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Lucid Logic
The Essentials of Logic
Paul Stearns
Teachphilosophy on YouTube
Copyright © 2015 Paul Stearns
All rights reserved.
Table of Contents
Introduction
Chapter 1: What is an argument?
Chapter 2: The Two Steps to Evaluate Arguments
Chapter 3: Fallacies
1. Appeal to Nature Fallacy
2. Black and White Thinking
3. Ad Hominem Fallacy
4. Genetic Fallacy
5. Slippery Slope
6. Argument from Ignorance
7. Cherry Picking
8. Appeals to emotion:
9. Post Hoc ergo Propter Hoc
10. Straw Man
11. Relativist Fallacy
12. Absolutism
13. Begging the Question (Petitio Principii) or Circular Reasoning
14. Equivocation
15. Hasty Generalization
16. Composition
17. Division
18. Lottery Fallacy
19. Appeal to Inappropriate or Dubious Authority
20. Red Herring
21. Playing God Fallacy
22. Non Sequitur
Chapter 4: The Socratic Method
Chapter 5: Logical Consistency
Chapter 6: Scientific Problem Solving
Chapter 7: Falsifiability
Chapter 8: Is anything impossible?
Chapter 9: Vagueness and Ambiguity
Chapter 10: Deductive and Inductive Arguments
Chapter 11: Logic Vocabulary in one Diagram
Chapter 12: Formal Fallacies
Introduction
Text Description in Kindle:
How do you think logically? This clear, concise, and interactive text will help you master the twelve most essential concepts and skills needed to think logically. These include the Socratic Method, logical consistency, the two ways to evaluate arguments, informal fallacies, formal fallacies, scientific reasoning, falsifiability, vagueness, ambiguity, deduction, and induction.
This text is ideal for readers with no background knowledge in logic and philosophy or for instructors seeking materials to teach logic and critical thinking. Each chapter contains an answer key and enough practice to internalize the concepts and skills.
Most of the content of this book can also be found at . I continually add to these 12 chapters on my website for those interested in continuing to higher level logical concepts and skills.
I recommend taking my fun quizzes at to evaluate your understanding of each chapter.
Enjoy,
Paul Stearns
Chapter 1: What is an argument?
Introduction: This chapter is mostly a vocabulary lesson in that it attaches technical terms to the rational thinking you do on a daily basis. A video is available here:
Concept: We philosophers use the word “argument” in a different way than you may use it in everyday life. In Philosophy, an argument is not a disagreement or yelling match. An argument is a claim (called a conclusion) supported by other claims (called premises). It may be easier to think of the conclusion as what you are trying to prove and the premises as the evidence. Consider the following argument:
Premise 1: The universe is either infinite or it has a beginning.
Premise 2: The universe cannot be infinite (because energy cannot cross an infinite time to get here).
Conclusion: The universe has a beginning.
Notice that arguments are like math problems. When you add up the premises, they supposedly equal (or support) the sum that is the conclusion. Notice too that every argument has exactly one conclusion, but may have any number of premises. To test your knowledge, do at least one of the three following exercises.
Exercise 1 Questions and Answers: Underline the conclusion and circle the premise(s) in the following arguments.
1. The universe must be infinite since there would have to be an uncaused first cause if it had a beginning, and an uncaused first cause is impossible.
Answer: “The universe must be infinite” is the conclusion. It is followed by two premises.
2. If there were an infinite timeless God, finite minds could not grasp this God. Therefore, the failure to grasp God is evidence for God.
Answer: “The failure to grasp God is evidence for God” is the conclusion. It’s preceded by one premise.
3. God probably does not exist because there is so much gratuitous suffering in the world.
Answer: “God probably does not exist” is the conclusion. It is followed by one premise. There is also a hidden premise (i.e. enthymeme), “God would not allow gratuitous suffering.”
4. Water is gentle, but it can erode the hardest of rocks. Therefore, you will effortlessly achieve when you act gently (derived from Taoism).
Answer: The first sentence is the premise and the second is the conclusion.
5. All men are mammals. Todd is a man. So, Todd is a mammal.
Answer: “Todd is a mammal” is the conclusion. It is preceded by two premises. This type of argument is called a syllogism. Syllogisms have three terms, two premises, and one conclusion.
6. Your value lies in what is not within (i.e. ego). After all, the value of cups, doorways, and windows is what is not there (Tao Te Ching).
Answer: The first sentence is the conclusion. The second is the premise. We could also interpret this as an illustration instead of an argument.
Notice that you can usually identify the conclusion of an argument because it is preceded by words or phrases like thus, therefore, consequently, accordingly, so, it must be that, it follows that, implies that, and as a result. These are called conclusion indicators.
Similarly, premise indicators are words or phrases that identify premises: since, because, may be inferred from, and given that.
Exercise 2: Underline the conclusion, identify the premise(s), and discuss the following arguments.
1. Killing is not always wrong because it is morally permissible to kill in self-defense.
Answer: “Killing is not always wrong” is the conclusion. One premise follows.
2. If God’s knowledge is perfect and God knows exactly what you will do in five minutes, then you must do what God knows you will do. But if you must do what God knows you will do, then you cannot act other than you will act or have acted. Therefore, you are not free.
Answer: “You are not free” is the conclusion. It is preceded by two premises.
3. The Tao is beyond time and space. Therefore, nothing in time and space can prove or disprove the Tao.
Answer: The first sentence is the premise and the second is the conclusion.
4. Vampires suck blood. Beings that suck blood are called phlebotomists. Therefore, vampires are phlebotomists.
Answer: The first two sentences are premises and the third is the conclusion.
Exercise 3: Underline the conclusion, identify the premise(s), and discuss the following arguments. Notice that each of these arguments is obviously bad. Since they contain bad inferences, logicians call them “fallacies.”
1. I’ve met three red heads and they were all mean. Ergo, all redheads are mean.
Answer: The first sentence is the premise and the second is the conclusion. Notice “ergo” is a conclusion indicator. You may have noticed this is a poor argument, a hasty generalization fallacy (see chapter three on fallacies).
2. You cannot prove science will not explain everything, therefore it will.
Answer: The first sentence is the premise and the second is the conclusion. “Therefore” is a conclusion indicator. This is a poor argument, the fallacy of arguing from ignorance (see chapter three on fallacies).
3. I can trust my senses because your senses agree with my senses.
Answer: “I can trust my senses” is the conclusion and is followed by one premise. “Because” is a premise indicator. This seems to be a weak argument, the fallacy of popularity or begging the question. However, it is one of the better arguments we have for trusting our senses.
4. If you give me a beer then I will be happy. I am happy. Therefore, you gave me a beer.
Answer: The last sentence begins with “therefore” and is, therefore, the conclusion. The first two sentences are the two premises. This is a poor argument, the fallacy of affirming the consequent.
5. It is natural to want to kill and eat animals. Since goodness comes from naturalness, it is good to kill and eat animals.
Answer: “It is good to kill and eat animals” is the conclusion. The preceding two statements are the two premises. This is a weak argument, the appeal to nature fallacy.
6. Galileo said mathematics is the language of reality, which is why I should focus solely on the study of mathematics.
Answer: “I should focus solely on the study of mathematics” is the conclusion. This could be an appeal to authority fallacy. Some arguments could be more than one fallacy, it depends on how you interpret the structure of the argument.
Final Question: What are the parts of an argument?
Answer: Every argument has exactly one conclusion and at least one premise. Each argument also has an invisible inference, which is the movement from premise(s) to conclusion (see next chapter).
Application and Value
As you do philosophy, clearly identify the premise(s) and conclusion for each argument. This takes time and effort, but it is important to accurately identify arguments before evaluating them. It improves the quality of discussion and helps you avoid straw men.
Also, remember that I presented simple arguments in this chapter. As you read books on philosophy, science, and other topics, you may have to read five, ten, or even one thousand pages to identify the structure of the argument (i.e. the premises and conclusion). The first step in thinking logically is identifying the “bare bones” logical structure of the paragraph, chapter, or text you are reading.
Resources
I have a video covering the major concepts in this chapter, as well as quizzes on my website.
*Open Links by right clicking and selecting open Hyperlink.
Chapter 2: The Two Steps to Evaluate Arguments
There are two ways arguments go bad. The argument may have a faulty inference or the premise(s) may be false, dubious, or unclear. In other words, every argument could be faulty because there is a problem with the facts or the reasoning/inference from the facts.
Let’s start with the latter concept since most students struggle with it. If you get confused, the exercises should clarify. If you need additional help, please visit my video or other online resources listed at the end of this chapter.
Step 1: Bad Inferences
An inference is the reasoning or movement from premise(s) to conclusion. It is the process of deriving a conclusion from premise(s) assumed or known to be true.
Many people confuse the conclusion with the inference, but the conclusion is your final destination and the inference is how you arrived there. An inference is not a statement like premises and conclusions, it is the reasoning process from premises to conclusion. I will explore this idea later in the text.
When testing inferences, you should assume the premises are true and then ask whether the conclusion is well supported by those premises. Consider the following two arguments:
Argument 1
Premise 1: All whales are mammals.
Premise 2: Shamu is a whale.
Conclusion: Shamu is a mammal
Argument 2
Premise 1: All whales are mammals.
Premise 2: Shamu is a mammal.
Conclusion: Shamu is a whale.
Take a moment to see if you can explain why argument 1 has a good inference and argument 2 has a bad inference.
Got it? Let’s check your answer.
Argument 1 has a good inference because the premises support the conclusion. Indeed, it is a good argument (logicians call it a “valid deductive argument”) because it is impossible for the conclusion to be false if we assume the premises are true.
Argument 2 is bad/invalid because you cannot infer “Shamu is a whale” from the facts that “Shamu is a mammal” and “all whales are mammals.” This is because saying “all whales are mammals” is not equivalent to saying “all mammals are whales.”
Take a moment and think about that. “All A are B” is not the same as “All B are A.” For example, “all cats are animals” is not the same as “all animals are cats.” You cannot infer one statement from the other. The second argument about whales is invalid because it indirectly tries to do just that.
Notice too that argument 2 has a true conclusion and true premises, but it is still bad because the reasoning (i.e. inference) is faulty. Many students new to logic think that if they have all the facts correct, then they have a good argument, but this is not true. Even if you have all the facts, your argument may be bad because you have a poor inference (i.e. poor reasoning) from those facts.
To better grasp this point, consider another bad argument with the same form as argument 2:
Argument 3
Premise 1: All cats are animals.
Premise 2: Lassie is an animal.
Conclusion: Lassie is a cat.
It is easier to see the bad inference in this argument because the conclusion is obviously false (since we know Lassie is a dog). Indeed, most students initially say it is bad because the conclusion is false, but this is incorrect and irrelevant. That is, both argument 2 and the Lassie argument are bad for the same reason . . . they have a bad inference.
In short, it does not matter if arguments with bad inferences have true or false premises. The problem with bad inferences is that the conclusion would not follow from the premises even if the premises were true.
To evaluate the inference of any argument, simply assume the premises are true and ask whether the conclusion is well supported by those premises. If it is, the inference is strong. If the conclusion is not well supported by the premises, the inference is weak. Yes, it is that simple.
Exercise 1: Underline the conclusion in each argument, and explain why each has a bad inference.
1. Hitler was a bad man, so you should not believe anything he believed.
Answer: Even when we assume Hitler was bad, the conclusion does not follow because Hitler obviously held some true beliefs (e.g. 2+2=4, the world isn’t flat, automobiles exist).
2. I've met three redheads and they were really mean and stinky. So, all redheads are mean and stinky.
Answer: The conclusion (i.e. all redheads are mean and stinky) does not follow even if we assume the premise is true (i.e. I’ve met three mean and stinky redheads). In this case, I am generalizing from a sample that is too small and unrepresentative. It is the hasty generalization fallacy.
3. Everyone has DNA, so fire trucks make noises.
Answer: The conclusion (i.e. fire trucks make noises) does not follow from the premise. There seems to be no connection between the premise and conclusion. It is a non sequitur fallacy.
4. It is unreasonable to believe God exists because his nature doesn’t make sense.
Answer: The conclusion (i.e. God does not exist) does not follow from the premise (i.e. the nature of God does not make sense). After all, I know light exists even though I do not understand the nature of light. This is a non sequitur because there are many paradoxical realities known to exist. This does not prove God exists, but it does prove argument 4 is fallacious.
5. I am not free because my cells are not free.
Answer: The conclusion (i.e. I am not free) does not follow from the premise (my cells are not free). This is the composition fallacy. The whole does not have to have the same property as the parts, just as the whole of water may be wet though hydrogen and oxygen are usually dry.
6. You cannot prove God does not exist, so he does.
Answer: The conclusion (i.e. God exists) does not follow from the inability to prove he does not exist. This is the fallacy of arguing from ignorance.
Step 2: False or Unclear Premises
Arguments also go bad because they have false, dubious, or unclear premise(s). Most people understand this pretty well, but let’s do some exercises to ensure understanding.
Exercise 2: Underline the conclusion and identify the problematic premises.
1. All whales are stars. I am a whale. So, I am a star.
Answer: The inference is good/valid, but the premises (i.e. all whales are stars, and I am a whale) are false.
2. Everyone is selfish, so you are selfish.
Answer: The inference is good/valid, but the first premise is dubious. Intelligent people disagree about the meaning of selfish and whether everyone is selfish.
3. Every rational person should agree with the Libertarian Party Platform, so you should too.
Answer: The conclusion follows from the premise, but the premise that every rational person should agree with libertarianism is dubious.
4. If time travel were possible, I could travel to the year 1800 and be both born and not born. But it is a logical impossibility to be both born and not born. So, it is impossible to travel back in time to the year 1800.
Answer: The conclusion is the last statement (i.e. it is impossible to travel back to the year 1800) and it seems to follow from the premises. However, the word “born” is unclear. Some philosophers argue you could be born in personal time, but not absolute time. Therefore, you could be both born personally and not born absolutely in 1800. The problem with this argument is not the inference, but the ambiguity of what it means to be born.
5. Since light is a wave and must travel through a medium, there must be an invisible aether through which it travels.
Answer: The inference is good/strong, but the premise is false. Light does not have to travel through a medium like water waves do. This was a turning point in the history of science.
6. The universe is complex and orderly like a watch. Just as we can infer an intelligent mind made the watch, so we can infer an intelligent mind made the universe.
Answer: This is a simple version of the teleological argument. One criticism is the first premise is false, the universe is not ordered like a watch. Even if this premise is reasonable, intelligent people disagree about what we can infer from the orderliness of Nature. So, you can question both the premise and the inference in this argument.
Summary
When evaluating arguments, take the following two steps:
Step 1: Assume the premises are true even if you know they are not true. Now ask, “Do the assumed premises provide good reasons for believing the conclusion?”
If not, the inference is poor.
If yes, the inference is good.
Step 2: Are the premises true or reasonable?
So, that’s it. That is how you evaluate any and all arguments.
Exercise 3: Evaluate the following arguments? Is the inference good? Are the premises good?
1. All libertarians are brilliant. I am a libertarian. Therefore, I am brilliant.
Answer: The inference is good, but the two premises are dubious.
2. All dogs are animals. Lassie is an animal. So, Lassie is a dog.
Answer: The inference is bad, but the premises are probably true.
3. Eating meat is moral because it is natural.
Answer: The inference is bad (see the appeal to nature fallacy in the next chapter), and some people would also challenge the premise that it is natural.
4. Most people have 28 fingers, so we should make 28 fingered gloves.
Answer: The inference is strong, but the premise is false.
Application and Value
When you evaluate arguments, it is not enough to examine the truth of the premise(s). You should also examine the inference. If you disagree with the conclusion of the argument, be specific about whether you disagree with the premise(s) or the inference to the conclusion. And, yes, you could disagree with both the inference and the premises in an argument (see #6 in Exercise 2).
Again, we could have all the facts, but still draw poor inferences from those facts.
Notice then that every argument is one of these 4 types:
1. Good premises and a good inference.
2. Good premises and a bad inference.
3. Bad premises and a good inference.
4. Bad premises and a bad inference.
So, as you read the newspaper, watch television, or argue with your spouses, think about whether you disagree with their premises or the inference from the premises.
Yes, you may disagree with their conclusion, but that is irrelevant. To justify your position and rationally explain your disagreement, you should clearly explain whether you disagree with the facts (premises) or the reasoning from the facts (inference) . . . or both.
By the way, I do not recommend using logic too much with your spouse(s). For marital issues, find a book on rhetoric, patience, or love.
Addendum to Chapter 2
If you understand this chapter well, you have the foundation needed to understand all of logic. The vocabulary of logic (e.g. deductive, inductive, valid, invalid, strong, weak, cogent, uncogent, formal fallacies, etc.) derives from the simple concept presented in this chapter. If you would like to immediately be a Master Jedi on logic vocabulary, make sure you understand this chapter and then skip to Chapter 11.
