6: Logic and Structure
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Identify patterns of logical organization in texts
- Identify basic features of rhetorical patterns (narrative, comparison, definition, etc.)
- Identify logical structures in argument
- Identify logical fallacies
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Human beings love order, and we will try to impose order in almost every situation. That includes reading. Clearly, most reading relies on understanding words in the order they appear in a sentence. Even beyond that, we anticipate patterns and shapes that particular types of writing will take, and we build expectations based on the first few sentences that we read.
This section will help you understand what you can learn from a piece of reading based on the shape it takes, in addition to what the words themselves convey.
Rhetorical Modes
Since most of the reading (and writing!) you’ll do throughout your college career falls into the “academic writing” category, this is a good point to slow down and examine the building blocks of academic writing more closely.
Rhetoric is the study of writing, so the basic types of academic writing are referred to as rhetorical modes. Let’s look at 10 of the most common types.
1. Narration
The purpose of narration is to tell a story or relate an event. Narration is an especially useful tool for sequencing or putting details and information into some kind of logical order, usually chronological.
Literature uses narration heavily, but it also can be useful in academic writing for strong impact.
An academic essay about the impact of lead in the drinking water in Flint, Michigan, for instance, might include a narrative section that tells the story of one particular family that’s been impacted. This will help illustrate the broader impacts on the community.
2. Description
The purpose of description is to re-create, invent, or visually present a person, place, event, or action so that the reader can picture that which is being described. It is heavily based on sensory details: what we experience through our five senses.
Description is very useful in writing of all types.
In our essay about lead in drinking water, sensory details such as the color of the lead-contaminated water coming out of the tap, or the taste of it when used for cooking, will be informative and help clarify the dangers to the community of Flint.
3. Example
In our discussion of rhetorical modes, we’ve been looking at examples with the lead in the water of Flint, Michigan. An exemplification essay (sometimes also called an illustration essay) extends this idea even further: it carries one or more examples into great detail, in order to show the details of a complex problem in a way that’s easy for readers to understand. Paragraphs can also use the example pattern if they contain multiple examples to support a claim within a topic sentence.
Writing in detail about the drinking water crisis in Flint might be used to exemplify the political situation where a state governor appoints an emergency manager over a city, taking authority away from a mayor or a town council. On the surface, it seems like these two ideas aren’t connected, so the extended example of the drinking water situation will help readers to understand the potential consequences of removing local leadership.
4. Definition
A definition essay takes the concept of “definition” more broadly, moving beyond a dictionary definition to examine a word or concept as we actually use and understand it. Paragraphs that use the definition structure often focus on defining a single concept.
If we use the term “drinking water crisis” to apply to the situation in Flint, Michigan, what does that actually mean? At what point does the term “crisis” apply? A definition essay would examine the various factors that shape a public crisis, such as the level of lead contamination in water determined to be dangerous, the costs of drinking water to citizens, the difficulty in accessing water in other ways, and the damage lead exposure can have to children.
5. Process Analysis
Analyzing a process can also be thought of as a “how-to” essay or paragraph. Technical writing includes a lot of process analysis, for instance. Academic writing can incorporate process analysis to show how an existing problem came to be, or how it might be solved, by following a clear series of steps.
Tracing the steps that led to the current drinking water problems in Flint would prove a useful exercise in a process analysis essay. Showing exactly what steps were taken, and in what order, would help illustrate for readers how similar situations could be avoided in other communities in the future.
6. Division/Classification
A classification essay takes one large concept, and divides it into individual pieces. A nice result from this type of writing is that it helps the reader to understand a complex topic by focusing on its smaller parts. This is particularly useful when an author has a unique way of dividing up the concepts, to provide new insight into the ways it might be viewed.
Part of the reason that the Flint drinking water issue has gotten so much attention, is that it’s such a thorny issue with so many potential long-term effects. A classification approach to this topic could divide the overall concept of “crisis” into individual threads: the political implications, the public health implications, the financial implications, and the educational implications.
7. Comparison/Contrast
Comparison focuses on similarities between things, and contrast focuses on their differences. We innately make comparisons all the time, and they appear in many kinds of writings. The goal of comparison and contrast in academic essays may be to show that one item is superior to another, based on a set of evaluations included as part of the writing.
A path to deeper understanding of the Flint drinking water crisis would be to look at another community that has experienced something similar. Comparisons and contrasts might be made in how the situation arose in each location, how it was handled by public officials and private citizens, and how it was ultimately resolved.
8. Cause/Effect
If narration offers a sequence of events, cause/effect essays offer an explanation about why that sequence matters. Cause/effect writing is particularly powerful when the author can provide a cause/effect relationship that the reader wasn’t expecting, and as a result see the situation in a new light.
We recognize that lead contamination in drinking water is a problem, but many readers may not know exactly why that is. Drawing a cause/effect relationship between lead exposure in childhood, and later learning disabilities and physical problems once these children grow up, would be helpful for understanding the long-term impacts possible from the current situation in Flint.
9. Problem/Solution
This type of academic writing has two equally important tasks: clearly identifying a problem, and then providing a logical, practical solution for that problem. Establishing that a particular situation IS a problem can sometimes be a challenge–many readers might assume that a given situation is “just the way it is,” for instance.
