24 The Logical Structure of Arguments
Core Curriculum and Kirsten DeVries
Learning Objectives:
- Recognize the differences between inductive and deductive reasoning
- Learn how an argument can be structured given a particular rhetorical situation
The Logical Structure of Arguments
This section of the Handbook will use the term argument in a very specific way. An argument in the sense used here isn’t a “quarrel”, but rather a group of statements, some of which, the premises, are offered in support for another, the conclusion. Often “argument” is used interchangeably with “persuasion”, but here we will treat persuasion as covering a wide range of tactics intended to move people to accept a belief or a course of action. Argument, on the other hand, will be considered a category within persuasion. It is a form of persuasion that emphasizes rational thinking and is based in principles of logic and evidence.
Within the category of argument are two subtypes of argument: inductive reasoning and deductive reasoning. Inductive reasoning results in conclusions that are likely or probable but that can never be proven beyond a shadow of a doubt. Deductive reasoning can lead to unquestionable results—but only if certain rules of reasoning are followed.
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 existence of additional data,
- the relevance of the warrant, and
- the existence of additional warrants.
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.
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.
Example:
- 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.
Example:
- 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.
A standard way of capturing the structure of an argument, or diagramming it, is by numbering the premises and conclusion. For example, the following represents another way to arrange the littering argument:
- Littering is harmful.
- Litter is dangerous to animals.
- Litter is dangerous to humans.
This numbered list represents an argument that has been put into standard argument form. A more precise definition of an argument now emerges, employing the vocabulary that is specific to academic and rhetorical arguments. An argument is a set of statements, some of which (the premises: statements 2 and 3 above) attempt to provide a reason for thinking that some other statement (the conclusion: statement 1) is true.
Example:
- Argument: Public libraries should be funded in every community because they provide learning resources for all ages and provide safe spaces for people to read, study, and gather.
- Premise 1: they provide resources for all ages
- Premise 2: they provide safe spaces for people to read, study, and gather
- Conclusion: public libraries should be funded in every community.
How Do You 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?
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.
Example:
- 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.
Why Should I Evaluate Unstated or Suppressed Premises as Well as Stated Ones?
An unstated or suppressed premise is assumed rather than voiced outright but is nevertheless needed for an argument to work. Consider this highly unscientific poll conducted by a TV news station. “Which do you believe Senator Hillary Clinton is most out of touch with: illegal immigration, border security, or the American people?” The pollster is operating as if it is unquestionable that Clinton is out of touch with something. In other words, the question presupposes that she is “out of touch.” However, this unstated premise is debatable once it is brought out into the open. Is she in fact out of touch at all? This is actually a type of logical fallacy, begging the question, which will be covered in a later section.
A listener or reader who is not alert to such unstated or suppressed premises is, without realizing it, agreeing to debate on the communicator’s terms—when those terms may be unfair. In fact, on more complex or serious issues it is often things people take for granted that may actually deserve the most critical scrutiny. For example, in the argument “This medication is labelled as totally natural, so it is safe for me to take it,” the suppressed premise—that “natural” guarantees “safe”—is not trivial and can certainly be challenged.
How Does Argument Diagramming or Outlining Help to Illuminate the Structure of an Argument?
Besides recognizing the use of induction and deduction, you can use diagramming or outlining to develop an understanding of an argument’s overall structure. Remember that an argument as defined here isn’t a “quarrel”, but rather a group of statements, some of which, the premises, are offered in support for another, the conclusion. So the first order of business in analyzing an argument is to recognize what the main claim is—the conclusion—and what other claims are being used to support it—the premises, which is much easier to do when the arguer is explicit about the steps in the argument. The arguer can make the steps clear by using premise and conclusion indicator terms as signposts. Below is a list of such terms.
Words that introduce or signal an argument conclusion include therefore, so, we may conclude/infer, thus, and consequently. Words that introduce or signal argument premises include it follows that, implies that, as a result, because (non-causal meaning), since, for the reason that, for, and.*
*and often signals the introduction of a further premise, as in “You should believe Z because reason 1 and reason 2″.