Resources
How to Evaluate Logical Arguments, YouTube Video
(logic course)
Open Links by right clicking and selecting open Hyperlink.
Chapter 3: Fallacies
Congratulations! You just advanced to the longest chapter of the book (35 pages). Because it is so long, you may want to read it in stages. For example, read and do the exercises for a few pages and then explore the other shorter chapters, which are between two and six pages. Return to this chapter whenever you feel like it.
While I do have a fifty minute video on this chapter, it does not contain the many activities this book contains. If you enjoy interactive quizzes, check out my interactive fallacy quizzes on
For each fallacy, I provided a definition, examples, discussion, advice, and activities to help you recognize the fallacy and better understand the subtle points.
Why should you care about fallacies? Well, studying fallacies is an important part of logic and one that can immediately enrich your life. It will help you develop the vocabulary and skills needed to better evaluate the arguments of politicians, neighbors, advertisers, authorities, and people who loved you before you began studying logic.
In my classes, I emphasize the study of fallacies early because they outline the “rules of philosophy.” Not only is knowing the names of fallacies the mark of a well-educated mind, it greatly enriches the quality of philosophical discussions. For example, imagine a student argues that “It is good to eat animals because it is natural to do so.” Instead of getting bogged down in a vague argument about naturalness, another student could simply ask, “Why isn’t that argument the appeal to Nature Fallacy?” In short, students who studied both formal and informal fallacies can more easily engage in philosophy at the highest levels.
Even if you are not interested in philosophy, studying fallacies will help you better evaluate all kinds of arguments, including your own crazy ideas. Indeed, I encourage you to turn your developing ability to critique arguments unto your own ideas and arguments, and I believe it will most likely lead to humility (i.e. Socratic wisdom) and a better life. As a side note, the fallacy I am most guilty of is cherry picking. Indeed, we are all human and recognizing our fallacious tendencies and cognitive biases can make us more human.
Finally, I provided a list of popular informal and formal fallacies in the appendix. A brief definition is included next to the name of each fallacy. These lists are helpful to have in your hand as you work through the end of chapter questions or as you try to determine which fallacy your mother is committing when she tells you to “get a job or move out.”
Surely, it’s a false dilemma.
1. Appeal to Nature Fallacy
Definition
We infer something is good because it is natural or something is bad because it is unnatural. The naturalistic fallacy has other meanings, but we will focus on this meaning.
Examples
1) It is morally permissible to eat cows and pigs because it is natural. It is natural because humans have the teeth for it, it is part of the cycle of life, or because other animals do it.
2) Some people argue homosexuality is immoral because it is unnatural.
3) It is ok to throw poo because I saw some monkeys throwing poo at the zoo.
4) It is A OK to be promiscuous because science has proven that men are naturally promiscuous.
5) Naaaaa, we shouldn’t help the poor. Survival of the fittest, baby. Survival of the fittest!
Discussion
Even if we could prove the naturalness of eating meat, it would not necessarily be right. To see why, think of the many acts you believe to be both natural and immoral. For example, some biologists believe humans evolved natural predispositions towards rape, aggression, and xenophobia, but it does not follow they think it is morally good to aggressively rape or be xenophobic. I may be naturally violent, but it does not follow that I think it is good to act on those violent instincts. I may be born naturally self-centered, but it does not follow it is good to be self-centered.
Now consider health. Poisonous berries may be natural, but it does not follow they are healthy. Chemotherapy may be unnatural, but it does not follow it is bad.
In short, you think some natural acts are immoral and some moral, so it is logically inconsistent to argue an act is moral simply because it is natural. . . or that an act is immoral simply because it is unnatural.
The vagueness of the term “natural” is another problem with the appeal to nature fallacy. The problem is people disagree about what is natural. For example, people disagree about whether homosexuality, violence, and altruism are natural. Are skyscrapers natural since they are made from natural human minds? In short, “natural” is a vague term that causes confusion.
How to avoid
Do not assume natural is good or unnatural is bad.
Exercise
1. Find examples of natural acts that are good and natural acts that are bad (in your opinion). Next, find examples of unnatural acts that are good and unnatural acts that are bad.
2. Give examples of how the appeal to nature fallacy arises in debates about homosexuality, the environment, euthanasia, or other controversial issues.
3. Imagine an environmentalist argues that we should not interfere with an ecosystem because the natural order is good. Explain why this is an appeal to nature fallacy and how the environmentalist could strengthen the argument.
Some possible answers
Answers for #1
A) Natural and immoral: It may be natural to lie, but I think it is wrong to lie (in most cases).
B) Natural and moral: I naturally feel empathy for the starving child, and I think this empathy is moral.
C) Unnatural and immoral: I think the enjoyment of torture is unnatural for most people, and I also think it is immoral.
D) Unnatural and moral: I may naturally want to strike back in revenge, but I choose the ‘unnatural’ act of nonviolent resistance and love towards my enemy.
Some people miss the point and argue that good and bad are subjective. The point, though, is that it is inconsistent for you to argue goodness can be derived from naturalness since you believe some natural acts are bad. Ethical thinking involves reason giving and referring only to “natural” reasons is fallacious.
2. Common Arguments: Homosexuality is moral because it is natural; Homosexuality is immoral because is unnatural.
Uncommon Arguments: Homosexuality is immoral because it is natural like violence; Homosexuality is moral because it is unnatural.
3. A better argument would consist in showing the unintended and negative consequences of disturbing ecosystems. This would not be based on a vague appeal to naturalness.
2. Black and White Thinking
Definition
This fallacy arises when we illegitimately limit the number of alternatives available.
Example
1) You must be a Republican or Democrat. You are not a Democrat. Therefore, you must be a Republican.
The problem is the options are illegitimately limited; you could be a libertarian, anarchist, or socialist.
The premise for this fallacy is common:
Either support this bill or be unpatriotic. Either buy this car or be unhappy. Either vote for this law or be a Nazi. Either support all forms of abortion or be against all forms. You must support dualism or materialism. Either absolutely prove your point or it is all relative. Strong artificial intelligence is possible now or never. The president is either a genius or an idiot. It is always wrong to lie or it is never wrong to lie. I need an A or my life will be ruined. I am either a success or a failure.
Discussion
It is important to remember that sometimes there really are limited options. For example, the following premises really do present a limited number of alternatives:
1) I am either alive or dead.
2) God either exists or does not exist.
3) 2+2 equals 4 or it does not equal 4.
Keep in mind that people may use different names for the black and white thinking fallacy: false dilemma, false dichotomy, and the either/or fallacy, but they are all pretty much synonymous.
Cognitive therapists call it polarized thinking, and it often arises in therapy. For example, I might believe I am either a complete success or a complete failure, that everyone is for me or against me, or that each person is either entirely good or bad. The therapist can help me see how these fallacious forms of thinking cause destructive emotions. The stoics also recognized this and were, in a way, the first cognitive therapists. In short, logical thinking is one key to mental health.
How to avoid
Think about each situation to identify whether there really are a limited number of options. Do not rely on emotion alone, which often sees in black and white.
Exercise
1. Create or find some examples of this fallacy.
2. For what conscious and subconscious reasons do we artificially limit our options?
3. Is the “us/them” mentality a form of black and white thinking?
4. How could an unethical salesperson use this fallacy to persuade?
Answers
1. Answers will vary.
2. According to Peg Tittle in Critical Thinking: An Appeal to Reason (2011), one reason people fall for this fallacy is because they lack imagination and cannot see more than two alternatives. Another reason people use this fallacy is to make it seem as though there is only one opposing and awful solution. If that is the only option, then any other solution looks good in comparison!
3. Arbitrarily dividing the world into superior us and inferior them is the source of much evil and suffering. One of the causes of this type of thinking is seeing others as entirely good or bad.
4. Answers will vary.
3. Ad Hominem Fallacy
Definition
Ad Hominem is Latin for "to the man." This is when we try to disprove a conclusion by criticizing the person or the person's circumstances instead of the argument.
Examples
1) Some argue Catholic Priests are pedophiles, so their beliefs about God must be false.
2) Your argument against eating meat is bad because you hypocritically eat meat.
This is an ad hominem fallacy because your hypocrisy has nothing to do with the logical structure and content of your vegetarian argument.
3) One of my students dismissed a conclusion by observing that environmentalists are “long-haired potheads who live in carbon-emitting Volkswagon campers.”
Discussion
It is important to understand that an insult is not an ad hominem fallacy. The insult becomes a fallacy only when we erroneously infer a conclusion from the insult. For example, if I argue "Clinton’s law is bad because he is a jerk who cheated on his wife," then I have argued in a fallacious way. The problem is his cheating has nothing to do with the law. In general, the problem with the ad hominem fallacy is “the attacked person's circumstances or actions do not usually affect the conclusion” (Parker & Moore, 2009).
There are various types of ad hominem arguments (e.g. circumstantial, abusive, guilt by association, poisoning the well, ad feminin, Tu quoque), but what they have in common is they illegitimately focus on the person instead of the argument.
How to Avoid
Focus on the evidence and argument, not the person’s negative (or positive) qualities.
Exercise
1. Identify ad hominem fallacies in a political debate. Remember, not every insult is fallacious.
2. When is an ad hominem approach not fallacious? That is, when is a person's character or circumstances relevant to the conclusion?
Answers
1. Answers will vary.
2. In a courtroom, the character of the witness is relevant because the jurors need to know whether they can trust the witness’ testimony. Focusing on character defects weakens any claim based on the trustworthiness of a witness.
4. Genetic Fallacy
Definition
The genetic fallacy arises whenever we dismiss a claim or argument because of its origin or history.
Examples
1) You cannot believe Bob’s idea because it came from his dream.
2) The psychologist says Tim believes in God because Tim lost his father at a young age. So, God doesn’t exist.
3) That is not possible because he got the idea from a science fiction film.
4) Volkswagons are poor cars because the Nazis created them.
5) Slavery is wrong because my culture taught me it was wrong.
Discussion
Here is an example of a genetic fallacy I recently read in a student paper:
6) God does not exist because people are raised to believe in God.
While this is an interesting hypothesis about the origin of belief in God, it is irrelevant to whether the arguments for God's existence are strong. After all, I may have been raised to believe the Pythagorean Theorem, but the fact that I believe it because of my upbringing does not make the theorem false.
To better understand the problem, imagine Pythagoras created his theorem after smoking a joint. The drug-induced origin does not make the idea false. Just as we can examine the mathematical proofs for Pythagoras' Theorem and ignore the drug-induced origin, so we can rationally examine the arguments for God’s existence and ignore the cultural origins of belief. In short, even if God does not exist, this is not the type of argument you want to use to justify this claim.
Let’s go deeper. The genetic fallacy also arises when a person gives causal reasons to explain away beliefs. The problem is explaining the cause for the claim is usually irrelevant to whether the claim is true. For example, let's say there is evidence that belief in causation arose for evolutionary reasons/causes. I would be committing the genetic fallacy if I argued belief in causation is false because evolution caused this belief. The evolutionary explanation is only helpful in such debates if I already have strong and independent arguments against causation.
So, the genetic fallacy often arises when people confuse reasons with causes. To understand the difference, notice that the cause of your deducing “All As are Cs” from “All As are B's” and “All Bs are Cs” is brain activity. Let's say the cause of this operation is "Q Fibers firing" in the brain.
However, your reasons for believing “All As are Cs” are the two premises and their logical relation (i.e. “All As are Bs” and “All Bs are Cs” implies “All As are Cs”). It is important not to confuse reasons and causes because the neuroscientific causes of my deduction are irrelevant to the logical operations of my deduction. The relationship between reasons and causes is complex, but the point is that we do not usually prove or disprove a belief by identifying its cause. To think otherwise is to commit the genetic fallacy.
How to avoid
Focus on the arguments, not on the origin or history of the arguments. Remember that a bad source does not make an argument bad. Only false premises or a faulty inference make an argument bad.
Exercise
1. Are the following genetic fallacies?
a) Volkswagon Beetles are poor cars because the Nazis created them.
b) Kekule has an interesting theory about the ring structure of Benzene, but it cannot be true because he got the idea from a dream.
c) “Your honor, we cannot trust Bob’s testimony because several psychiatrists have diagnosed him as a pathological liar, and records show he lied under oath in several other cases.”
2. Why do people fall for this fallacy?
Answers
1. The first two are genetic fallacies; the third is not fallacious.
2. This fallacy arises because even intelligent people confuse a) reasons with causes, b) psychological with logical explanations, and C) sources with arguments.
5. Slippery Slope
Definition
This is when we argue A will cause B, and B will lead to undesirable C. Since we do not want C, we should avoid A.
All slippery slope fallacies present a chain of reasoning in which the first step leads to others, but no good justification is given for why the first step will lead to the others.
Examples
1) If I loan you a dollar today then you will eventually ask me for ten dollars and then one hundred dollars. I do not want that to happen, so I cannot give you the one dollar loan (Law, 2003).
2) Humans will eventually be marrying trees and raccoons if we allow homosexual marriage.
3) All types of murder will become legal if we legalize voluntary active euthanasia.
4) I must accept the existence of soul if I believe some form of dualism.
Notice the slippery slope could be much longer (A leading to D and E) or shorter (A leading only to B).
Search Youtube for “Direct TV Commercials” to find several humorous slippery slope commercials.
Discussion
It is important to remember that all above examples are good arguments if there is good evidence for why A will lead to B, B will lead to C, and so on. It is only a fallacy if I do not give good reasons for why this slide will occur, or if there are no good reasons for why the end of the chain is undesirable.
In short, not every slope is fallacious.
Exercise
1. Give an example of a slide/slope that is not a slippery slope fallacy.
2. Create or find a few examples of the slippery slope fallacy.
3. Read the following argument and discuss whether it is a slippery slope fallacy. "If we let the communists take Vietnam, they will then take Laos, Cambodia, and much of the eastern world. Communism will continue to spread across the world until it is on our borders thereby posing an immediate threat to our security. Therefore, we shouldn’t let the communists take Vietnam."
Answers
1. If I push the domino, it will fall and hit the second. The second will fall and hit the third, and so on.
2. Answers will vary.
3. Answers will vary. This debate occurred in the 1960s and illustrates how people can disagree about whether a slide is legitimate or fallacious.
6. Argument from Ignorance
Definition
This is when we illegitimately appeal to ignorance to support a conclusion. It usually takes the following form: “No one has proven not A, therefore A is true.” It may also take this form: “No one has proven A, so A is false.”
Notice this fallacy is not about an ignorant person; rather it is when we mistakenly believe that something must be false because it has not been proven true, or that something must be true because it has not been proven false.
Examples
1) You cannot prove God does not exist, therefore God exists.
2) You cannot prove God exists, so God does not exist.
3) You cannot prove vegetables are not sentient, so we should treat them as if they are sentient.
4) You cannot prove invisible fairies do not live in my nose; therefore they live in my nose.
5) You cannot prove that we will not create strong artificial intelligence in the future, therefore we will.
6) You cannot prove time travel won't be possible in the future, therefore it will be possible.
Discussion
The point of this fallacy is a claim is not true simply because we cannot prove it false. Also, a claim is not false simply because we cannot prove it true. We cannot usually move from our ignorance (i.e. not knowing) to claims about reality.
However, it is sometimes permissible to argue from ignorance. For example, our court system mandates that a person is innocent until proven guilty. If the prosecution cannot prove he is guilty beyond a reasonable doubt, the jury must conclude his innocence and acquit. In the courtroom, it is permissible to argue, “You cannot prove he is not innocent, so he is innocent.”
Another exception to the argument from ignorance fallacy arises when we test very specific claims. For example, imagine I claim there are three orange trees growing in my backyard. Let’s say you visit my backyard, but do not see any trees. In this case, the absence of evidence is evidence of absence. That is, my inability to show you the orange trees is good evidence for there not being orange trees. It is permissible for you to argue, “You cannot prove there are orange trees in this yard, so there are not any.” So, it is sometimes permissible to argue “You cannot prove A exists, so A does not exist.” In short, it is not a fallacy if there should be evidence in this case, but we do not find it after seriously looking.
The fallacy of misplacing the burden of proof is closely related and arises “when people are misled into thinking they have to disprove a claim, when their opponent should be proving his claim” (Parker & Moore, 2009). Determining who has the burden of proof can be complex, and the burden of proof usually shifts back and forth during debate.
For example, the person making a positive assertion usually has the burden of proof (e.g. the theist who asserts God’s existence). Once the theist presents an argument for God’s existence, the burden of proof is now on the atheist who denies God’s existence. Once the atheist shows what is wrong with the argument or presents a new argument against God’s existence, some or all of the burden shifts back to the theist. And so it continues.
