Chapter 6. Causal Reasoning and Explanations
Practice Exercises: Chapter 6
These exercises are designed to help students master the distinction between types of conditions, apply Aristotelian and Millian frameworks, and identify common causal fallacies.
Group 1: Necessary and Sufficient Conditions
Identify whether the underlined factor is a Necessary Condition, a Sufficient Condition, both, or neither for the result described.
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Having four sides to be a square.
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Stepping on a cat’s tail to make the cat meow.
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Being 35 years of age or older to be the President of the United States.
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Turning the key in the ignition to start a functioning car.
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Being a mother to be a female.
Group 2: Aristotle’s Four Causes
Identify which of Aristotle’s Four Causes (Material, Formal, Efficient, or Final) is being described in the following scenarios.
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A carpenter uses a saw and hammer to build a kitchen table.
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The blueprint for a new library shows the structural layout and dimensions.
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A block of marble is used by a sculptor to create a bust of Socrates.
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The primary reason a student studies for an exam is to achieve a passing grade.
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The biological “instructions” (DNA) that determine the growth pattern of a tree.
Group 3: Mill’s Methods of Discovery
Identify which of Mill’s Methods (Agreement, Difference, Joint, Concomitant Variation, or Residues) is used to reach the conclusion in each scenario.
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A scientist observes that as the dosage of a new medication increases, the patient’s blood pressure decreases proportionally.
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Two identical chemical solutions are sitting in a lab. One is exposed to sunlight and turns blue; the other is kept in the dark and stays clear. The scientist concludes sunlight caused the color change.
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Everyone who got sick at a wedding ate different appetizers and main courses, but they all drank the same brand of sparkling cider. The cider is identified as the source of the illness.
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A gardener knows that her fertilizer accounts for most of her plant growth and the sun accounts for some. There is still a small amount of extra growth she can’t explain, which she attributes to a new soil additive she used.
Group 4: Causal Fallacies and Confusions
Identify the causal fallacy committed in each statement: Post Hoc, Ergo Propter Hoc, Confusing Correlation with Causation, Reverse Causation, or Fallacy of the Single Cause.
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“I started drinking green tea every morning, and two weeks later I got a promotion. The tea clearly improved my work performance.”
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“Data shows that cities with more police officers also have higher crime rates. Therefore, hiring more police officers causes more crime.”
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“The reason our local economy is failing is solely because of the increase in the minimum wage.”
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“Research shows that people who own a lot of books tend to have higher intelligence scores. Therefore, buying more books will make you smarter.”
Answer Key
Group 1: Conditions
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Necessary. A square must have four sides, but having four sides is not sufficient (it could be a rectangle or a rhombus).
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Sufficient. Stepping on the tail will guarantee a meow, but it is not necessary (the cat could meow for food).
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Necessary. One cannot be President without being 35, but being 35 does not guarantee the presidency.
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Sufficient (in this context). If the car is functioning, the action guarantees the start.
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Sufficient. Being a mother guarantees that one is female, but it is not necessary (one can be female without being a mother). (Alternatively, neither necessary nor sufficient for trans mothers)
Group 2: Aristotle’s Causes
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Efficient Cause (The agent/force performing the work).
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Formal Cause (The pattern or design).
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Material Cause (The physical “stuff” the object is made of).
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Final Cause (The purpose or “telos”).
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Formal Cause (The essential structure or “account” of what the thing is).
Group 3: Mill’s Methods
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Method of Concomitant Variation (Correlating the intensity of the dose with the intensity of the result).
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Method of Difference (Comparing two identical cases with only one varying factor).
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Method of Agreement (Finding the one common factor among different cases).
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Method of Residues (Subtracting known causes to find the cause of the remaining effect).
Group 4: Fallacies
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Post Hoc, Ergo Propter Hoc (Assuming sequence implies consequence).
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Confusing Correlation with Causation (Ignoring the “Third Factor”—higher crime rates lead the city to hire more police).
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Fallacy of the Single Cause (Oversimplifying a complex economic issue).
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Reverse Causation (It is more likely that highly intelligent/educated people are the ones who tend to buy books).