When you are diagramming or outlining an argument, if the “flow” of an argument from premises to conclusion isn’t readily apparent, then remember to use the above indicator terms to help you decide which claim is the conclusion and which claims are the premises. Using the indicator terms is particularly helpful because a conclusion may be stated first, last, or anywhere in between. People do all three when they write or talk in real life, so we cannot tell whether a statement is a conclusion simply by where it is positioned in the argument.
What is the Purpose of Diagramming or Outlining an Argument?
Diagramming or mapping someone else’s argument serves a double purpose. First, the process helps you clearly see just what the other person is saying. It helps you identify the logical structure of the argument, which is necessary if you are to assess the strengths and weaknesses of the argument in order to know whether or not to accept it. Second, you develop skills of analysis that you will need in order to organize and present arguments in support of a position that you may want to take on some question or issue.
What Are the Steps to Diagramming or Outlining an Argument?
Here are the basic moves that are required in order to create a clear diagram or outline of an argument.
Identify all the claims made by the author. Since a sentence can contain multiple claims, rewrite statements so that you have one claim per sentence. Adopt some sort of numbering or labeling system for the claims—your instructor may have one that she wishes you to follow.
Eliminate “fluff.” Ignore repetitions, assurances (assertions not backed by evidence or reasons), and information that is unrelated to the argument.
Identify which statements are premises and which statement is the main conclusion.
Recognize that there may be sub-conclusions in addition to a final or main conclusion. You may think of a sub-conclusion as the end point of a sub-argument nested inside the larger argument. Although the sub-conclusion is itself the conclusion of a nested argument, supported by premises, it also functions as a premise supporting the final or main conclusion.
Recognize that some premises are independent and others linked. If you were drawing or mapping the argument, you would be able to draw an arrow from an independent premise directly to the conclusion it supports. Linked premises, however, are multiple statements that must be combined to provide support for a conclusion. If you were drawing or mapping the argument, you would have to find some way to show that the linked premises as a group support the conclusion. You might use color coding, or underlining, or circling, or + signs—some way to connect the linked premises before drawing one arrow from the clustered premises to the conclusion they support.
How Can the Argument’s Paragraphing Help You Evaluate How the Author uses Premises?
An author must organize the material to guide the audience through their argument. One tool available to an author is the paragraph. The sentences clustered together in a paragraph should be tightly connected in terms of content. In the commonest form of paragraph, the clustered sentences collectively develop an idea explicitly stated in a topic sentence and don’t contain any extra material related to other ideas. The paragraphs themselves should be placed in an order that reflects some overall plan so that the paragraphs reveal the steps or stages of the argument.
The premises may be said to be key steps or stages in the argument. A well-constructed argument therefore may use each premise as a topic sentence for a paragraph. Additionally, a premise may serve as the guiding idea for a group of paragraphs, each developing a subtopic. For example, the premise, reached by induction, that “College students overestimate the amount of binge drinking that is taking place” might introduce a cluster of three paragraphs, each showing that the overestimation varies by subgroup—with member of sororities, member of fraternities, and non-Greek populations arriving at different estimates.
Look to see whether the author has used paragraphing-by-premise to organize their argument and outline its structure for the audience. You should also ask yourself whether any paragraphs are missing. That is, as you consider what premises serve as the foundations of the argument, be alert for the suppressed ones, the premises that the author assumes to be automatically true. These unacknowledged premises may be ones that the author hopes the audience will not notice or question. In your analysis, call them on it by determining where a paragraph on that premise should have appeared in the argument.
Adapted from Radford University Core Handbook, by Core Curriculum, Public Domain
Adapted from Let’s Get Writing! by Elizabeth Browning; Kirsten DeVries; Kathy Boylan; Jenifer Kurtz; and Katelyn Burton, CC BY-SA 4.0