Philosophy of Religion is the field of study that thoroughly and systematically studies the arguments on both sides. Most theists and atheists have poorly reasoned opinions because they have not studied these works; they are not standing on the shoulders of the giants who preceded them.
A digression: If there were a God, why should we expect to know it through physics or the other sciences? Perhaps poetry, art, and metaphor are the only ways to know such a “being”? Is belief in God like belief in orange trees? Also, how can the theist detect purpose if purpose is not empirical?
Philosophy of Religion is fascinating, but one should study logic to do it well. As a sidenote, I believe the strongest argument against God’s existence is a logical argument (the evidential argument from evil), not a scientific one. And I believe the strongest argument for God’s existence is religious or mystical experience, not a scientific argument.
How to avoid
Be skeptical whenever someone attempts to prove a claim by using your inability to disprove one. Be skeptical when people use a lack of understanding (i.e. ignorance) to make a claim about reality. Be suspicious whenever someone says, “Well, you cannot prove it is not true!”
Exercise
1. Discuss the problems with the following arguments.
a) You cannot prove aliens do not exist, so they do.
b) You cannot prove aliens do exist, so they do not exist.
c) You cannot prove there is a ten foot tall pink elephant in this room, therefore there is one. Assume that 20 people have tested the claim by looking around the room, but only one claims to see the elephant. Is the absence of evidence ever evidence of absence?
d) Let's say we are all sitting around a picnic table and I make the following negative statement, "There is no picnic table here." Who has the burden of proof?
Answers
1. Answers will vary, but it is important to understand that the first two arguments are both the fallacy of arguing from ignorance because both illegitimately argue from a limitation of knowledge to a claim about reality.
The third argument about the pink elephant is not fallacious. This is because there should be evidence if there were a pink elephant in the room. The absence of seeing or feeling the elephant in the enclosed room is good evidence for inferring there is no elephant. In this case, the absence of evidence is evidence of absence.
In the final case, I have the burden of proof even though I am making a negative statement about the table not being there. This demonstrates the complexity of determining the burden of proof. Specifically, it is false that the person making a negative assertion always avoids the burden of proof.
7. Cherry Picking
Definition
Cherry picking is when we look only for confirming evidence for our ideas. We ignore, suppress, do not see, or do not test for disconfirming evidence for our ideas.
Examples
1) A presidential candidate mentioned all the cities where his tax policy decreased crime and failed to mention all the cities where his policy increased crime.
2) A survey of participants in a workout program gets very positive results because only those with positive results responded.
3) To prove cigarette smoking is not harmful to your health, I cite my grandpa, a ninety year old smoker who runs marathons. Anecdotal evidence is often a form of cherry picking.
4) I argue men are shallow by appealing to the men appearing on daytime talk shows.
Discussion
Cherry Picking is also known as the seeking only to confirm fallacy or the fallacy of incomplete evidence, and it is similar to confirmation bias.
Cherry Picking is difficult to overcome because we do it on both a conscious and subconscious level. Many studies suggest we do not believe what we see, rather we see what we believe and seek to confirm our ideas in subtle ways. Being aware of this tendency is the first step in overcoming it. To become more aware of this tendency, study a book on optical illusions or paradoxes.
Consider too an analogy derived from Immanuel Kant.
Imagine every human is born with irremovable green spectacles. They are part of your brain, your apparati, by which you not only view the world, but constitute it.
So, you perceive all as green…. and you are not capable of perceiving anything as “not green” because your brain/spectacles colors all as green. Notice too that you think the greenness is out there in the world because you learn all things must be green from your experience of the world. However, you are mistaken if you believe greenness comes from empirical experience because the greenness comes from the spectacles (the lenses), not the world.
This is an introduction to Kant’s metaphysics, but it also explains how cherry picking may be inescapable. That is, how can I question my ideas if I see the world through my colored ideas? See the Youtube video “An Introduction to Kant’s Critique of Pure Reason” by teachphilosophy for more.
Of course, this is a deep case, and most cases of cherry picking are superficial and avoidable.
How to Avoid
Study optical illusions and paradoxes. Seek out all the data, not just the data that supports your belief. Think about what observations would make your belief false, and then test for them. If you cannot imagine what would make your belief false if it were false, then this is actually a weakness, not a strength, of your belief. See Youtube Video “Falsifiability” and “Introduction to Kant’s Critique” by teachphilosophy.
Exercise
1. Why is the image of picking cherries used to describe this fallacy?
2. Give a few examples of the cherry picking fallacy.
Answers
1. Imagine picking all the red cherries and leaving the undesirable green cherries. In picking cherries, we are picking what we want. In cherry picking evidence, we are only seeing the evidence confirming our position (red cherries) and suppressing the disconfirming evidence (green cherries).
2. Answers will vary. See above examples.
8. Appeals to emotion:
(ad populum, appeal to tradition, apple polishing, outrage, guilt trips, peer pressure, and group think).
Definition
Ad populum (Latin for "appeal to the people") or appeal to popularity is when it is argued a conclusion must be true or good because most people believe it true or good. The argument from tradition is closely related because it is argued a conclusion must be true or good because people have historically believed it to be true or good.
There are many related fallacies that appeal to emotion. In Critical Thinking (2009), Parker and Moore identify several ways to fallaciously appeal to emotion: argument from outrage (inflammatory words followed by a conclusion), apple polishing (flatter person and then offer conclusion), guilt trips (create guilt in people to force acceptance of a conclusion), peer pressure (accept conclusion to get acceptance), and group think (pride of group membership causes the acceptance of some beliefs).
Examples
1) Dualism is silly; you just cannot believe it (appeal to emotion).
2) Most people believe dualism is true, so it probably is true (ad populum).
3) Eating animals is moral because we have been eating them for thousands of years (appeal to tradition).
4) Only very intelligent people like you recognize the truth of relativism and determinism. Or, only people like you are smart enough to know God exists (apple polishing or appeal to emotion).
5. Everyone knows Elvis is alive! (Ad populum)
Discussion
The problem with many of these fallacies is you cannot logically infer what is true from what people believe, feel, or want to be true. If everyone believes the earth is stationary, it would not make it so. If everyone believes the earth is moving, it would not make it so. If most people believe slavery is good, it would not make it so. See my YouTube video on slavery if you have doubts about the last claim
How to avoid
Put aside emotions and examine the evidence.
Of course, avoiding emotional fallacies is easier said than done. The truth is most of us want to be loved and accepted, so we feel enormous pressure to agree with these fallacious appeals to emotion. Also, it is very difficult to examine every issue, so we often end up following the herd at a conscious or subconscious level. I know that if I had lived eight hundred years ago, I would have thought the earth was flat and stationary.
There is also a complex and interesting relationship between emotion and reason. Indeed, it seems recent research suggests reason cannot exist without emotions. Still, our emotions and billions of people can be wrong… and wanting something to be true does not make it so.
Feeling a belief to be true is not usually a good argument for it being true (exceptions include “I feel happy” or “I feel hungry”). The best we can do when logic is required is to attempt to put aside emotions and follow the evidence where it leads.
Exercise
1. Is one ever justified in appealing to emotion? Explain.
2. Create or find a few examples of these fallacies.
Answers
1. Yes. For example, I can infer “I feel sad” from the feeling that I am sad.
Also, the stoics and modern cognitive therapists recognize that many emotions are essentially judgments (or based on judgments). For example, my fear of a lion is based on the judgment that lions can harm. My feeling of loss is based on the judgment that something of value was lost. In short, some people argue the emotion is “in error” if it is based on a false belief.
The relationship between logic and emotion is complex, and we are just beginning our exploration of it. Still, it is clear that most appeals to emotion are fallacious.
2. Examples will vary.
9. Post Hoc ergo Propter Hoc
Definition
Latin for "after this therefore because of this.” This is when we infer A caused B simply because B happened after A.
Examples
1) I ate chili fries in March and had stomach cancer in July. Therefore, the chili fries caused my stomach cancer (Thanks for this example, Steve Hansen).
2) Caveman Bob beat the wall of the cave and the sun reappeared. Therefore, beating the wall of the cave caused the sun to reappear.
3) My wife must be driving the car incorrectly because we never had transmission problems until she drove the car.
4) We raised the tax rate and crime went down, so the tax rate caused crime to go down.
5) We prayed for a Mercedes and then got one. Prayer works!
6) Since I began eating my boogers last month, I haven't been sick. Therefore, eating boogers is like getting a flu shot.
7) Henry received a vaccine and became ill. Therefore, the vaccine caused his illness.
Discussion
It is important to understand that there really might be a causal connection between these events, but we cannot infer there is one merely because one event chronologically preceded another.
The post hoc fallacy is very similar to the axiom that correlation does not imply causation, which is the idea that related variables are not necessarily causally related in a direct way. The crime rate may increase as people watch more violent television, but we cannot infer violent television caused the increase in crime from the correlation alone. Further research is needed.
How to avoid
Create a scientific experiment to test for a causal connection. You can also use the inductive techniques created by philosopher John Stuart Mill to test for a causal connection.
Most importantly, do not assume causation simply because one event precedes another or simply because one event is correlated with another.
Exercise
1. List some superstitions that seem to be based on the post hoc fallacy.
2. Explain what might be the problem with the following reasoning of some scientists in 2009: “HDL Cholesterol is negatively correlated with the incidence of heart attacks. Therefore, you should take HDL-raising medications to decrease your risk of heart attack.”
Answers
1. Break a mirror and have seven years bad luck. It is bad luck to walk under a ladder. Also, getting x after praying for x may be a post hoc fallacy leading to a superstition about the effectiveness of prayer. Prayer might be effective, but this type of argument is poor.
2. This example is from Wikipedia’s article, Correlation does not imply Causation (2012). The problem is other underlying factors like genes, exercise, and diet may be causing both HDL levels and the likelihood of having a heart attack. That is, an HDL medication may simply treat the symptom, not the cause. This is one negative consequence of believing correlation implies causation.
10. Straw Man
Definition
This is when we misrepresent an argument so we can more easily defeat it. Just as a straw man is easier to knock down than a real man, so a distorted version of an argument is easier to defeat than the actual argument.
Examples
1) My girlfriend recently told me I should take out the trash. I responded, "Why do I have to do everything? If I spent my entire weekend doing housework, I wouldn't have any time to watch sitcoms."
This is like a straw man fallacy because I took her claim that I should do something (i.e. take out the trash) and misrepresented it as saying I should "do everything."
2) A student critiqued third trimester partial birth abortions when her opponent was only defending the moral permissibility of first trimester abortions.
3) While discussing animal welfare, a student criticized the claim that we shouldn’t kill living things when the original argument was we shouldn’t kill sentient living things.
Note: sentience refers to an organism’s ability to experience pleasure and pain. It is reasonable to believe a rock is not sentient, but rational people believe dogs, cows, and humans are sentient.
Discussion
In the above examples, each person misrepresented and weakened the original argument thereby making it easier to criticize. Sometimes people intentionally do this and sometimes they simply misunderstand the original argument. Either way, it is the straw man fallacy.
How to avoid
First, be charitable and interpret your opponent’s argument in the strongest way possible.
Second, suspend your disbelief for a moment and try to believe what your opponent believes. Look for the strongest sources defending this position. Yes, this requires imagination and emotional maturity.
Third, remind yourself that many claims are partially true. For example, it may be appropriate to raise taxes in City A, but not City B. Ask yourself whether this idea is applicable to some situations, but not others.
Finally, seek truth, not victory. You may still disagree in the end, but following these steps will help you avoid straw man caricatures of positions you disagree with.
Exercise
1. The straw man fallacy often arises in political debates. Find some examples.
2. Do you think most people intentionally or unintentionally give straw man arguments? Explain your reasoning.
Answers
1. Answers will vary.
2. While people intentionally present straw man arguments, I believe many do it unintentionally. This is because most of us only see the data in support of our position (i.e. confirmation bias and cherry picking). It takes special effort to seek out and see disconfirming evidence for our views. Because of these bad habits, it is easy to misunderstand and then misrepresent opposing views.
It is a bit like looking at Hill’s Old Lady and Young Lady visual paradox (see below). If we clearly see the old lady, it can be very difficult to believe a young lady is also present (and vice versa). For some people, it is difficult enough to seek out and see both ladies, much less alternative political views to the ones they are emotionally attached to and through which they constitute their reality.
[pic]
W.E. Hill’s Boring Figure (Old and Young Lady Puzzle)
11. Relativist Fallacy
Definition
The relativist fallacy arises when we illegitimately argue that “nobody is incorrect because what is true for you is false for me, and we are both correct.” Some claims may be relative, but this fallacy arises when someone relative and objective claims.
Examples
1) “2+2=5” is true for me and false for you.
2) “Arsenic is healthy” is true for me, but false for you.
3) “The earth is flat” is true for me and false for you. So, respect my opinion.
4) “Water is composed of nitrogen and corn” is true for me and false for you.
5) “God exists” is true for me and false for you.
Discussion
Relativism is based on the idea that each culture or person creates their own truth, so nobody is objectively incorrect. Some philosophers are relativists, but they do not subscribe to this crude form of relativism.
Many people new to philosophy are drawn to relativism because they think all answers are equally good since many philosophical questions have no final answer. Well, this is false. Imagine arguing the universe was created by a rabbit because we are not really sure how the universe began. The fact that we do not know (i.e. skepticism) does not mean every opinion is true or strong (i.e. relativism).
Now, some ideas are relative. For example, "Green is my favorite color" may be true for me and false for you, and we are both correct. Many intelligent people believe “Kilts are beautiful” is another relative statement since “beauty is in the eye of the beholder.” Also, Einstein proved time is relative (in a certain sense), and philosophers debate whether morality is wholly or partly relative.
However, not all ideas are relative. The relativist fallacy arises when we apply relativism to objective areas. The examples in the preceding section illegitimately apply a relativistic approach to nonrelativistic (i.e. objective) fields like math, science, and logic.
So, the fundamental problem with relativism is that truth is not determined by what people believe; “Truth is what is the case” (Ruggiero, 2011).
Relativism is a deep philosophical issue that I cannot fully explore in this work, but I hope it is clear that not all opinions are equal. Again, it is fallacious to argue “my opinion is just as good as your opinion because they are simply opinions” or “2+2=4 is true for you, but false for me.” Such statements commit the relativistic fallacy because they confuse opinions with reasoned opinions, skepticism with relativism, and well supported claims with arbitrary claims. To further explore relativism, see my lecture in the ethics course at
How to Avoid
Remember that believing a claim does not usually make it true or good. Even if everyone believed it, that would not make it true or good.
Remember too that we study logic, science, math, ethics, and many other fields because we believe there are better and worse solutions, true or false beliefs, valid or invalid arguments. If crude relativism were true, there would be no point studying these fields because every opinion would be equally true and good. Not even the relativistic philosophers adopt this crude form of relativism.
Exercise
1. What is wrong with arguing logic does not apply to me?
2. Explain why the following claim is objective (i.e. not relative): "God either exists or does not exist."
3. Does having an open mind mean "considering all ideas" or "accepting all ideas?"
Answers
1. It seems contradictory to use logic to argue logic does not apply to me. How can I argue for a position without arguing for it? Am I cutting off the branch I am sitting on?
2. “God either exists or does not exist.” I may not know if God exists, but I know there are only two options: existence or nonexistence.
It is similar to saying “The table in that room either exists or does not exist.” This is objectively true. Even if we cannot open the door or see through a window to verify the table is there, it is objectively true that the table “either is or is not there.”
The statement “God exists” is not made true because someone believes it is true, and the statement “the table in the room exists” is not made true simply because someone believes the table exists. These statements are objectively true or false, even if we cannot determine their truth value.
Many people miss this point at first because they think everyone is right in matters of religion. But this is false. A person’s belief can be incorrect even if nobody knows it to be incorrect. I do not know if the religious or nonreligious folk are incorrect about God’s existence, but I know someone is incorrect since God cannot both exist and not exist.
Finally, do not confuse ambiguity with relativism. The fact that there are different conceptions of God (i.e. ambiguity) does not mean all conceptions are relative. Once two people agree on a certain conception of God, they can then examine the arguments for and against this God’s existence.
3. I think it is best understood as “considering all ideas.” If you accept all ideas, you believe the earth is both flat and round. You believe “It is best to invade Iran” and “It is not best to invade Iran.” Surely, you do not accept all ideas. If you disagree, then you reject my idea that you don’t accept all ideas…. and therefore you do not accept all ideas.
12. Absolutism
Definition
Absolutism arises when we make no exceptions for rules that have exceptions. It is similar to the fallacy of accident.
Examples
1) Bob believes you should never lie. So, he tells the Nazis where the Jews are hidden.
