Vagueness, Ambiguity, Fallacies of Equivocation, Composition and Division


In your teams look at the sample claims.  Identify the common problem.  When your team has figured it out to complete the challenge you must also create your own example. Once you’ve written it down on a piece of paper, jump up and down while saying “I’m a monkey! I’m a monkey!” A TA or myself will come verify your answers.  

Part 1:
A:  “Everything is love…maaaaaaaan”
B: Happiness is a continuation of happenings which are not resisted.
–Depak Chopra
C:  To think is to practice brain chemistry.
–Depak Chopra
D:  A person is a pattern of behavior, of a larger awareness.
–Depak Chopra
E:  New and Improved Formula!
–Every advertisement ever
F:  Product X “boosts your immune system and help support and maintain a healthy lifestyle.”
–Every supplement ever.
otis wonders.jpg

Vagueness:   A term is vague it has no specific meaning for the intended audience. Note on vagueness: Vagueness is a relative quality.Depending on the context of a claim we might need a more or less specific understanding of a term. For example, in an everyday conversation I might talk about “evolution.” However, in the context of a scientific paper I’ll need to be more specific and identify the kind of evolution I’m talking about.

Part 2A:
To win this round you must rewrite the sentences 2 reflect the (at least) 2 possible meanings.  First group to roar like a lion and hand in their answers wins.

A:  I like her more than you.
B:  He shot the elephant in his pajamas.
C:  Ami said on Monday he’d give an exam.
D.  Feel free to respond to my comments or disagree with me. (An actual message sent by a friend inviting me to follow him on twitter)

Part 2B:
A:  He was found by his friend.
B: Apparently my parking is quite good. Someone left an official note on my window that said “parking fine.”
C:  Vitamin E is good for aging people.
D:  Sign: Watch repairs here.

E. I’m not a big banana pancake fan.

Otis: “I am a hot dog”

Terms are ambiguous when they have more than one plausible interpretation. (“Ambi” means “two”). Ambiguity comes in two flavours: syntactic and semantic. Syntactic ambiguity (also called “amphiboly”) is when the sentence structure offers more than one plausible meaning. Semantic ambiguity is when a word can have two possible meanings. Generally, context sorts outs semantic ambiguity (but not always).
Part 2C
A. People actually eat more sushi in America than in Japan.
B. The girls at BGSU study more hours than the guys.
C. Teachers earn more than administrators.
D. More women support Trump than evangelicals.
Explanation of group ambiguity: Group ambiguity is a special kind of ambiguity that can be thought of as a mix of vagueness, semantic ambiguity and misleading comparisons. In the above sentences it’s not clear if we’re comparing absolute numbers (i.e., total aggregate amount for each group), group averages, or percentages of a group. In example A, it could be that Japanese people eat more sushi on average (i.e., per person). However, since there are roughly twice as many Americans as Japanese, to total amount of sushi eaten in America is greater than the total amount in Japan. Or it could mean that the average American eats more sushi than a Japanese person. From the sentence it isn’t clear.
Part 3:
A:  Person 1:  Everything in life happens for a reason…maaaaaaaaaaaaaaaan.
Person 2:  That’s ridiculous.  What’s the reason for my moving my finger right now?
Person 1:  Because you had the thought “move your finger” which caused the nerves leading to your finger to fire in succession, culminating in the movement of your finger…duh. See? Everything does happen for a reason.

B:  Science has discovered many laws of nature. This surely constitutes proof that there is a God, for wherever there are laws, there must be a lawgiver.  Consequentially, God must exist as the great lawgiver of the universe.

C:  Since, as scientists tell us, energy neither comes into being nor goes out of being, there can be no energy crisis.

Fallacy of Equivocation:  The fallacy of equivocation is when a key term in the argument isn’t used with a consistent meaning throughout the premises and/or conclusion.  In other words, a term might be used differently between premises or between the premises and the conclusion.  Test hint: This is Ami’s faaaaaaaavorite fallacy.

Part 4:
A:  Everything in the universe has a cause, therefore the universe also must have a cause.
–William Paley’s Teleological Argument
B:  If everyone pursues their own best interest, societies best interests will also be served.
C:  Since everyone cares about their own individual happiness, they will also care about the aggregate happiness of society.
–J.S. Mill in Utilitarianism
D:  This dinner is going to taste delicious:  Every ingredient it’s made from is delicious.
–My mom.
E:  Every person in the class was born to a mother therefore this class was born to a mother.
F:  He/She’s got every quality I like in a person. I’m sure we’ll get along.