If the fact that the drinking water supply in Flint contains lead is the problem, then an academic problem/solution essay will establish WHY it’s a problem. This might include noting the EPA guidelines for lead in the water supply, and what Flint’s water testing results reveal. Then, this essay would need to establish a solution for the situation that would be both practical and feasible. The temporary solution many residents are using currently is to buy bottled water to drink, cook, and bathe with. A problem/solution essay on this subject will need to offer a more manageable long-term solution for these residents.
10. Argument & Persuasion
The purpose of argumentation (also called persuasive writing) is to prove the validity of a point of view, by presenting sound reasoning to thoroughly convince the reader. These assume that the reader is initially uninformed about the topic, or holds a viewpoint that differs from the author’s. The author’s goal is to bring the reader around to his or her way of thinking on the matter.
Many different people, organizations, and political groups have been blamed along the way for the water crisis in Flint. A persuasive paper looking at who’s ultimately responsible would offer a definitive answer for which group or person deserves the bulk of the blame. It would also effectively address why this matters to the reader–why a reader should care about making sure that the guilty party is ultimately held responsible for their actions.
As the examples of the Flint, Michigan drinking water situation show, there is a lot of overlap between the different rhetorical modes. Many academic essays combine two or more different rhetorical modes in one finished product. This leads to a rich reading experience.
At the paragraph level, however, there is typically one dominant pattern of organization (rhetorical mode) present. This structure helps readers to understand how the text is organized, allowing readers to more easily grasp the main idea of each paragraph.
Logical Arguments
Anything you read that includes an attempt to persuade you to think a certain way is likely to include logical argument as part of that persuasion.
The text below introduces the idea of premises and conclusions. As you read, think about the relationship of premises and conclusions as they align with main ideas and supporting evidence.
Elements of an Argument
Claim: a statement or opinion that people may disagree upon
Argument: a claim supported by premises
Premises: reasons that support a claim, thus supporting a particular argument
A claim is an assertion about the truth, existence, or value of something that can be debated. Claims are also called statements or propositions.
When supported by premises, a claim becomes an argument. For example:
- This class is easy.
- The Baltimore Ravens have the potential to make the NFL playoffs.
- Abortion before the point of fetus viability should be legal in all of the United States.
Each of the above are claims, but they only become arguments when the writer gives reasons WHY the above are true, logical statements (premises).
Which of the following statements is an argument?
- Vending machines stocked with soda or candy should be removed from all public schools.
- Star Wars is the best movie ever.
- We’d better leave now. If we don’t, we might miss the last train and we’ll be stuck here all night.
- Answer
-
If you answered #3, then you are correct! The first and second statements are not arguments because they offer no support. The third statement is an argument because it offers support (premises) to support the claim.
As we have learned thesis statement in previous modules, we have come to know that term as the main idea. But in argumentation, the thesis contains the main claim of an argument that is supported by premises. It is the logical result of the relationship between the premises. Identifying the thesis is the first step in understanding the argument.
But how do you identify the thesis? Follow these steps:
- Ask, “Is this statement the main point, or is it a premise given to support another statement in the argument?"
- Look for indicator words that often precede main ideas, such as
| Therefore | Thus | As a result | That’s why | Consequently | So |
| This Means | This shows | It follows that | This suggests | Hence | Accordingly |
What is the main claim in each of the following arguments?
- Abortion is wrong because all human life is sacred.
- It’s flu season and you work with kids, so you should get a flu shot.
- We should believe that rocks exist because we are able to see them.
- John will probably receive the next promotion since he’s been here the longest.
- We must reduce the amount of money we spend on space exploration. Right now, the enemy is launching massive military buildup, and we need additional money to purchase military equipment to help match the anticipated increase in the enemy’s strength.
- It’s a beautiful day. We should go to the park. Besides, I need some exercise.
- That movie has had horrible reviews. My sister saw it and said it was boring, and her friend spotted three mistakes. Pick a different movie. I am sure we can find something better.
- Answer
-
- Conclusion: Abortion is wrong.
- Conclusion: You should get a flu shot.
- Conclusion: Rocks exist.
- Conclusion: John will receive the next promotion.
- Conclusion: We must reduce amount of money we spend on space exploration.
- Conclusion: We should go to the park.
- Conclusion: We should pick a different movie.
A premise is a reason offered as support, or evidence, for a claim. It is often indicated by these words:
| Because | For | As |
| Since | Inasmuch as | As shown by |
| Given that | As indicated by | The reason is that |
Consider the following statement: Today’s freshmen cannot write very well. Joe is a freshman, so he must be a poor writer. The premises and claim are identified as follows:
| Premise | Today’s freshmen cannot write very well |
| Premise | Joe is a freshman, |
| Claim | so he must be a poor writer. |
Critical Thinking and Logical Fallacies
Many of the texts you’ll read in college will rely heavily on logical arguments. Logic is highly valued as a way of persuading readers, since it can be confirmed to be true.
However, logic can be used badly. When you’re reading, you’ll want to be able to pick out bad logic as well as good logic. This video series helps us identify different types of “bad logic” in reading we might encounter.
Broken Logic
The Man Who Was Made of Straw
Getting Personal
Additional Resource on Logic... (Optional)
More on Logic ↵