2) A teacher believes a student should never be late. So, she expels a late student without asking the student why she was late.
3) Bob believes it is always wrong to kill, so he lets an assassin kill dozens of defenseless citizens.
4) Politician Paul knows his city needs a tax hike, so he begins to believe that all cities need a tax hike.
5) Akin believes hard work leads to flourishing. Therefore, he thinks starving children in Africa simply do not work hard.
Discussion
We usually think absolutely when we seek simple answers for complex issues. The problem is many issues are complex and ambiguous, and the answer often depends on the situation.
For example, hard work leads to success, but there are situations where you will fail no matter how hard you work (e.g. if you live in an impoverished and war-torn country).
Of course, there may be rules that do not have exceptions. For example, the rule that “any imaginable entity either exists or does not exist” seems to be an absolute rule.
Those who study formal logic may be familiar with some absolute rules, but the point is the absolutist fallacy arises when we fail to make exceptions for rules that have exceptions . . . and most rules have exceptions.
How to avoid
Identify the exceptions for any rule (see Socratic Method Chapter). Also, be patient when exploring complex issues. Do not jump to simplistic answers.
Exercise
1. Create or find examples of the absolutist fallacy.
2. Why are we drawn to absolutist thinking?
Answers
1. Answers will vary.
2. It is simple, clear, and requires less effort (in most cases).
13. Begging the Question (Petitio Principii) or Circular Reasoning
Definition
To beg the question is to assume what we are trying to prove. That is, the conclusion is stated or assumed in the premises.
Examples
1) God exists because the Bible says so, and the Bible is true because it is the word of God.
2) I should knock you on the head because it is right and good to knock persons like yourself on the head.
3) Consciousness is physical because consciousness just is the brain.
4) You can trust John because Sue told me he is trustworthy, and Sue believes it because Bob told her, and Bob believes it because John told him.
5) Of course smoking pot should be illegal! After all, it's against the law!
6) All knowledge is scientific because all nonscientific claims are not really knowledge.
7) Of course the future will be like that past… and scientific laws will continue to operate in the future! After all, past futures have been like past pasts, so future futures will be like the past futures.
Discussion
An argument that begs the question is a valid argument, but it is trivial. For example, if I argue "everyone is selfish because all people are always selfish" then the conclusion validly follows from the premise, but only because the conclusion is simply a rewording of the premise. I have assumed in the premises what I supposedly proved in the conclusion.
The bottom line is you cannot assume what you are trying to prove.
This may seem like a simple fallacy, but very intelligent people fall for complex versions of it. This is illustrated in number 7 above.
Keep in mind that people may use the phrase “begging the question” in different ways. For example, some people mean a premise has been omitted. Sometimes people say “it begs the question” when there is a question that should be part of discussion. For example, in discussing prayer in school, a debater might say, “It begs the question as to what the First Amendment says.” But in the field of Logic and Philosophy, begging the question means arguing in a circle or assuming what you are trying to prove.
How to avoid
Make sure your conclusion is not a mere rewording of your premises. Do not argue in a circle.
Exercise
1. If you could prove Muhammad was a trustworthy man who never lies, would citing the Koran to prove God's existence still be a case of begging the question?
2. Try to construct an argument proving you have free will (that you could have acted otherwise and have some control) without begging the question.
3. Try to prove the external world exists without begging the question. Note: the external world is the world of people, tables, trees, cars, and other things that you believe exist “outside” of your mind.
Answers
1. Answers will vary. Some will argue that “extraordinary claims require extraordinary evidence” and even if he was trustworthy, he may be experiencing some sort of hallucination. So, his claims are probably false. It is interesting to think about when we should and should not trust testimony.
2. Philosophers have presented some interesting arguments. However, most people present circular arguments. For example, “I’m free because, look, I just freely raised my hand,” or “I’m free because I could have skipped class today.”
Some also confuse the different meanings of “free,” which leads to the next fallacy (equivocation).
3. Many beg the question because they argue or assume that our senses can be trusted without giving a good reason why. The fact that other peoples’ senses agree with my senses is not a good reason. It is the ad populum fallacy.
14. Equivocation
Definition
Equivocation is when a word shifts meaning in an argument.
Examples
1) Hot dogs are better than nothing. Nothing is better than Hamburgers. Therefore, hot dogs are better than hamburgers.
This is a popular example, and I do not know the original source. Notice how "nothing" means "no thing" in the first premise, but it means "all things" in the second premise.
2) Feathers are light. What is light cannot be dark. Therefore, feathers are not dark.
Notice how “light” refers to weight in the first sentence, but to color in the second.
3) I cannot freely break the speed limit or fly to the moon. Therefore, I do not have free will.
Notice “free” is being used in two different senses. In the first sentence, “free” means the “ability to do anything.” In the conclusion, “free” means “the ability to sometimes act other than I did.”
4) Something must be done. This bill is something. So this bill must be done (unknown origin).
Notice “something” can mean “an effective solution” or “any solution.”
5) Everyone is selfish because everyone always seeks pleasure.
Notice “selfish” is ambiguous because it can mean “seeking pleasure” or “what you seek pleasure in” (i.e. the object of pleasure).
Discussion
Equivocation is probably the most common fallacy of ambiguity, but there are others: amphiboly, accent, composition, and division. There are many ambiguous words in philosophy (e.g. free, God, knowledge), which lead to the equivocation fallacy and discussions in which people talk past each other.
How to avoid
Precisely define your words and use the same meaning throughout the argument.
Now, I agree that life without ambiguity, equivocation, poetry and intuition would be dull and boring. But this is a logic course, not a course in ambiguity, equivocation, poetry, or intuition.
Exercise
1. Create or find humorous examples of ambiguity in the media.
Answers
Answers will vary:
Mother of Eight Makes a Hole in One.
Dean appears with his wife, Jimmy Carter.
Kids make nutritious snacks.
15. Hasty Generalization
Definition
Hasty generalizations arise when we illegitimately generalize from a nonrepresentative sample. They are the source of many stereotypes.
Examples
1) I've met three redheads and they were all mean, so all redheads are mean.
2) The car that just cut me off is from South Dakota, so all South Dakotans are jerks.
3) Everyone who responded to the survey said the exercise program helped them lose weight. Therefore, everyone who used the program lost weight.
4) I have seen Texans wearing cowboy hats on television, so all Texans wear cowboy hats.
Discussion
The most common type of hasty generalization is generalizing from too small a sample size. For example, it is a hasty generalization to infer all redheads are mean after meeting only three redheads.
However, sometimes it is valid to generalize from a small sample size. For example, I can generalize stoves will burn my hand after experiencing only one stove burn my hand. This is valid because one stove is usually representative of all stoves. You should carefully examine each situation to determine if it is representative.
Also, large sample sizes do not always prevent this fallacy. For example, I might fallaciously conclude that most Americans support the Democratic President because a poll of thousands of Democrats recorded a 70% approval rate. Clearly, this poll is not random and does not accurately represent all Americans since it is only polling Democrats. To avoid a hasty generalization, a large sample size is a good start, but it should also be random and representative.
How to avoid
Do not generalize from small and/or unrepresentative samples.
Exercise
1. Identify a few stereotypes that are probably based on hasty generalizations.
2. Identify some ways to make sample sizes random and representative.
Answers
1. Answers will vary: Italians love spaghetti. Texans wear boots. Philosophers are ugly. Just look at me… oh wait, I am an exception. Yes, that’s it.
2. Answers will vary. Take a statistics course.
16. Composition
Definition
Composition is invalidly inferring the quality of the whole from the quality of the parts.
Examples
1) Hydrogen and oxygen are dry, so water is dry.
2) My organs are not conscious, so I am not conscious.
3) Every player on the team is great, so the team is great.
4) My cells are not free, so I am not free.
5) If we assume everything in the universe has a cause, then the universe itself has a cause.
6) My cells are less than an inch, so I am too.
Discussion
It is important to remember that it is sometimes valid to infer the quality of the whole from the quality of the parts. For example, "Every brick in the wall is entirely white, and there is nothing but bricks in the wall, so the wall is white." Assuming there are only bricks in the wall, this is a good argument.
Since these are informal fallacies, you should be sensitive to each case and how the parts and whole are connected.
How to avoid
Be careful when inferring the qualities of the whole from the qualities of the parts. Be sensitive to each case and how the parts and whole are connected. Sometimes the whole is more than its parts, sometimes it is not. Sometimes it is debatable.
Exercise
1. If the parts are physical, must the whole be physical?
2. Create some examples of the composition fallacy.
Answers
1. This is a difficult and controversial question. Some say yes. They argue the mind is composed of neurons, but the mind itself is not physical. Some dualists argue this is why you can weigh the brain, but not your mind/thoughts.
Others disagree and argue the mind must be physical even if we do not yet understand how.
2. Answers will vary.
Are you ready for the fallacy quizzes yet?
17. Division
Definition
Division is invalidly inferring the quality of the parts from the quality of the whole. It is helpful to think of it as the opposite of the composition fallacy. Composition moves up from parts to whole, and division moves down from whole to parts.
Examples
1) Water is wet, so hydrogen and oxygen are wet.
2) I am conscious, so my organs are conscious.
3) The team is great, so each player on the team is great.
4) I am free, so my cells are free.
5) Assuming the universe does not have a cause, it follows that everything in the universe is causeless.
Discussion
It is important to remember that it is sometimes legitimate to infer the quality of the parts from the quality of the whole. For example, this argument does not seem fallacious as long as we assume there is nothing but bricks in the wall: “The whole wall is white so each brick in the wall is white.”
In short, since this is an informal fallacy, you should be sensitive to each case and how the parts and whole are connected in that case.
How to Avoid
Be careful when inferring the qualities of the parts from the qualities of the whole. Sometimes the whole is more than its parts, sometimes it is not. Sometimes it is debatable.
Exercise
1. If the whole is physical, must the parts be physical?
2. Create or find a few examples of the division fallacy.
Answer
1. I do not know. On the surface, it seems this must be the case. However, are the smallest particles physical? How would we know if they weren’t? Leibniz was a philosopher who attempted to reduce all of reality to nonphysical “monads.”
2. See example arguments.
18. Lottery Fallacy
Definition
The lottery fallacy arises when we invalidly infer x must be designed because x is improbable.
Examples
1) I conclude that Bob must have cheated when he won the lottery because the odds of him winning were twenty million to one.
2) Some argue the teleological argument commits this fallacy because it is argued the universe must be designed because the laws of the universe (or some things in the universe) are so improbable.
Discussion
The fact that Bob won does not mean the lottery was rigged or that Bob was meant to win. Rather, we say Bob was lucky. After all, somebody had to win. Improbability does not always support design.
This fallacy is important in philosophy of religion where it is sometimes argued that the life- sustaining conditions of the universe are highly improbable, so the universe must be designed and that God is probably this designer. It is hotly debated, but this might be a lottery fallacy since some universe had to arise, and we are just incredibly lucky this one arose.
However, at some point, crushing improbabilities do indicate design. For example, I would be suspicious if Bob won the lottery every day for an entire year. I would infer that his is not simply lucky, but has a system to win or is cheating. Do you think this is a good inference or am I confusing independent and dependent probability (i.e. Gambler’s Fallacy)? Whatever the case, people can agree that it is fallacious to infer design from simple improbability.
How to avoid
Understand that something has to happen even if all possibilities are highly improbable. Understand that someone will probably win the lottery even if each person has a very low probability of winning. Be careful about jumping from improbability to design. Study math, probability, and statistics.
Exercise
1. Sometimes it is valid to infer x must be designed because x is improbable. Can you give any examples?
2. How can we tell when the lottery fallacy is applicable?
Answers
1. If I win the state lottery every day for a year (not just once), you should infer design. It is highly probable that I am cheating or that I discovered a successful formula. Or is it?
2. There is no formula, but formulas can help. Again, do the math to calculate the probability of winning the lottery once and compare it to the probability of winning the lottery every day this year. If we do the math correctly, we can get an idea of whether the lottery fallacy is applicable. In short, consult a mathematician.
19. Appeal to Inappropriate or Dubious Authority
Definition
This is when we support a conclusion by appealing to a person who is not an authority on the subject. Or, it is when we appeal to an authority with whom other authorities disagree.
Examples
1) Peace is the best strategy because Einstein said so.
Note: this is fallacious because Einstein was an expert in physics, not political science.
2) You should take those vitamins because Brad Pitt said they are the best.
3) God does not exist because Stephen Hawking said so.
4) God exists because the Pope and Francis Collins said so.
5) Psychiatry is rubbish because Dr. Smith said so.
Discussion
If you appeal to an authority, you should appeal to the appropriate authority. For example, you should appeal to an authority in physics if you are debating a topic in physics. This sounds simple, but many intelligent people confuse areas of expertise.
However, even appeals to appropriate authorities can be fallacious. This is because it is not the person that makes a claim true, it is the evidence and arguments. For example, Einstein did not make space and time relative, he discovered it. It is the evidence he presented that supports claims for the relativity of space and time, not his authority.
How to avoid
One approach is to not trust anything on authority.
Of course, this is very difficult to do because we cannot be experts in everything. And so I trust my doctor on some medical matters, and I trust the community of physicists on other matters. So, the best we can do is carefully research authorities before trusting them.
Exercise
1. Create or find a few examples of this fallacy.
2. List some authorities you trust and explain why you trust them.
Answers
1. See above examples.
2. I trust the computer technician when she diagnoses my computer problems.
I trust my doctor on most issues, but may occasionally seek a second doctor’s opinion.
In Introduction to Logic (2010), Harry Gensler observes that he trusts his calculator and computer for mathematical calculations.
20. Red Herring
Definition
This is when we change the subject or give an irrelevant response to distract.
Examples
1) Bob: You really shouldn’t charge them 30% on their loans. It’s unethical.
Mean Dan: Well, someone else would charge that rate if I didn’t.
*Explanation: The fact that someone else would do it is irrelevant to whether it is ethical.
2. John: KIPP Schools work. Their students score higher on standardized tests, demonstrate emotional intelligence, and get admitted into the best colleges. We should support KIPP Schools.
Mary: Well, I think education should teach people to intrinsically love learning.
*Explanation: Mary is presenting very general ideas about education without responding to the arguments in favor of KIPP Schools.
3. Theist: There must be a God or something transcendent because there is a common transcultural core to all mystical experiences.
Agnostic or Atheist: Well, I just think religious people are hypocrites and that religion does more harm than good.
*Explanation: Whether religious folk are hypocrites or whether religion is harmful is irrelevant to whether mystical experiences are good evidence for the existence of God.
4. Atheist: Studies have shown that religious children are meaner than atheistic children.
Theist: Look, God obviously exists.
*Explanation: The theist is not addressing the studies, but changing the subject. The argument is not about God’s existence, but whether religious children are meaner.
Discussion
Some have suggested the red herring fallacy is derived from the practice of dragging smelly fish (i.e. red herring) along the ground to distract dogs in pursuit of a fox. The dogs with the best noses and training would avoid the red herring scent and continue pursuing the fox. The inferior dogs would pursue the smelly herring instead of the fox.
Whatever its history, this fishy story is a nice way to visualize what happens in the red herring fallacy. We are sometimes like those deceived dogs, being led astray by interesting, but irrelevant, ideas.
You may have noticed the red herring is very similar to the straw man fallacy. This is because both fallacies arise when we avoid the original argument either through misrepresentation (i.e. straw man) or by changing the subject (i.e. red herring).
How to avoid
Repeat and paraphrase your opponent’s argument before responding to it. That is, carefully listen before responding.
Also, If you ever feel tempted to change the topic because you have an inadequate response to an argument, simply say, “I need to think about that argument more” instead of presenting a red herring in the guise of a real response.
Of course, this is easier said than done because we are sometimes prideful and want to win the argument now. Therefore, perhaps the best way to avoid this fallacy (and all other fallacies) is to be humble and emotionally mature.
When studying Philosophy, it is also important to remember that some of the most fundamental and philosophical questions often have contradictory answers, both of which are supported by equally valid arguments (Kant). For example, the question of whether the universe has a beginning or is infinite may be one such question.
I may have a sound argument for a beginning thesis, and you for the infinite thesis. When good reasoning leads to contradictory answers, we should dig deeper and perhaps question Reason itself. In short, it is not always a red herring for someone to “ignore” your argument and present an equally valid and opposing argument. We need to be sensitive to the context of debate to determine whether the red herring fallacy is at work.
Perhaps the best one can do to avoid this fallacy (and all fallacies) is to humbly and carefully listen to opposing arguments and directly respond to the premises or inference of those arguments.
Exercise
1. Give an example of a straw man and red herring fallacy. Explain their similarities and differences.
Answers
1. Answers will vary. See above examples and discussion. Remember, changing the subject is not the same as misrepresenting an argument.