Fallacy of Composition: Inferring that since the parts that make a whole have a property then the whole also has that property.  In fancy talk:

(P1)  The parts P, Q, R which make up X have property(ies) a, b, c.
(C) Therefore, X must also have properties a, b, c.

Part 5
A:  This food tastes awful.  You must have used horrible ingredients.
B: The Seattle Seahawks were the best team in the NFL this year. They must have the best players.
C:  The science man says there’s supposed to be global warming, so why is it so cold in the D?
D. Housing prices are up this year, therefore my house must also have risen in value.
E. Sodium Chloride (Table salt) is safe to eat on my food, therefore sodium and chloride are safe to eat on my food.

Fallacy of Division:  Inferring that what is true of a whole (or a group) must be true of its parts. In fancy talk:

(P1)  Some whole or group has property a,
(C) Therefore, it’s parts (X, Y, Z) must also have property a.
Obvious Example: H20 is a liquid at room temperature therefore H and 02 are also liquid at room temperature.

Homework Exercises

A. Vagueness or Ambiguity? (a) If a premise is vague explain why and/or two or more possible interpretations of the term. (b) If a statement is ambiguous identify whether it is semantic, syntactic ambiguity and give at least two possible interpretations of the statement. (HW: Do 1-12, Optional 13-18)

1. You should only use natural products on your skin.

2. A recent study shows that 1 in 3 women have been sexually harassed at work. Link (Links to an external site.)

3. Cows release more greenhouse gasses than cars.

4. To do well in this course you’ll need to pay careful attention during lectures and do all the homework or study really hard for exams.

5. More vaccinated people get measles than unvaccinated people.

6. The government is not to be trusted.

7. Coconut water helps to detoxify the toxins.

8. Headline: Lung Cancer in Women Mushrooms.

9. The rich control the political system

10. You should avoid rollercoasters because they’re dangerous.

11. Drinking frequently may be hazardous to your health.

12. The fish is ready to eat.

13. Headline: British Left Waffles on Falkland Islands (various problems)

14. Teachers earn more than principals.

15. Headline: Reagan Wins on Budget, but More Lies Ahead.

16. Headline: Squad helps dog bite victim.

17. I don’t like it when you smoke.

18. I’m not a big banana pancake fan.


B. Fallacies of Equivocation, Composition, and Division. Identify which fallacy is being committed and briefly explain your answer.  (HW: Do odd numbers. Do even numbers for optional extra practice.)

1. Elemental sodium is toxic even in small does and so is elemental chlorine, therefore sodium chloride is also toxic in small doses.

2. Last year the BGSU’s foosball team won the championship match, therefore they had the best players in the league.

3. The average salary US salary is around 50 000/year, therefore most people are doing well.

4. Friends was a really popular show, therefore a spin-off show based on one of its characters will also be popular.

5. A ton of feathers is lighter than a ton of lead.

6. I’ve selected only the most creative individuals for the design team thereby ensuring that we have the most creative design team.

7. A: You probably shouldn’t make such offensive comments.

B: I have a right to exercise free speech, therefore it’s right for me to say what’s on my mind.

8. While it’s true that studying critical thinking allows you to argue better, is it really a good idea to encourage people to argue?

9. Criminal actions are illegal, and all murder trials are criminal actions, thus all murder trials are illegal.

C. Thinking About Cases in Real Life

HW: Do All

1. Suppose it’s true that no police officers are intentionally discriminatory toward visible minorities. (a) Does it follow that the law enforcement institution cannot possibly be discriminatory? In more general terms: If nobody in an institution intentionally discriminates does it follow that the institution cannot be discriminatory? (b) If I argue that an institution cannot be discriminatory because none of its members are discriminatory, do I commit the fallacy of composition?

2.  Am I allowed to pick mushrooms? (Vagueness) Explain your answer.
From Oak Openings Rules and Regulations (Links to an external site.): Within the parks and public lands of the Park District, no person shall without lawful authority or privileged to do so cut down, destroy, remove, girdle, or injure a vine, bush, shrub, sapling, tree, or crop standing or growing therein, or sever, injure or destroy a product standing or growing therein or other thing attached thereto; nor shall any tree, flower, shrub, or other vegetation, or fruit or seed thereof, or soil, or rock, or mineral be removed, injured or damaged; nor shall any form of wildlife, except fish, be injured, damaged or removed without specific written permission from the Director or his/her agents. (MM)*

3. When a corporation or political organization engages in bad behavior does it mean that the people in the company are also bad people? Is this a case of the fallacy of division or is this a legitimate inference? Briefly explain your answer.