Logic 101 — Lesson 2 — Fallacies — Propositional Fallacies
Lesson 2
Logical Fallacies
An example of a cool fallacy with a cool name
Two weeks ago, Jeff went to his Aunt Clara’s house for the afternoon. His nick name for Aunt Clara is ‘Mother Earth.” Jeff’s fondest memories of staying with Aunt Clara as a child are of smelling the incredible, herbal smells from her plants and of listening to Jerry Garcia music as he and Aunt Clara played card games and sipped odd looking lemonade. During his recent visit, Jeff noticed that his nose was beginning to run and that his throat felt scratchy. He remembered feeling this way at the beginning of his last nasty cold and was sure he was headed for a week of misery. Aunt Clara immediately recognized his symptoms, walked out into her garden, picked an assortment of herbs, made a tea from the concoction and told Jeff to drink it. She said that he would feel great in about an hour.
Jeff wasn’t sure it would work, but he drank the tea, said good bye and went home. Later that night, his symptoms began to clear up and by morning he felt great. By 8:00 he was on the phone with Aunt Clara asking her for her recipe. “My aunt has discovered the cure for the common cold,” he thought, “and I’m going to be rich.” Jeff got the recipe, went into production and two weeks later was selling his product on line for $14.95 per bottle.
Jeff ‘s cold symptoms went away, but he contracted a severe case of logical fallacy sickness. The most obvious is one of my favorite fallacies, “Post Hoc Ergo Proctor Hoc.” This fallacy is represented by the two hawks in Joseph Spider and the Fallacy Farm.
The truth is that Aunt Clara took in a stray cat two days prior to Jeff’s visit. Had the cat appeared during Jeff’s visit, he could have concluded that his symptoms were due to his cat allergy and not to a cold. Jeff felt much better after leaving Aunt Clara’s house because he was not longer near the cat. Jeff still might get rich on his concoction. Snake oil sales are as strong as ever partly because so few people are able to recognize the Post Hoc Fallacy.
Post Hoc Ergo Proctor Hoc arguments are a member of the Non Causa Pro Causa argument group. All of the fallacies in the group are false cause fallacies. Post Hoc ergo Proctor Hoc’s specific false cause is, this thing happened before that thing, therefore this thing caused that thing to happen. The video below shows a good example and explanation of Post Hoc Ergo Proctor Hoc.
Even Frosty the Snowman commits the Post Hoc ergo Proctor Hoc fallacy…
Fallacies in General
A fallacy is a violation of a rule of logic. We hear them and commit them nearly every day. Some are the result of and an invitation to stupidity like the fallacy above. Some are funny like the one in the next video.
Same are threatening…
Some intend to get you to buy things that you don’t want or get you to do things that are not in your best interest. Logicians have categorized fallacies into informal and formal. Understanding the precise difference between the two requires more background in logic than you currently have if you are getting started. Generally speaking, and with exceptions such as the Begging the Question Fallacy, formal fallacies are associated with problems with Deductive arguments and informal fallacies are associated with problems with Inductive arguments. For the purposes of lesson 2, knowing that there is a division is what is important.
Formal Fallacies
Within formal fallacies, there are seven fallacy categories. For lesson 2, we will explain five of the categories.
Propositional Fallacies
We have already defined logic as rules and structure for correct verbal and written communication. Propositional logic deals with propositions (statements that claim something) and things that connect those statements. Propositional logic finds itself all over graduate school entrance exams. There are several questions on the LSAT, GMAT and GRE exams that test the test taker’s ability to understand and identify propositional fallacies. Consider the following compound proposition:
Will Smith is my favorite actor and Will Smith was the star of the movie, Hitch.
It is a compound proposition because it contains two simple propositions connected with the connector, and. In order for the compound proposition to be true, both of the simple propositions MUST be true. Said another way,
If will Smith is in fact my favorite actor, AND if Will Smith was in fact the star of the movie, Hitch, then the compound proposition is true.