21. Playing God Fallacy
Definition
This is when we argue that we should not intervene in the “natural” course of events because intervening would be playing God.
Examples
People use the playing God defense when arguing against euthanasia, cloning, and embryonic stem cell research. For example, “We should not legalize euthanasia because we would then be allowing doctors to play God.”
Keep in mind that there may be good arguments against these positions, but the playing God argument is probably not one of them.
Discussion
The idea that we should not play God has several weaknesses. First, not everyone believes in God. Second, believers disagree about what God wills. Third, many people who use the “Don’t play God” defense are committing the appeal to nature fallacy. This is because they believe God created everything with a natural purpose and that we should not interfere with that purpose. This seems to be a version of the appeal to nature fallacy since the argument is that not interfering in God's Creation (i.e. Nature) is what makes something good.
While these criticisms are significant, we can identify the central problem with the playing God defense by considering the following questions:
1) Are doctors playing God when they remove a patient’s appendix or cancerous growth?
2) Is the hero playing God when she jumps in front of a car to save a life?
3) Would a future geneticist be playing God if she removed a baby’s cancer-causing genetic sequence?
I think most people will agree that these are morally praiseworthy acts even though they are examples of playing God since each involves interfering with the natural course of events. So, why is it good to play God in these cases, but not others? Reflecting on these cases should help us clarify our moral ideas; it should help us see that we believe it is often good to play God and to interfere in the natural course of events. For that reason, it is fallacious to claim that playing God makes an action wrong.
But maybe you have a different definition of playing God? Well, consider some more objections.
Another problem with the playing God defense is people often present it when no good reasons can be found. That is, it is an emotional and empty response. The following example should clarify:
When I ask people why playing God applies in one case but not another, they give reasons that are different from the playing God defense. For example, when I asked one student why it was wrong to play God in the genetic engineering case, the student responded that messing with the genetic code may lead to unintended consequences.
This is a good point, but notice the student is no longer relying on the playing God argument. The student shifted to a utilitarian argument (a utilitarian argument is one that focuses on net future happiness and suffering). This student really disagrees for utilitarian reasons, not because he thinks the doctor is playing God. His appeal to playing God is empty because he is actually relying on God-independent reasons for why he thinks it is wrong to remove the cancer-causing genetic sequence. His appeal to playing God seems to be an emotional reaction, not a real argument.
Again, let's say there is a God. The appeal to playing God is still weak because we can always ask, "Why does God will x?" When we ask this question, people will give God-independent reasons for why x is good or bad.
To summarize, the playing God defense is fallacious because it is vague, a form of the appeal to nature fallacy, or an empty emotional phrase based on God-independent feelings or beliefs. *They are independent in an epistemological sense.
How to avoid it
Do not speculate about God’s Will. If you believe in God, use the mind, intuition, empathy, and conscience God gave you to discover right and wrong. If you believe in God, this belief can still play an important role, but it seems fallacious to argue it is wrong to play God.
Exercise
1. Playing God is an ambiguous phrase. What are some of the possible meanings of "Playing God?"
2. If playing God is interfering with the natural course of events, are the following acts wrong?
1) A Downs Syndrome Baby is born with an intestinal blockage that will kill him unless the doctors perform a routine operation. The doctors do the operation.
2) 75,000 Americans have their appendix removed each year. Most would die if doctors did not interfere.
3) Conjoined twins are both about to die unless doctors do a surgery that will kill one twin and save the other. They do the surgery thereby killing one and saving the other.
4) Congress passes a law stating everyone must wear a seat belt when driving.
5) A runaway trolley is about to run over and kill five people on a track. You have only one way to prevent this from occurring. You can pull a lever to push the trolley unto a second track where it will only kill one person tied to that second track. You would thereby save a net of four lives. Assuming you cannot escape these conditions, is it wrong to pull the lever to save a net of four lives? Would it be playing God?
Answers
1. We should not:
A) Interfere with the natural course of events.
Problems: What is natural? Appeal to Nature fallacy?
B) Interfere with God’s plan.
Problems: What is God’s plan? Is this a subtle appeal to nature fallacy?
C) Make life and death decisions (take life).
Problem: We often think it good to make life and death decisions. For example, we make decisions about who will be at the top of kidney recipient lists.
D) Make unnecessary life and death decisions.
Problems: What is God’s will? Does God will that you make the decisions (be his instrument) or just sit around and watch the unfolding of events? What makes a choice “unnecessary?”
E) Kill (in most cases).
Problem: Even if this is true, we can discover this through reason. A study of ethics can help one determine in which cases it is and is not permissible to kill.
2. The examples should challenge the idea that it’s wrong to play God. Consider this related question from the ethicist, James Rachels:
“Would it be best to let a comatose person starve to death by removing her feeding tubes (i.e. let die), or is it best to quickly euthanize her (i.e. kill)?”
Again, is it more humane to quickly kill a cow or to let it slowly die from a painful disease?
Sometimes it seems moral to kill, especially when the only alternative is to let Nature take its gratuitous and gruesome course.
22. Non Sequitur:
Non sequitur means “it does not follow.” It is another way of saying “the argument is fallacious” or “the conclusion does not follow from the evidence/premises.”
Chapter 3 Optional Activities
Activity 1: As you read or watch media reports in which arguments are presented, identify the arguments and determine whether they are justified or fallacious. If fallacious, identify the specific fallacy. I ask my students to find 10 fallacies in the media and to share some with the class.
Activity 2: Try my fallacy quizzes on and review this chapter by watching the YouTube Video 22 Common Fallacies by teachphilosophy.
Activity 3: The following sixty simplified arguments are fallacious. Identify the conclusion and premise(s) and then discuss which fallacy is present. Some arguments may contain more than one fallacy depending on your interpretation, but I list the best answers in the key. I also provide answers for every five questions so you don’t have to scroll back and forth too much. Welcome.
1. You cannot prove the multiverse doesn’t exist, therefore the multiverse exists.
2. Although I could have saved the drowning child, I am not blameworthy for letting her die because she would have died if I wasn’t there.
3. According to some evolutionary biologists, males are more promiscuous than females, so you shouldn’t judge Bob for cheating on his wife.
4. You either support this bill or you are unpatriotic. You don’t support it, so it seems you are unpatriotic.
5. God exists because the Bible says so, and the Bible is trustworthy because it is the word of God.
Answers 1-5: 1 argument from ignorance, 2 appeal to nature or playing god, 3 appeal to nature, 4 false dilemma, 5 begging the question.
6. Intelligent consumers shop at Wal-Mart.
7. You should reject the Health Care Bill because its supporters are idiots.
8. Nobody believes dualism anymore, so it must be false.
9. You are either a Christian or an atheist. Which is it? You aren’t Christian, so you must be an atheist.
10. Strong Artificial Intelligence is possible now or never. It’s not possible now, so it will never be possible.
Answers 6-10: 6 apple polishing, 7 ad hominem, 8 ad populum, 9 false dilemma, 10 false dilemma.
11. San Antonio has the best players, so they will surely have the best team and win the championship.
12. If we give homosexuals full legal rights, people will eventually be marrying animals. I don’t think people should be allowed to marry their pets, so I’m against giving homosexuals full legal rights or the ability to marry.
13. It is a good argument, but he is a priest. Therefore, there must be something wrong with the argument.
14. There are evolutionary reasons for why people believe God exists, therefore God does not exist.
15. You got the idea from a science fiction film, so it cannot be true.
Answers 11-15: 11 composition, 12 slippery slope, 13 ad hominem/poisoning the well, 14 genetic, 15 genetic.
16. Of course Free will exists! Only an idiot would deny it.
17. God does not exist because people are raised to believe God exists.
18. They must have weapons because there is no evidence disproving they have weapons.
19. Most people believe God exists, so God probably exists.
20. Drinking a glass of wine each day is good for you, so drinking a bottle of wine each day is good for you (Hurley).
Answers 16-20: 16 ad hominem, 17 genetic, 18 argument from ignorance, 19 ad populum, 20 composition.
21. Most people once believed the earth was not moving, so it’s true that the earth was not moving back then.
22. Cloning is wrong because it is wrong to interfere with what Nature or God intended.
23. Pythagoras got his idea after smoking a joint, so it cannot be true.
24. Legalizing euthanasia will lead to the legalization of nonvoluntary and involuntary euthanasia (i.e. murder). This, in turn, will lead to a devaluing of human life, and a collapse of society. Therefore, we should not legalize euthanasia.
25. Most people believed slavery was good back then, so it was.
Answers 21-25: 21 ad populum or relativist, 22 appeal to nature or playing god, 23 genetic, 24 slippery slope, 25 ad populum or relativist.
26. Every part of the universe has a cause, so the universe has a cause.
27. Those evil Republicans say we should lower taxes, so we shouldn’t lower taxes.
28. Those emotional Democrats say we should raise taxes, so we shouldn’t raise taxes.
29. Consciousness is physical because it just is your physical brain.
30. Whataburger has superior burgers because they are the best.
Answers 26-30: 26 composition, 27 ad hominem, 28 ad hominem, 29 begging the question, 30 begging the question.
31. Americans are overweight. Therefore, Slim Jim (an American) is overweight.
32. The human mind is conscious, so each neuron must have consciousness in it.
33. Every atom is determined, so the human being (composed of atoms) must be determined.
34. Although I understand your arguments for why water is composed of hydrogen and oxygen, I have a different truth. For me, water is not composed of hydrogen and oxygen.
35. All knowledge is scientific because all nonscientific claims aren’t really knowledge.
Answers 31-35: 31 division, 32 division, 33 composition, 34 relativist, 35 begging the question.
36. Stephen Hawking does not believe God exists, so God probably does not exist.
37. “God exists” is true for me and false for you, and we are both correct.
38. I know you say we shouldn’t kill living things, but then it follows that we cannot even kill plants! That’s absurd, so it’s ok to kill living things (note: the original argument was we shouldn’t kill sentient living things).
39. It should be illegal to smoke marijuana because it’s against the law.
40. I know several smokers who lived long lives, so I don’t think smoking causes cancer.
Answers 36-40: 36 appeal to authority, 37 relativist, 38 straw man, 39 begging the question.
41. 2+2=4 if objectively true for you, but it’s objectively false for me because I subscribe to an alternative system of mathematics.
42. I don’t believe in an invisible man in the sky, so I’m not religious.
43. I’m not an atheist because invisible things obviously exist. For example, atoms exist.
44. Since she has been president, the debt has decreased. She’s been a great economic president.
45. If God exists there is good in the world. There is good in the world. Therefore, God exists.
Answers 41-45: 41 relativist, 42 straw man, 43 straw man, 44 post hoc, 45 affirming the consequent. I know it was unfair of me to ask number 45 since you haven’t studied the chapter on formal fallacies yet. I deeply apologize.
46. If God exists there is good in the world. God does not exist. Therefore, there is not good in the world.
47. I understand your argument for why there should be pensions, but I reject it because there are more important problems like the problem of world hunger.
48. I would intervene, but I would then be interfering with the natural order of things.
49. Everyone disagrees on this issue and has an opinion. So, no one opinion is any better or worse than another opinion.
50. It must be a miracle. The chances of me surviving that crash are incredible.
Answers 46-50: 46 denying the antecedent (see formal fallacies chapter), 47 red herring, 48 appeal to nature or playing god, 49 relativist, 50 lottery fallacy.
51. We are wearing our lucky underwear because we win every time we wear them.
52. I would help the drowning child, but the sign clearly says “keep out.”
53. We each create our own reality. That’s my truth.
54. You should never lie or kill. The circumstances don’t matter.
55. There are several policies we can enact to improve the economy. We need change; we need to vote for Paul.
Answers 51-55: 51 post hoc, 52 absolutist, 53 relativist, 54 absolutist, 55 non sequitur.
56. String theory is ridiculous! You don’t believe it, do you?
57. Six months ago, I said that If Denver wins every game then they will go to the playoffs. They must have won every game because they are now in the playoffs.
58. There are two types of people in the world: those who love the Yankees and those who hate them.
59. If a claim cannot be doubted then it is knowledge. Claim X is knowledge so it cannot be doubted.
60. We’ve always done it this way, so we should continue doing it this way.
Answers 56-60: 56 appeal to emotion, 57 affirming the consequent, 58 black and white thinking, 59 affirming the consequent, 60 appeal to tradition/ad populum.
See for more practice… and to save the world from the Death Star.
Can you prove the external world is real without committing fallacies? Check out this video to see.
Chapter 4: The Socratic Method
A mesmerizing video of this chapter is available.
Socrates was one of the greatest thinkers of all time. Since this is a logic text, I will not outline his life, but will instead reduce his way of thinking to a simple and powerful method.
Well, I should say it is simple in theory, but usually difficult to apply. Much of philosophy (and debate) is an application of this method, and no other method is as effective in both humbling and clarifying. Of course, this method is also a good way to test friendships and get yourself killed… like Socrates did.
The Socratic Method is a way of thinking that involves three steps:
1) Give an initial definition or opinion.
2) Ask a question that raises an exception to that definition or opinion.
3) Give a better definition or opinion.
Repeat these steps until you achieve a full understanding of the concept. If you do not achieve this, you will at least achieve rational ignorance (i.e. aporia). That is, you will know what it isn’t and you will know why you do not know (i.e. Socratic Wisdom).
Consider an example:
Step 1 (Define): A triangle is a shape.
Step 2 (exception question): This isn’t a sufficient definition for triangle because there are many shapes that are not triangles (e.g. circles). This definition of triangle includes too much because it does not exclude all non-triangles. Socrates would ask, “Is a circle a triangle?”
Step 3 (new and improved definition): A triangle is a closed figure consisting of three line segments forming three interior angles that add up to 180 degrees.
Notice how challenging this way of thinking is. I can recognize triangles, but it is challenging to sufficiently define them (i.e. to discover their essence). According to Socrates, one does not really know until one can give such definitions. The consequence is that people know very little. To better understand why, try giving sufficient definitions for Justice, Goodness, Truth, Beauty, Love, and Circle.
Now, many people believe that concepts like justice are simply opinions so there is no truth about them. However, the Socratic Method is still valuable because it helps people discover their real opinions about justice. For example, imagine I define Justice as “giving people what belongs to them.” A modern day Socrates would then ask, “Would it be just to give your drunk friend his car keys since the keys belong to him?” My answer is no, which means I do not really think Justice is giving people what belongs to them. Indeed, I now recognize my ignorance. Thanks Socrates!
In short, Socrates did not believe all opinions were equal. Some opinions are tested in this way and some aren’t. Some opinions are based on facts and some aren’t. Some opinions are based on a lifetime of experience and some aren’t. I could go on and on and on…
Exercise and Answers
Use the Socratic Method to test the following definitions/knowledge claims.
1) Knowledge is belief
Answer: Not all beliefs are knowledge. For example, my belief in flying pink elephants is not knowledge. So, Socrates could ask, “Is Paul’s belief in flying pink elephants a form of knowledge?”
2) Knowledge is holding a true belief.
Answer: But I could guess the right answer, and that is not knowledge. Socrates might ask, “What if I really believe x will happen, but I have no reasons for why I believe?” To have knowledge, I need some good reasons for my belief.
3) A fish is an animal that swims.
Answer: Turtles, snakes, dogs, and humans swim. Are they fish?
4) Justice is saving the maximum number of lives.
Answer: Would it be just to steal the organs of a healthy person to save five sick people? Your answer is probably no, so your idea of justice is not simply about saving the maximum number of lives. This definition does not capture all of what you mean by justice.
5) A circle is an enclosed shape
Answer: A circle is an enclosed shape, but a square is also an enclosed shape. Therefore, the definition is too broad. Socrates might ask, “Is a circle a square?”
6) Games are things people play.
Answer: This is a difficult one. Perhaps, there are no necessary and sufficient conditions for something to be a game. See Wittgenstein’s family resemblance. Socrates might ask, “Is a violin a game?”
7) Love is affection towards people that please you.
Answer: Can you love a child with whom you are displeased? If you can, then that definition is too narrow.
8) Love is a feeling of attraction.
Answer: Is it love if I give one hundred dollars to charity even though I don’t feel like it (i.e. I do it solely from a sense of duty)? If so, then love is not just a feeling. Perhaps we should categorize and describe the different types of love (e.g. Four Loves).
9) Michael Jackson was a singer.
Answer: So, Michael Jackson is John Denver?
10) Vampires are people who suck blood.
Answer: So, vampires are phlebotomists?
Application and Value
The Socratic Method reminds us that good ideas take work and are based on rigorous thinking.
It shows us that not all opinions are equal or deserving of respect because some opinions are tested and consistent while others are not. Do you see how Socrates created enemies yet?
