientific standard that goes well beyond reliance upon intuition.

What is required for an appropriate generalization?

Generalization may be the approach that people have in mind when they think of inductive reasoning. To generalize, a person begins with particular observations and then pools those individual observations in order to draw a conclusion that accounts for all the individual cases. For example, a person observing swans on a number of occasions may notice that each swan is white. Pooling these observations may lead him to the generalization that “All swans are white.”

Generalizations rarely lead to absolute certainty. They are subject to revision because they are based on a sample (reported swan sightings) rather than on direct observation of all possible evidence (a tally of every swan in the world). Because the generalization is based on a sample, it could be falsified any time additional evidence turns up that is not consistent with the claim. (As a matter of fact, there are black swans in Australia.)

However, if the sample is large enough and representative of the target population, inductive generalization can be a very powerful—even essential—tool.

What is deductive reasoning?

Deductive reasoning is built on two statements whose logical relationship should lead to a third statement that is an unquestionably correct conclusion*, as in the following example.

All raccoons are omnivores.

This animal is a raccoon.

Therefore, this animal is an omnivore.

If the first statement is true (All raccoons are omnivores) and the second statement is true (This animal is a raccoon), then the conclusion (This animal is an omnivore) is unavoidable. If a group must have a certain quality, and an individual is a member of that group, then the individual must have that quality.

Unlike inductive reasoning, deductive reasoning allows for certainty as long as certain rules are followed.

*In some contexts, the word conclusion is used to refer to the final paragraph of an essay. Here conclusion means the claim that is the outcome of deductive reasoning.

What is a premise?

In a deductive argument, the premises are the statements whose logical relationship allows for the conclusion. The first premise is checked against the second premise in order to infer a conclusion.

Premise:      All raccoons are omnivores.

Premise:      This animal is a raccoon.

Conclusion: This animal is an omnivore.

Why should I evaluate the truth of a premise?

A formal argument may be set up so that, on its face, it looks logical. However, no matter how well-constructed the argument is, the premises must be true or any inferences based on the premises will be unsound.

Inductive reasoning often stands behind the premises in a deductive argument. That is, a generalization reached through inductive reasoning is the claim in an inductive argument, but a speaker or writer can turn around and use that generalization as a premise in a deductive argument.

Premise (induced): Most Labrador retrievers are friendly.

Premise (deduced): Kimber is a Labrador retriever.

Conclusion: Therefore, Kimber is friendly.

In this case we cannot know for certain that Kimber is a friendly Labrador retriever. The structure of the argument may look logical, but it is based on observations and generalizations rather than indisputable facts.

How do I evaluate the truth of a premise?

One way to test the accuracy of a premise is to determine whether the premise is based upon a sample that is both representative and sufficiently large, and ask yourself whether all relevant factors have been taken into account in the analysis of data that leads to a generalization. Another way to evaluate a premise is to determine whether its source is credible. Are the authors identified? What is their background? Was the premise something you found on an undocumented website? Did you find it in a popular publication or a scholarly one? How complete, how recent, and how relevant were the studies or statistics discussed in the source?

How do I know if a source is credible?

Who is an expert?

How do I decide if someone is an expert?

How do I decide if someone’s expertise is relevant?

How do you know if you should trust the expert?

The following argument is based upon research published in a peer-reviewed medical journal. The author has an extensive background in public health including a medical degree and doctorate in medicine. He is employed by the Public Health Agency in Barcelona, Spain.

Citation:

Plans-Rubío, P. (2012). The vaccination coverage required to establish herd immunity against influenza viruses.          Preventive Medicine 55, 72-77.

Judging from what we know about credible sources, we can feel confident using the following the following argument in our own research even though it is based upon inductive premises.

Premise (induced):  Against most influenza viruses, an 80-90 % vaccination rate for adults is required for herd immunity (Plans-Rubío, 2012, p. 76).

Premise (induced):  In 2009-2010, the influenza vaccination rate for adults was 42 % (p. 76).

Claim:   In 2009-2010, the influenza vaccination rate among adults was not sufficient for herd immunity.

The source is highly credible in part because it is written by an expert for experts. That fact may make a source a challenging read for ordinary readers. It is a medical study based on sufficient, representative, and relevant data that has been carefully analyzed by someone highly qualified in the field. Depending on the nature of an assignment and whether a course is for majors or non-majors, you may be allowed to use some sources that report on studies rather than the original studies themselves. However, you should consult the primary sources whenever possible.

How is a conclusion like a thesis statement?

When we talk about a paper, we usually talk about the paper’s main claim as being its thesis statement. But of course a paper that just makes a claim or states an opinion but offers no supporting reasons or arguments isn’t much of a paper. We would be bothered by reading an editorial in which someone stated a strong opinion on some public issue yet did nothing to justify that opinion.

When an author supports a thesis with reasons, then the thesis statement can be described as the conclusion of an argument, with the supporting reasons being that argument’s premises.