The most frequently studied connectors in propositional logic are:
- Conjunctions “and”
- Disjunctions “or”
- Negations “not”
- Conditionals “only if”
- Biconditionals “if and only if
One key characteristic of propositional logic is it is impossible for the premises of a propositional argument to be true and for the conclusion to be false. The specific Propositional Fallacies are these:
- Improper Transposition
- Affirming the Consequent
- Commutation of Conditionals
- Denying the Antecedent
- Denying a Conjunct
- Affirming a Disjunct
We will deal with Affirming the Consequent and Denying the Antecedent and mention Affirming a Disjunct and Denying a Conjunct.
For the first two propositional fallacies, assume that the following compound is true:
Anyone who gets an A on Mrs. McKinnon’s test had to have studied for hours.
Stated another way, more clearly as a conditional,
If anyone gets and A on Mrs. McKinnon’s test, they must have studied for hours.
If this is true, which of the following must also be true?
- Harold studied for hours therefore, he must have gotten an A on the test.
- Walter got an A on the test, therefore he must have studied for hours.
- Denise did not study for the test, so she must not have received an A on the test.
- Grace did not receive an A on the test, therefore, she must not have studied for the test.
Number one does NOT logically follow from the original conditional. The form of the original conditional is,
if p then q
Number one concludes that, q, therefore p. The logical fallacy committed is called Affirming the Consequent. The way the conditional is written, it is possible to study for hours and get a B on the test or any other grade. It is not possible, to get an A on the test and not study for hours.
Reality Check!
You may say, “Wait a minute! It’s possible for someone to guess on every question on the test and guess right, so it’s not true that you have to study for hours to get an A on Mrs. McKinnon’s test!” You are right. But for the present, we are not concerned with the truth of propositions. We are only concerned with things that we are able to logically conclude from the proposition. We will deal with truth later. For now, it is important to understand logical connections.
Number two is correct and logically follows from the original proposition. Its valid form is,
if p then q
p, therefore q.
Number three is also correct and logically follows from the original proposition. Number three is called a contrapositive and has the following valid form.
if p then q
not q, therefore not p
Number four is wrong. The fallacy is called, Denying the Antecedent. Its form is,
if p then q
not p, therefore not q
The following proposition was placed on Facebook by my friend, Charity Hawkins Dodson,
If my son doesn’t stop barking at me, I’m going to put him the the dog run with the dogs.
Its time to test your skills again. Please indicate whether or not each of the following propositions logically follows from Charity’s Facebook status. If the proposition does not logically follow, indicate whcih fallacy is being committed.
- “My son is not in the dog run, therefore he stopped barking at me.”
- “My son is in the dog run, therefore he must have kept barking at me”
- “My son stopped barking at me, therefore he is not in the dog run.”
- “My son did not stop barking at me, therefore he is in the dog run.”
Answers
Let’s start by diagramming the propositions.
Original
If p then q
Propositon 1
“My son is not in the dog run, therefore he stopped barking at me.”
if p then q (from original)
not q therefore not p.
This is a contrapositive and is a valid logical inference.
Proposition 2
“My son is in the dog run, therefore he must have kept barking at me”
if p then q (from original
q, therefore p
This is an Affirming the Consequent Fallacy. After all, there may be several reasons why the boy is in the doghouse other than continued barking.
Proposition 3
“My son stopped barking at me, therefore he is not in the dog run.”
If p then q (from original)
not p, therefore not q.
This is a Denying the Antecedent Fallacy and does not logically follow from the original proposition.
Proposition 4
“My son did not stop barking at me, therefore he is in the dog run.”
if p then q (from original)
p, therefore q.
This is a valid inference from the original proposition.
Denying a Conjunct
A conjuct is either side of a compound proposition separated by the word, “and.” A Denying a Conjunct Fallacy is committed when it is assumed that because one side of the conjunct is false, therefore the other must be true. Consider the following compound proposition:
Out football team is not both the best team and the worst team,
Our football team is not the worst team
Therefore, our football team is the best team.
The conclusion is invalid because it is possible for our team to be neither the best or the worst.
Affirming a Disjunct
Affirming a Disjunct is a little tricky. The word “or” could mean either “either this or that but not both,” or “this or that and maybe both.” If you apply the second meaning to an disjunctive argument, but you assume the first definition, then you commit the fallacy.
Lesson 2 Fallacies — Probabilistic Fallacies