Testing your ideas with the Socratic Method will give you more confidence and increase the probability that your ideas are true. It will take you from inside the cave where you recognize triangles and some just acts to the sunlit world outside the cave where you discover the essence of Triangles and Justice. See Youtube Socratic Method by teachphilosophy for more. To learn more about Socrates, check out the cave video or Botton’s concise documentary on Socrates.
Chapter 5: Logical Consistency
A set of statements is logically consistent if they can all be true at the same time. A set of statements is logically inconsistent if they cannot all be true at the same time. It may also be helpful to think of logically consistency as a set of beliefs that do not contradict each other regardless of whether they are true.
When evaluating logical consistency, assume the statements are true and think about whether they fit together like the pieces of a puzzle. That is, consistency is about understanding the relationships between your beliefs, not proving a belief true.
Exercise
Identify the following sets of statements as logically consistent or inconsistent. Explain your reasoning.
Example: All men have blonde hair. I am a man. I have brown hair.
Answer: These three beliefs are logically inconsistent. If the first two statements are true, the third must be false. If the third is true, the first or second must be false. They cannot all be simultaneously true.
1. I am a man. I have brown hair. You have blonde hair.
Answer: Logically consistent. All three statements can be true at the same time.
2. All dogs are brown. Some dogs are not brown.
Answer: Logically inconsistent. They are contradictory statements.
3. Killing another person is always wrong. It is not wrong to kill a person in self-defense. It is also not wrong to kill people in times of war.
Answer: Logically inconsistent. One way out is to change “always” to “usually” in the first statement. As it stands, if the first statement is true, the next two are false and vice versa.
4. Everyone should be tolerant because there is no way to judge another person's beliefs.
Answer: Logically inconsistent. If there is no way to judge beliefs then how can one judge that others should hold tolerant beliefs? Isn’t that a form of judging intolerant beliefs to be bad/incorrect? If “everyone should be tolerant is true” then “there is no way to judge” must be false.
5. Nobody is ever wrong. 2+2=4. Harry is wrong in believing that 2+2=5.
Answer: Logically inconsistent. The first statement contradicts the second two together.
6. This sentence is false.
Answer: Logically inconsistent. If the sentence is false then it’s true; if it’s true then it’s false. It’s logically inconsistent because it’s simultaneously true and false. Perhaps we should make a rule saying that a sentence cannot be self-referential (since it leads to such paradoxes)? This is a famous paradox that you can further research if you so desire.
7. If God exists then Bob is mistaken. Bob is not mistaken. God exists.
Answer: Logically inconsistent. If the second and third statements are true, the first must be false.
8. It is raining. It is not raining.
Answer: Logically inconsistent. If the first sentence is written in one place or time and the second in another place or time, then they are logically consistent. However, most people interpret these two sentences as referring to the same exact place and time.
9. I love beer, and I hate beer.
Answer: Hmmmm. I believe it is logically inconsistent unless the person means they love beer until they experience the consequences, which they hate. My opinion is most beers taste like horse urine.
10. Light is simultaneously both a wave and a particle.
Answer: Logically inconsistent, but why do we suppose the universe must be consistent? Where does consistency originate?
Application and Value
As you do philosophy, you will identify and evaluate many arguments. You should also evaluate the consistency of sets of beliefs/opinions. In short, logical thinking is not just about what can be inferred from premises, it is also about the relationship between your opinions.
Since most philosophers believe truth is logically consistent, they value logical consistency because it is a tool to discover truth. Although consistency is no guarantee of truth since one could create a consistent story that is false, it seems to be a necessary condition for truth.
Of Course, some thinkers believe truth is logically inconsistent. For example, many mystics speak of God in paradoxical language because they do not believe God can be understood in logical ways. They believe logic is best used to show the limits of logic. Understanding your limits is the first step to transcending them. Many existentialists also argue that life is absurd, not logical. Discoveries in modern physics too seem to indicate that we can describe a paradoxical reality, but not logically understand it. Nevertheless, logical consistency is still valued as a way to get at truth. Certainly, anyone who claims to be logical should take logical consistency seriously.
I am eternally grateful to Juliana Baggini and Peter S. Fosi for their lucid chapter on consistency in The Philosopher’s Toolkit: A Compendium of Philosophical Concepts and Methods. Yes, I recommend this book.
Chapter 6: Scientific Problem Solving
Science is a method to discover empirical truths and patterns. Roughly speaking, the scientific method consists of
1) Observing
2) Forming a hypothesis
3) Testing the hypothesis
4) Interpreting the data to confirm or disconfirm the hypothesis
The beauty of science is that most scientific claims can be tested if you have the proper knowledge and equipment.
You can also use the scientific method to solve everyday problems: 1) Observe and clearly define the problem, 2) Form a hypothesis, 3) Test it, and 4) Confirm the hypothesis, or disconfirm it and start over.
So, the next time you are cursing in traffic or emotionally reacting to a problem, take a few deep breaths and then use this rational and scientific approach. Slow down, observe, hypothesize, and test.
Indeed, scientific thinking is not simply something that occurs in laboratories, it can be applied to most of your personal and professional problems. Nor is it simply rationalistic… it requires creativity to generate good hypotheses. It also requires patience and emotional maturity. Ok, enough preaching…. Let’s do some exercises.
Exercise
Explain how you would solve these problems using the four steps of the scientific process.
Example: The fire alarm is not working.
Answer: 1) Observe/Define the problem: it does not beep when I push the button. 2) Hypothesis: it is caused by a dead battery. 3) Test: try a new battery.
4) Confirm/Disconfirm: the alarm now works. If it does not work, start over by testing another hypothesis like “it has a loose wire.”
1. My car will not start.
2. My child is having problems reading.
3. I owe $20,000, but only make $10 an hour.
4. My boss is mean. I want him/her to stop using rude language towards me.
5. My significant other is lazy. I want him/her to help out more.
6-8. Identify three problems where you can apply the scientific method.
Answers: I have no answers for you. You must test and experience what works. No, I will not chew your food for you.
Application and Value
Science is more of a process than a body of knowledge. In our daily lives, we often emotionally react and jump to quick solutions when faced with problems, but following the four steps of the scientific process can help us slow down and discover more intelligent solutions.
In your study of philosophy, you will explore deeper questions about science. For example, are there any forms of knowledge that are nonscientific? Can science tell us what we ought to do? Can logical and mathematical truths be proven in a scientific way? Does introspection give knowledge even though I cannot scientifically observe your introspective thoughts? These are challenging questions that should help you discover the scope of science without diminishing its awesome power.
But the first step in answering these questions is knowing what science is, and this chapter does just that. Again, science is not so much a body of knowledge as it is a method of observing, hypothesizing, and testing. This method is what all the sciences have in common.
Perhaps too science should involve falsifiability, which is a concept explored in the next chapter.
A video version of this chapter is available.
Chapter 7: Falsifiability
A video covering most of this chapter is available.
A theory is stronger when it is falsifiable.
Good scientific theories are testable, but no theory can be completely tested because scientists cannot observe the future or past. This is one reason why Karl Popper proposed that good scientific theories are those that can be falsified in principle. This means a good theory is one in which we can imagine what would make it false. If we can imagine what would make it false then we can, in principle, test it. We may not have the equipment yet, but we can, in principle, test it.
To clarify, consider the following theories that are falsifiable in principle:
Theory 1: There is a planet between Mercury and Earth.
Theory 1 is falsifiable because we can imagine what would make it false. For example, imagine we looked through a telescope in the area between Mercury and Earth. Imagine we did this for years and even traveled there, but never saw a planet. If that happened, the theory would be false. Since we can imagine what would make it false, the theory is falsifiable.
Of course, in reality, Theory 1 is true. When we look through a telescope, we see Venus between Mercury and Earth. So, we can say the theory is falsifiable in principle, yet true in reality. Indeed, we are more justified in believing Theory 1 because we can imagine the conditions that would make it false if it were false, and test to see if those conditions are present.
Theory 2: All swans are white.
This is a good theory because one can imagine what would make it false (e.g. observing a nonwhite swan). Unlike the first theory, this theory also turns out to be false since there are black swans.
Notice how falsifiable theories take risks. We can imagine what would make them false and then test to see if they are false. They are bold theories that dare us to test them. When no tests can disconfirm or falsify them in reality, then we are more justified in believing them. We are more justified in believing them precisely because we know exactly what would make the theory false, but do not find those falsifying conditions in reality.
Now, some theories do not take risks; they are unfalsifiable. This is usually a weakness, not a strength, of these theories.
Theory 3: Nonspatial and nontemporal fairies live inside my nose.
Theory 3 is unfalsifiable because I cannot imagine anything that could make it false. Again, I cannot imagine any test (e.g. looking through a telescope) that would show this theory to be false. Since there is no way to disprove this theory, it is unfalsifiable. Again, this is not a strength of the theory because we cannot really test it. So, most people will not take my fairy theory seriously precisely because it is unfalsifiable.
Theory 4: Everyone is always selfish.
Under some definitions of selfish, this theory is unfalsifiable. If you cannot imagine any conditions where someone could act unselfishly then we cannot test this claim. If we cannot test it, then, arguably, we should not be confident that it is true.
In short, the central idea behind falsifiability is that good theories (especially in science) are testable in some way.
However, there are exceptions. Some philosophers argue some unfalsifiable claims are justified.
Theory 5: I am currently conscious.
There is nothing I can imagine that would make Theory 5 false, but I am more justified in believing that I am currently conscious than I am in believing anything else. I recommend thinking deeply about Theory 5 in order to identify why it is certainly true even though it is unfalsifiable.
There are other exceptions as well, which we will explore in the exercise (e.g. space and time exist, I am conscious, and every possible object either exists or does not exist).
For now, simply remember that a theory is usually stronger if it is falsifiable in principle.
Exercise
Discuss whether the following claims are falsifiable in principle. If they are unfalsifiable, discuss whether one is justified in believing them.
1. For every action, there is an equal and opposite reaction.
2. Everyone is always selfish (i.e. every human motivation is exclusively selfish).
3. There is something beyond the limits of space and time. Or, space and time exist.
4. Invisible gremlins live in my freezer.
5. There is something it is like to be me. That is, I am conscious; I am having subjective experiences.
6. 2+2=4
7. The car is in the garage.
8. For every entity, it either exists or does not exist.
9. God exists.
10. The Earth is 8,000 years old, and humans lived with dinosaurs.
Discussion/answers
1. Yes, Newton’s laws are falsifiable in principle.
2. No, it is not falsifiable in principle because no matter what happens, one could list a possible selfish motivation/interpretation. However, this theory is unfalsifiable only if we use a certain definition of selfish. See “Psychological Egoism: Scientific Evidence” Video on YouTube for a discussion of this point.
3. No, neither is falsifiable in principle. Something outside of space/time cannot be observed and would make no difference to space/time. So everything would be the same regardless of whether the first statement is true or false. The same holds for the second statement (arguably) because, even if there were no space/time, people cannot help but live as if there is space/time. Another way to get at this truth is to argue that observation presupposes space so one cannot prove space exists through observation.
4. No, this is probably unfalsifiable in principle. If one looks in the fridge, I reply they cannot be seen because they are invisible. If one pokes around, I argue they are too fast to be felt/touched. If one cannot hear them, I argue one must believe they exist to hear them. No matter what test is devised, I have an ad hoc reply to save my theory.
5. No, it is not falsifiable in principle. A scientist can infer that you are probably conscious based on brain behavior, but only you know with certainty that there is something it is like to be you. How can you doubt that there is something it is like to be you in the moment you are experiencing something it is like to be you?
6. It seems falsifiable in principle. It seems falsifiable because one could build a building with 2+2=5 math to prove that 2+2=5 is false (since the building would collapse). That is, 2+2=4 works in the real world, and 2+2=5 doesn’t. However, deeper issues about the nature of mathematics may arise in such discussions.
7. It is falsifiable in principle. Go look in the garage. If you see nothing, it is probably false.
8. It is not falsifiable in principle. Logic commands that things either exist or do not exist. What other option could there be? Notice that even though it’s unfalsifiable, it is rational to believe things either exist or do not exist. This is one limitation of falsifiability.
9. God exists is a difficult one because it depends on how you define God. If God is a timeless, spaceless being that is also omnipresent, then there is nothing that could falsify a person’s belief in God. If God is essentially meaning or purpose, then there is nothing that would falsify belief in God since there is no way to measure or test for meaning and purpose. However, if God is a physical being that lives behind some planet, then the belief in God is falsifiable in principle. We can imagine visiting that area to see if God exists.
So, does the unfalsifiablity of belief in God make the belief weak? Not necessarily. After all, “I am currently conscious” is unfalsifiable, but I am more justified in believing that than I am anything else. The key is to think about how God would be known if God existed.
Since people have different concepts of God, some would be testable and some would not be testable. However, a very intelligent theist could defend the unfalsifiability of belief in God in a way similar to how each of us can justify the belief that I am currently conscious.
10. Yes, we can imagine what would make these statements false. The first is probably false if we use techniques like carbon dating and find something older than 8,000 years old. Also, we can calculate the rate at which a river is carving through rock and use its depth to calculate its age. If it is older than 8,000 years old, then it is false. There are many imaginable conditions that would make this false.
Anyway, tests verify that the earth is much older than 8,000 years old.
As for humans and dinosaurs, we can look at the fossil record. If we never find humans living with dinosaurs, the theory is most likely false.
Application and Value
A theory that is falsifiable in principle seems stronger than one that is unfalsifiable in principle (assuming all other qualities of the theories are equal). This is especially true in science.
However, some foundational beliefs seem to be true even though they are unfalsifiable, but it is important to remember that they are not justified because they are unfalsifiable. In short, one can use the falsifiability test to evaluate many claims and theories. If it is unfalsifiable, we need to give very strong reasons for why the theory is justified.
Questions?
I made a video of this chapter for your viewing pleasure: “Falsifiability” by teachphilosophy on YouTube. You can ask me questions there. Or, you can visit my nonspatial castle just west of Austin, Texas and ask me questions in person.
Chapter 8: Is anything impossible?
When I tell friends that some things will always be impossible (or impossible in principle), their first response after smacking me is usually something like the following:
“Many things we thought were impossible are now possible. We thought it was impossible to fly to the moon, but now we can. Nothing is really impossible. To think otherwise is to lack humility.”
However, some “things” may always be impossible. Impossible means something is impossible at some point(s) in time. Always impossible (or impossible in principle) means something is impossible at all points in time. The point of disagreement is whether we can know if anything is always impossible.
At one time, flying to the moon was impossible, but now it is possible. So, flying to the moon is not always impossible.
Some philosophers (e.g. Chalmers) have argued that the subjectivity, intentionality, and privacy of consciousness will always be impossible to explain using science, math, or logic. But how can they say this if we are never justified in claiming something is always impossible?
In short, it is important to consider whether it is rational to believe some things are always impossible because many philosophical debates depend on it.
Exercise
Are any of the following claims always impossible? Discuss/Explain.
1. In the future, I will meet a married bachelor (assume the words married and bachelor will have the same meaning they do today).
2. In the future, it may be possible to round the square or find a triangle with 18 sides.
3. It may be possible for me to both exist and not exist at this exact time and space.
4. In the future, I may be able to visualize an object outside of space (notice visualization presupposes space).
5. In the future, I will use this hammer to produce a beam of light and enlighten my path.
6. In the future, science will fully explain the subjectivity of consciousness.
7. In the future, I will eat 4,000 hot dogs in 20 seconds.
Answers
Some of these statements seem impossible in principle, though there are different reasons for why they seem impossible in principle. Statements 3 and 6 are the most controversial.
Application and Value
We know some things are always impossible because their starting points (or methodologies) cannot handle the qualitatively different nature of the problems they are addressing. For example, the fourth claim is always impossible because visualization presupposes space, so I will never be able to visualize an object outside of space. I could visualize the effects of an extra dimensional world on a three dimensional world, but I could never visualize an actual nonspatial or extradimensional world.
One of the deepest and most important points to think about is the importance of the methodology or tools we use. These methods and tools are like the lenses through which we view the world, and very few people take the time to think about the lenses themselves. Most people assume that what they see through the lenses is reality.
What are these lenses? Well, the lenses, or tools, are introspection, science, math, logic, past experience, and so on. None of the lenses have a monopoly on knowledge.
One genius who explored this theme in depth is Immanuel Kant. Check out my YouTube Video called “Introduction to Kant’s Critique of Pure Reason: Part 1 of 4” on YouTube. I guarantee it will blow your mind.
In short, we may recognize some things are always impossible when we focus on the methods or tools we are using to know.
A video covering some of these concepts is available. A video on consciousness is also available.
Chapter 9: Vagueness and Ambiguity
Whew! The last two chapters were pretty heavy. Let’s do something light… yet important.
Some disagreements are merely verbal, which means clearly defining terms can resolve such disagreements. Vagueness and ambiguity are the most common types of verbal disagreement.
Vagueness refers to a lack of clarity in meaning. For example, “Go down the road a ways and then turn right” is vague because “aways” does not precisely explain how far one should go down the road.
Ambiguity is when there is more than one clear meaning, and it is difficult to choose which meaning was intended. For example, Paul went to the bank is ambiguous because bank could mean a river bank or a financial institution. He was cut could mean he was cut from the team or he was cut by a sharp object. Bank and cut are ambiguous words.
Another example: “The Stool is in the garden” is ambiguous because “stool” could mean “poop” or “chair.” I always confuse the two at Walmart.
Exercise 1: Explain why these statements are vague.
1. I’ll be back later.
2. We should raise taxes on the wealthy.
Exercise 2: Explain why these statements are ambiguous.
1. The new pitcher is great.
2. I am renting the new apartment.
Exercise 3: Are the following statements ambiguous? Discuss/Explain.
1. Mother of eight makes a hole in one.
2. Kids make nutritious snacks.
3. God makes sense.
Answers
I have no answers for you. I have forsaken you. Use the Force, or use the voices in your head.
Application and Value
Precisely define your terms. This will reduce vagueness and ambiguity so that you are not talking past each other.
Logicians have taken this topic much further by identifying several fallacies of ambiguity (i.e. composition, division, equivocation, amphiboly, and accent), distinguishing ambiguity from indexicality, polsymey, and sense generality, comparing syntactic and semantic ambiguity, and exploring deeper issues related to this distinction. Yes, they have gone too far.
An ambiguous and vague video is available for your viewing pleasure.
Chapter 10: Deductive and Inductive Arguments
Ok, so you made it to Chapter 10. Congratulations! If you have been doing the activities as well as the readings, you are developing an impressive and practical logical mind/toolkit. This chapter will deepen your knowledge of Chapter 2 and prepare you for further study in symbolic logic. An extremely helpful and entertaining deductive and inductive video is available.
So, let’s get started with the difference between deductive and inductive.
Section 1: Deductive and Inductive
Can you see the different ways the premises support the conclusion in the following two arguments?
Deductive
All philosophers have a brain.
Bob is a philosopher.
Therefore, Bob has a brain.
Inductive
Most philosophers have a brain.
Sam is a philosopher.
So, Sam probably has a brain.
The deductive and inductive distinction describes how the premises support the conclusion. In deductive arguments, the arguer claims the truth of the premise(s) guarantees the conclusion. That is, it is impossible for the conclusion to be false if we assume the premises are true in a good/valid deductive argument.
In inductive arguments, the arguer claims the premise(s) provide probabilistic support. That is, it is improbable, but possible, that the conclusion is false in good/strong inductive arguments.
Argument 1 is a deductive argument because I am claiming the conclusion must follow if we assume the premises are true. That is, it is impossible for the conclusion to be false if we assume the premises are true. In example 1, it is impossible for the conclusion (i.e. Bob has a brain) to be false if the two premises are assumed true, so it is a good/valid deductive argument.
In Argument 2, it is improbable that the conclusion is false if we assume the premises are true. It is possible, but unlikely, that Sam does not have a brain.
Many websites present misconceptions about deduction and induction, which include the following:
Misconception 1: Deductive arguments always move from general to specific whereas inductive arguments move from specific to general.
Correction: Actually, some deductive arguments move from specific to general claims, and some inductive arguments move from general to specific. I will provide examples in the activity.
Misconception 2: Deductive arguments are based on facts. Inductive arguments are not based on factual premises.
Correction: Actually, the truth of the premises has nothing to do with whether an argument is deductive or inductive. Rather, deduction and induction is all about how the premises support the conclusion if we assume the premises are true. Both deductive and inductive arguments could have false premises.
Misconception 3: Science is only about inductive thinking.
Correction: Actually, science uses both inductive and deductive thinking as I will illustrate in the exercise.
Before concluding, I should add one final clarification. Deductive and inductive refer to how the arguer is claiming the premises support the conclusion. For example, the following is a deductive argument because I am claiming the conclusion must follow if the premises are assumed true:
All whales are mammals.
Shamu is a mammal.
So, Shamu is a whale.
This argument is deductive because I am claiming the conclusion must follow. But, of course, the conclusion does not follow even if we assume the two premises are true, so it is an invalid deductive argument.
Exercise and Answers: Identify the following arguments as inductive or deductive
1. In my experience, most people are happier when they have the Epicurean goods of friends, self-sufficiency, and time for reflection. Therefore, I think you will probably be happier if you focus on getting these three goods.
Answer: Inductive. “Probably” is a clue.
2. You cannot achieve peace of mind until you recognize what is under your control and what isn't under your control, and then not worry about what isn't under your control. What others think of you isn't ultimately under your control precisely because it's their thinking. Therefore, don't worry about what others think of you (Stoicism).
Answer: Deductive. If we assume the premises are true, the conclusion must follow.
3. All tigers are animals. Tigger is a tiger. Therefore, Tigger is an animal.
Answer: Deductive. It is impossible for the conclusion to be false if we assume the premises are true.
4. Humans usually use new technologies in times of war to destroy instead of build. The atomic bomb is a great example. Therefore, we will probably use strong artificial intelligence to destroy in times of war (if we ever invent it).
Answer: Inductive. The arguer is claiming the conclusion probably follows, not that it must follow.
5. We are going to have at least one day in which the temperature rises above 100 in Austin because this has happened in Austin for at least the last 300 years.
Answer: Inductive. An argument generalizing from a sample is inductive because the conclusion is supported in a probabilistic way; the conclusion could be false even if we assume the premises true.
6. Consciousness is either a physical thing or a nonphysical thing. Since it is not a physical thing, it must be nonphysical.
Answer: Deductive. If we assume the premises are true, the conclusion must follow. Of course, you might reject the premise as false, but deduction and induction have nothing to do with the truth or falsity of the premises (or conclusion). Deduction and induction are about how the premises support the conclusion.
7. Since the universe is like a watch, it is probably designed.
Answer: Inductive.
8. There are only two people in this house: Blaise and Catherine. Neither wear glasses. Therefore, Blaise does not wear glasses.
Answer: Deductive.
9. If God exists there is good in the world. God exists, so there is good in the world.
Answer: Deductive. If we assume the premises are true, the conclusion must follow.
10. Many inexplicable phenomena have eventually been explained by science, so consciousness will eventually have a scientific explanation.
Answer: Inductive.
11. Since every action has an equal and opposite reaction, this action will have an equal and opposite reaction.
Answer: Deductive. We aren’t generalizing; rather we are believing a general law is true and then deductively inferring a case from it. Scientists use deduction as well as induction.
12. Which of the two argument types (i.e. deductive or inductive) seem to add something new to the premises? Which seems to have its conclusion contained within its premises?
Answer: Inductive arguments add something new whereas deductive arguments seem to have the conclusion contained within the premises. This definition may help you better understand the distinction between deductive and inductive.
13. “Three is a prime number. Five is a prime number. Seven is a prime number. Therefore, all odd numbers between two and eight are prime numbers” (Patrick Hurley's Concise Introduction to Logic).
Deductive. Notice it moves from particular claims to general claims, so not all deductive arguments move from general to specific.
14. Some people incorrectly define deductive arguments as those that move from general to specific claims (e.g. all apples are red, so this apple is red) and inductive as those that move from specific to general claims (e.g. each apple is red so all apples are red). Examine arguments five & thirteen, and explain why this definition is sometimes incorrect.
Answer: Figure it out.
15. Imagine someone tells you that deductive arguments are based on facts and inductive arguments are based on opinions or observations. Explain why this is a misconception and how you would explain it to him.
Answer: Answers will vary, but both types of arguments could have all the correct facts. Logic is about the quality of inferences, not the truth or falsity of premises. That is, Logic is mostly about the reasoning/inferences from supposed facts, not determining whether the supposed facts actually are factual.
16. Why is the deductive/inductive distinction important?
Answer: The distinction helps us better understand any argument. Is the arguer arguing for a necessary or probabilistic connection between premises and conclusion?
17. In Patrick Hurley's Concise Introduction to Logic, he lists several types of deductive argument: argument based on math, argument from definition, categorical syllogism, hypothetical syllogism, and disjunctive syllogism. He also lists several types of inductive arguments: predictions, analogies, generalizations, argument from authority, argument based on signs, and causal inference. Give an example of each and explain why it's deductive or inductive.
Answer: you will most likely skip this because it involves research. If you want some interactive quizzes, check out .
18. Bob lives in Texas, so he lives in the U.S.
Answer: Deductive.
19. Bob lives in Texas, so he wears a cowboy hat.
Answer: “inductive, it is” Yoda.
20. Bob is taller than his wife, and his wife is taller than his son. So, Bob is taller than his son.
Answer: Deductive.
Value and Application
There are only two ways premises can support a conclusion. The words “deductive” and “inductive” give us a way to talk about these two ways and to thereby better analyze and evaluate any particular argument.
See video for more. Also, deductive and inductive quizzes will be available soon on .
Chapter 11: Logic Vocabulary in one Diagram
For an incredibly lucid overview of this chapter with extra practice, see my YouTube video entitled How to evaluate logical arguments. The second half of the video covers this chapter.
This chapter introduces the technical meanings of the following words: valid, invalid, sound, unsound, strong, weak, cogent, and uncogent. It will help you communicate more clearly with people like me. Interestingly, most people do not use the words listed above in the same way logicians do and this is one reason why logicians are so angry. So, this chapter may decrease the amount of anger in the world.
I know it has been a long time, but do you remember chapter 2? In that chapter, I summarized the two steps for evaluating arguments:
When evaluating arguments, take the following two steps:
Step 1: Assume the premises are true even if you know they are not true. Now ask, “Do the assumed premises provide good reasons for believing the conclusion?”
If not, the inference is poor.
If yes, the inference is good.
Step 2: Are the premises true or reasonable?
And that’s it. So, now let’s attach some vocabulary to it.
Part I: Only deductive arguments are valid, invalid, sound, and unsound.
Let’s say the argument is deductive.
Step 1: Test the inference. if the deductive argument has a good inference, it is a valid argument. If the deductive argument has a bad inference, it is invalid.
Step 2: Test the premises. If the argument is valid and the premises are true, the argument is sound. If the argument is valid and the premises are false, the argument is unsound. Finally, all invalid arguments are considered unsound.
Consider the following argument:
Premise1: All cows are stars.
Premise 2: I am a cow.
Conclusion: I am a star.
Step 1: Test the inference. If we assume the premises are true, the conclusion must follow, so this is a valid deductive argument.
Step 2: Test the premises. In this case, I believe “All cows are stars is false,” so this argument is valid and unsound.
Part II: Only inductive arguments are strong, weak, cogent, or uncogent.
Let’s say the argument is inductive. Again, follow the two steps for testing the inference and premises.
Step 1: Test the inference. If the inductive argument has a good inference, it is a strong argument. If the inductive argument has a bad inference, it is weak.
Step 2: Test the premises. If the inductive argument is strong and has true premises, the argument is cogent. If the inductive argument is strong and has false premises, the argument is uncogent. Finally, all weak arguments are considered uncogent.
Consider the following argument:
Premise 1: The last thirty Texas Governors have been women.
Conclusion: The next Texas Governor will probably be a woman.
Step 1: Test the inference. If we assume the premise is true, the conclusion is probably true, so this is a strong inductive argument.
Step 2: Test the premise(s). The premise is false, so this inductive argument is uncogent. That is, this argument is strong, but uncogent.
So all that intimidating logical vocabulary is not so difficult after all. It all derives from the two ways of evaluating arguments (i.e. testing inferences and testing premises) and the two types of argument (i.e. deductive and inductive).
By the way, if a deductive argument is sound, we do not have to say it is valid because soundness means it is valid and has true premises. Correspondingly, if an argument is cogent, we do not have to say it is strong because cogent means it is strong and has true premises. If you are confused, the examples and diagrams should clarify.
The following diagram nicely summarizes this information; it is derived from Patrick Hurley’s Concise Introduction to Logic:
[pic]
Exercise 1: Evaluate the following deductive arguments as valid, invalid, sound, or unsound.
1. All philosophers are cartoon characters. I am a philosopher. So, I am a cartoon character.
2. All dogs are animals. Lassie is an animal. So, Lassie is a dog.
3. All dogs are animals. Lassie is a dog. So, Lassie is an animal.
4. All phones are people. I am a phone. So, I am a person.
Exercise 1 Answers
1. Valid, unsound
2. Invalid, unsound
3. Valid, sound. Notice that we can simply say the argument is sound because soundness means it is both valid and has true premises.
4. Valid, unsound. If we assume the premises are true, the conclusion does follow, so the inference is good/valid. But, the premises are false, so the argument is unsound.
Exercise 2: Evaluate the following inductive arguments as strong, weak, cogent, or uncogent.
1. Every summer in Texas has averaged at least eighty degrees, so the next summer in Texas will probably average around eighty degrees.
2. Men produced the last 900 movies, so a man will probably produce the next movie.
3. Rex is from Texas and wears cowboy hats. Sam is also from Texas, so he probably wears cowboy hats.
4. The sun has risen every day for as long as we know, so it will probably rise tomorrow.
Exercise 2 Answers
1. The inference is good, so it is strong. The premise is true, so it is cogent. We could say this argument is “cogent and strong,” but since cogent implies strong, we simply say it is “cogent.”
2. Strong, but uncogent since the premise is false.
3. Uncogent because it is weak. Let’s assume the premises about Rex and Sam are true. Still, the conclusion does not follow, the inference is bad (e.g. hasty generalization or weak analogy). So, the inference is weak and, therefore, uncogent.
4. Cogent. If we use “risen” loosely, the premise is true and the inference is strong. So, this is a cogent argument.
*If you are feeling down and need something to cheer you up, watch my “How to evaluate logical arguments” on Youtube. It reviews this chapter and Chapter 2.
Chapter 12: Formal Fallacies
A video covering some of this chapter is available.
Before beginning this chapter, please evaluate the following arguments. If you hate starting chapters with such activities, skip it!
Argument 1: All cats are animals, therefore all animals are cats.
Argument 2: All bears are strange creatures, so all strange people are bears.
Argument 3: All whales are mammals, so all mammals are whales.
Argument 4: If I am happy then I am singing. I am singing. Therefore, I am happy.
Argument 5: If I am taller than Sue, then I am short. I am short. Therefore, I am taller than Sue.
Argument 6: If God exists then there is good in the world. There is good in the world. Therefore, God exists.
Argument 7: If you are correct then pigs are flying. You are correct, therefore pigs are flying.
Argument 8: If goodness rules the world then God exists. Good does not rule the world. Therefore, God does not exist.
In Chapter 3, we explored over twenty common informal fallacies. In this chapter, we will explore formal fallacies. Yay!
Informal fallacies (Chapter 3) are those in which you must examine the content; you cannot tell if it is fallacious by form alone. For example, the composition fallacy is informal because it is sometimes valid to infer the quality of the whole from the parts and sometimes invalid. You must examine the content in each case.
Formal fallacies, on the other hand, are arguments with a bad form or inference. You do not have to think about the meaning of the words, you can see the arguments are fallacious by their form alone. For example, the following argument is fallacious by its form alone:
All A are B, therefore all B are A.
This form of argument is always and absolutely fallacious or invalid. It does not matter what A and B represent (as long as A and B represent different things). Because we can tell by its form alone that it is always fallacious, it is called a formal fallacy.
To clarify, let's plug in some meanings for A and B in the argument: "All A are B, therefore all B are A:"
Argument 1: All cats are animals, therefore all animals are cats.
Argument 2: All bears are strange creatures, so all strange creatures are bears.
Argument 3: All whales are mammals, so all mammals are whales.
Notice all three of these arguments have bad form or, to use the vocabulary from Chapter 2, a bad inference. So, even if we assume the premise is true in each of these arguments, the conclusion does not follow. We do not even need to think about the content to evaluate these arguments because we can immediately see they are fallacious/invalid by their form alone. That is, we do not need to think about the relationship between cats and animals, bears and strange creatures, or whales and mammals because we can immediately see these arguments take the same bad form (i.e. All A are B, therefore all B are A). By the way, this formal fallacy is called “illicit conversion.” You can learn more about it by studying Categorical or Aristotelian Logic, which is the first form of symbolic/formal logic.
Perhaps you can now see one reason why studying symbolic/formal logic is so valuable. It trains you to see arguments in form, so you can more quickly and accurately evaluate their validity. In short, we can say it is always and absolutely invalid to infer "All B are A" from "All A are B" as long as A and B represent different things.
Ok, I started with a clear and easy example. Let's consider a more difficult argument form that often arises on IQ and entrance exams. Such exams may present one of the three arguments below and ask, "Is this a good argument?"
Argument 4: If I am happy then I am singing. I am singing. Therefore, I am happy.
Argument 5: If I am taller than Sue, then I am tall. I am tall. Therefore, I am taller than Sue.
Argument 6: If God exists then there is good in the world. There is good in the world. Therefore, God exists.
Interestingly, over sixty five percent of people mark these arguments as good, but that is incorrect. Now, a person who studies formal logic will know this immediately because these arguments take the same fallacious form called affirming the consequent:
If A then B.
B.
Therefore, A.
So, students of symbolic logic do not have to work out the relationship between singing and happiness in the first argument or think too deeply about Sue's height in the second. Nor will they be distracted by the highly emotional and connotative words in the third argument (e.g. God and goodness). They simply recognize that it takes this invalid form and are done.
Ok, let's look more closely at affirming the consequent.
Consider again the three fallacious arguments.
Argument 4: If I am happy then I am singing. I am singing. Therefore, I am happy.
Argument 5: If I am taller than Sue, then I am short. I am short. Therefore, I am taller than Sue.
Argument 6: If God exists then there is good in the world. There is good in the world. Therefore, God exists.
Can you explain how you would change each to make it a good/valid argument form? Let's focus on argument 1.
One possible answer is to change the second sentence to "I am happy" instead of "I am singing." This changes the argument form to the following:
If A then B.
A.
Therefore, B.
This argument form is called modus ponens and it is always valid. Instead of the fallacious argument, we now have a good argument:
If I am happy then I am singing. I am happy. Therefore, I am singing.
This is a valid argument because the conclusion must follow if we assume the premises are true.
A note on vocabulary: These arguments contain conditional statements, which are "if-then" statements. The antecedent is the part that comes first while the consequent is the part that comes second. For example, "If A then B" is a conditional statement because it is an if-then statement. A is called the antecedent because it comes first (just after "if") and B is the consequent because it comes last (just after "then"). This should help you better understand why this fallacy is called "affirming the consequent."
Ok, so we have now discovered two argument forms. One is fallacious and is called affirming the consequent. The other is valid and is called modus ponens. Let's put them side by side:
|Modus Ponens (always a good/valid form) |Affirming the Consequent (always fallacious) |
| | |
|If A then B. |If A then B. |
|A. |B. |
|Therefore, B. |Therefore, A. |
| | |
|Example: If it is a cat then it is an animal. Fido|Example: If it is a cat then it is an animal. Fido |
|is a cat. Therefore, Fido is an animal. |is an animal. Therefore, Fido is a cat. |
Now, substitute anything you want for A and B. The modus ponens argument on the left will always be valid because the conclusion must follow if you assume the premises are true. But, on the right, the affirming the consequent form of argument is a poor imitation of modus ponens. When we assume the premises are true, the conclusion just does not follow from those premises. Read over the cat example in the box and substitute in your own examples for A and B. You will find this argument form is always fallacious/invalid no matter what A and B represent, as long as they represent different things.
Interestingly, we can now see why some people believe formal logic is absolutist. Modus ponens is always and absolutely valid while affirming the consequent is always and absolutely invalid. No matter what we plug in for A and B, modus ponens has good form or a good inference, and affirming the consequent does not.
Now, remember what we learned in chapter 2. There are two ways arguments can go bad: bad premises or a bad inference/bad form. Formal logic is only concerned with inferences/forms (i.e. validity and invalidity). To drive this point home, consider the following argument:
Argument 7: If you are correct then pigs are flying. You are correct, therefore pigs are flying.
This argument is actually valid, it is not a formal fallacy. I immediately know this is a good form/inference because it takes the form of modus ponens: "If A then B, A, therefore B." A represents "you are correct" and B represents "pigs are flying." Again, this argument and any other argument that takes the form of modus ponens is valid because the conclusion must be true if we assume the premises are true (see last chapter for a review of what validity means).
Now, you might protest and argue "the first premise is false." It is false that "If you are correct then pigs are flying."
This is true, but formal fallacies and formal logic are not about whether the premises or conclusion are true. They are about whether the conclusion really follows when we assume the premises are true. In the vocabulary of chapter 2, formal logic is about inferences or form, not whether the premises are true or not. In the vocabulary of the last chapter, formal fallacies are about validity and invalidity, not soundness or unsoundness.
So, I would reject this argument because it has a false premise and is therefore unsound, not because it is invalid or formally fallacious. Indeed, it is a valid argument.
The important point is formal logic gives us the ability to immediately determine whether an argument is valid or fallacious/invalid. If it is valid, we can then leave the realm of formal logic and think about whether the premises really are true.
Ok, that was long winded. Let's consider two more argument forms.
Modus tollens is a good/valid argument form, but denying the antecedent is formally fallacious. Consider the following chart:
|Modus Tollens |Denying the Antecedent |
|(always valid) |(always invalid) |
| | |
|If P then Q. |If P then Q. |
|Not Q. |Not P. |
|Therefore, not P. |Therefore, not Q. |
| | |
|Example: If it is a cat, then it is an animal. It |Example: If it is a cat then it is an animal. It |
|is not an animal. Therefore, it is not a cat. |is not a cat. Therefore, it is not an animal. |
| | |
By the way, I am now using P and Q instead of A and B, but it doesn't matter what letters you use. I could have used A and B.
Denying the antecedent is always fallacious, it does not matter what P and Q represent. Nor does it matter if the premises are true or false, the form/inference is bad/invalid.
Consider argument 8: If goodness rules the world then God exists. Good does not rule the world. Therefore, God does not exist.
Many people will be confused and distracted by the terms in this argument. But students of formal logic- if they had a good teacher- bypass that because they can immediately see this argument is a formal fallacy, denying the antecedent. Such a person might say, “Even if the premises are true, the conclusion does not follow.” On the other hand, people who have not studied formal logic will ask complicated questions about the nature of god, goodness, and what it means to rule the world. So, what I am trying to sell you is the idea that the study of formal logic is indeed valuable, but most people do not believe it until they actually learn and practice it in the proper way.
So, there you have it. You learned three formal fallacies (illicit conversion, affirming the consequent, and denying the antecedent) and two valid argument forms (modus ponens and modus tollens). When you study the formally fallacious and formally valid argument forms, you are developing a new tool. . . or metaphorically loading new software unto your wet brain. You are learning to see the world in a new way. With this ability, you can more quickly and accurately evaluate most arguments. Also, studying formal fallacies will give you the ability to teleport to distant planets and dimensions, trust me.
So, as you listen to arguments coming from loved ones, the media, your brilliant professors, and so on, take a moment to put the arguments in form. Test the forms and learn the valid and fallacious forms over time. Eventually, you will have the advantage of seeing in form as well as content… you will have an advantage over creatures who only see the world in terms of content and cannot therefore transport themselves into the formal universe full of palm trees and ocean essences.
In Exercise 1 below, you can practice identifying the formal fallacies from this chapter, as well as some informal fallacies from chapter 3. In Exercise 2, you can discover some new formal fallacies. To learn even more formal logic, I recommend watching my Youtube video called “Part 1: Symbolic Logic, the Basics,” and reading Patrick Hurley’s Concise Introduction to Logic or Harry Gensler’s Introduction to Logic. Finally, do not forget to put the arguments you hear every day in form and then evaluate the form before you evaluate the content. Enjoy!
Exercise 1: Evaluate the following 15 arguments. Are they valid or fallacious? If fallacious, is it an informal (Ch. 3) or formal fallacy? An answer key follows.
1. If I'm happy then I'm singing & clogging. I'm singing & clogging. Therefore, I'm happy.
2. I I ace the test, I will ace the course. I aced the course, so I aced the test.
3. If Adam is a man, he is mortal. He is a man. Therefore, he is mortal.
4. If you are correct then pigs are flying. You are correct, so pigs are flying.
5. If God exists, then there is good in the world. There is good in the world. Therefore, God exists.
6. If Bob is washing dishes then Bob is angry. Bob isn't washing dishes, so he isn't angry.
7. If Bob is washing dishes then he is angry. Bob isn't angry, so he isn't washing dishes.
8. My consciousness is physical because my neurons are physical.
9. Every brick in the wall is red, so the whole wall is red.
10. I'm either an absolute success (100) or an absolute failure (0). I'm not an absolute success, so I must be an absolute failure.
11. Well, I don't believe cigarettes are harmful. After all, my grandpa smoked and drank for over 80 years and lived to be 100! My uncle, on the other hand, exercised every day and didn't smoke. He died at the age of 40. I wish people would be more logical & use their brains. Fools!
12. According to the Theory of Evolution, the fittest creatures will survive. Therefore we shouldn't make special efforts to feed the poor. If they can't survive on their own, that just means they aren't as fit as us. It's nature's way of weeding out defective human models.
13. If you don't work hard, you will be poor. Since Mary is poor, it's obvious she doesn't work hard.
14. Everybody knows vaccines are dangerous.
15. All clowns are dangerous people, so all dangerous people are clowns.
Answers to Exercise 1
1. Formal fallacy, affirming the consequent
2. Formal fallacy, affirming the consequent
3. Valid argument, modus ponens
4. Valid argument, modus ponens. Again, it's valid because the form is good. I still reject the argument as unsound because I believe the first premise is false.
5. Formal fallacy, affirming the consequent.
6. Formal fallacy, denying the antecedent
7. Valid argument, modus tollens.
8. Informal fallacy, composition.
9. Good argument, does not seem to be a composition fallacy since all the parts of the wall are red and redness seems to transfer from the parts to the whole.
10. Informal fallacy, black and white fallacy (also called false dilemma, false dichotomy, polarized thinking, or the either/or fallacy).
11. Informal fallacy, cherry picking.
12. Appeal to nature fallacy. Do you think this fallacy is formal or informal? Can we ever infer goodness from naturalness alone?
13. Formal fallacy, affirming the consequent
14. Informal fallacy, ad populum.
15. Formal fallacy.
Exercise 2: Discovering Formal Fallacies Activity
The purpose of the chart below is to help you discover formal fallacies and think in form. On the right, I listed valid arguments. On the left, I listed corresponding formal fallacies. Your job is to
1) Explain why the arguments on the right side are always valid and those on the left are always fallacious or invalid.
2) Complete any missing boxes.
3) Create example arguments for each form.
*This is a partial list of the formal fallacies.
|Formal Fallacy |Good/Valid Argument Form |
|1. Affirming the consequent |1. Modus ponens |
|If A then B. |If A then B. |
|B. |A. |
|Therefore, A |Therefore, B. |
|2. Illicit conversion |2. |
|All A are B. So, all B are A. |All A are B. So, some B are A (be careful about a|
| |fallacy called the existential fallacy). |
| | |
| |Conversion |
| |No A is B, so no B is A |
|3. Denying the antecedent |3. Modus tollens |
|If A then B. | |
|Not A. | |
|Therefore, not B. | |
|4. Undistributed middle |4. Create or research a name |
|All A are B. |All A are B. |
|All C are B. |All C are A. |
|Therefore, All A are C. |Therefore, All C are B. |
|5. Illicit minor |5.Create or research a name & argument |
|All A are B. | |
|Some C are not A. | |
|Therefore, some C are not B. | |
|6. Illicit Major |6.Create or research a name and argument |
|All A are B. | |
|All B are C. | |
|Therefore, All C are A. | |
Application and Value
Studying formal logic (i.e. the forms of arguments) will help you more quickly and accurately evaluate all arguments.
It will also give you the ability to teleport to distant planets and dimensions, such as Plato’s Formal Realm. To continue your study of formal logic, pick up a text like Hurley’s Concise Introduction to Logic.
Appendix
Short and Handy List of Common Fallacies
1. Naturalistic fallacy: we infer something is good because it is natural, or something is bad because it is unnatural.
2. Black and white thinking: we illegitimately limit the number of alternatives available.
3. Ad hominem: we try to disprove a conclusion by attacking the person or the person's circumstances instead of the argument. An insult alone is not an ad hominem fallacy.
4. Genetic fallacy: we dismiss a claim or argument because of its origin or history.
5. Slippery slope: we argue we shouldn’t do action A because A will lead to B, and B will lead to undesirable C. Since we do not want C, we should avoid A. All Slippery Slope fallacies present a chain of reasoning in which the first step leads to others, but no good justification is given for why the first step will lead to the others.
6. Argument from ignorance: we illegitimately appeal to ignorance to support a conclusion. It usually takes the following form: “No one has proven not A, therefore A is true.” It may also take this form: “No one has proven A, so A is false.”
7. Cherry picking: we look only for confirming evidence for our ideas. We ignore, suppress, do not see, or do not test for disconfirming evidence for our ideas.
8. Appeal to popularity (ad populum), appeal to tradition, appeal to emotion, argument from outrage, and other appeals to emotion: we argue a conclusion is true or good because most people think so, or we appeal to emotion alone to support a conclusion.
9. Post hoc ergo propter hoc: we infer A caused B simply because B happened after A. Post Hoc ergo propter hoc is Latin for "after this, therefore because of this.”
10. Straw man fallacy: we misrepresent an argument so we can more easily defeat it. Just as a straw man is easier to knock down than a real man, so a distorted version of an argument is easier to defeat than the actual argument.
11. Relativist fallacy: I argue that nobody is incorrect on any issue because what is true for you may be false for me, and we are both correct.
12. Absolutism: we make no exceptions for rules that have exceptions.
13. Begging the question (Petitio Principii) or circular reasoning: we assume what we are trying to prove. The conclusion is stated or assumed in the premises.
14. Equivocation: A word shifts between multiple meanings in an argument.
15. Hasty generalization: we illegitimately generalize from a nonrepresentative sample.
16. Composition: we invalidly infer the quality of the whole from the quality of the parts.
17. Division: we invalidly infer the quality of the parts from the quality of the whole.
18. Lottery Fallacy: we invalidly infer x must be designed because x is so improbable.
19. Appeal to Inappropriate or dubious authority: we support a conclusion by appealing to a person who is not an authority on the subject. Or, it is when we appeal to an authority with whom other authorities disagree.
20. Red herring: we change the subject or give an irrelevant response to distract.
21. Playing God: we argue that we should not intervene in the “natural” course of events because intervening would be playing God.
22. Non sequitur means “it does not follow.” It is another way of saying “the argument is fallacious” or “the conclusion does not follow from the evidence/premises.”
23. Fallacy Fallacy: we mistakenly think a conclusion must be false because that particular argument for the conclusion is fallacious.
24. Affirming the consequent: If A then B. B. Therefore, A. This is a poor imitation of modus ponens.
25. Denying the antecedent: If A then B. Not A. Therefore, not B. This is a poor imitation of modus tollens.
26. Illicit conversion: All A are B, so all B are A.
27. Undistributed middle: All A are B. All C are B. Therefore, All A are C.
Formal fallacies: numbers 23-26 and, arguably, number 1
Informal fallacies: numbers 2-22.
References and Further Reading
Thank you for reading my book. I have links to all of my recommended readings on my recommended readings page at You can also find me on my YouTube Channel where I will continue to produce educational videos. If you enjoyed this book, please leave a review or join my email list at
The Philosophy Gym, Stephen Law
This is a lucid and concise topical introduction to philosophy. It is one of the sources I use in my introductory classes, and it is a good way to “work out” your logical mind. If you disagree with the author in some chapters, that is a good sign!
The Story of Philosophy, Will Durant
This history of philosophy is the first philosophy book I read. It is beautifully written, I highly recommend it.
The Elements of Moral Philosophy, James Rachels.
This is a good short starting point in your study of ethics. Yes, logic is important in ethics.
A Concise Introduction to Logic, Patrick Hurley
This is a thorough introduction to logic and symbolic logic. To save money, use an earlier edition. Many university symbolic logic courses use this text.
Introduction to Logic, Irving Copi
This book is similar to Hurley’s and some schools still use it.
Introduction to Logic, Harry Gensler
This is an unusually interesting introduction to formal logic. Gensler uses interesting philosophical arguments to illustrate logical concepts.
The Philosopher’s Toolkit, Julian Baggini
This is an excellent overview of fundamental philosophical concepts and tools (e.g. falsifiability, thought experiments). It is an excellent reference to have nearby in case of emergency.
Critical Thinking, Moore and Parker
This is a popular introduction to informal logic, and just a wee bit of formal logic. The authors also attempt humor.
Critical Thinking, Kirby and Goodpaster
This interesting text covers informal logic and creative thinking, as well as critical thinking.
Introducing Philosophy, Robert Solomon
This is one of the better introductory philosophy texts that use a traditional textbook approach.
History of Philosophy, Frederick Coppleston.
This is the most detailed history of philosophy and is for the serious philosophy student, the one who wants to spend months or years studying it.
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