avoiding logical fallacies

A fallacy is a mistake in reasoning. The following argument contains no fallacies:
1. If P then Q
2. P
____________
∴ Q
This means that Q is a consequence of P. Another way to say this is that Q follows from P. An example might be:
1. If it rains, the street will be wet.
2. It rained.
______________________________
∴ The street is wet.
Formal fallacies occur when there is a problem with the form or structure of the argument. Below is a formal fallacy called “affirming the consequent”:
1. If P then Q
2. Q
___________
∴ P
This fallacy is so named because the consequence (Q) is placed before instead of after the cause (P). An example of this might be:
If it rains, the street will be wet
The street is wet.
____________________________
∴ It rained.
Where there are other reasons for the street to be wet (a broken water pipe, a police water cannon, a dog marking its territory, etc.)
Informal fallacies occur when the structure or form of the argument is correct, but there is a problem with one or more of the premises. For example:
  • one or more of the laws or propositions from which the fallacy attempts to deduce the conclusion is actually incorrect (e.g., “The world is flat, and the world is finite, so if I sail West far enough I will fall off it”);
  • one premise may not actually follow from another (e.g., “The world is round, and India is to the East, so if I sail west far enough the first thing I reach will be India”).
Examples
The three fallacies below are very common in ENG 101 essays (implicit premises in grey, explicit premises in blue, conclusions in red, ∴ = “therefore”):
1. Appeal to Authority – using support from a source as proof without giving your own evidence or arguments, e.g.:
“It is undeniable that, as Aristotle states, a person’s level of happiness can only be judged after their death.”
 
1. If a philosopher makes a statement about life, it is correct.
2. Aristotle states that a person’s level of happiness can only be judged after their death.
__________________________________________________________________
∴ A person’s level of happiness can only be judged after their death
2. Personal Assurance – appeal to personal authority! This often happens when a writer tries to informally agree or disagree, e.g.:
“Aristotle states that a person’s level of happiness can only be judged after their death. I completely agree with this.”
1. If I agree with a statement it is correct.
2. Aristotle states that a person’s level of happiness can only be judged after their death.
3. I agree with Aristotle.
____________________________________________________
∴ A person’s level of happiness can only be judged after their death
Correction for 1 and 2: Instead of appealing to Aristotle’s authority, or our own, we need to offer additional proofs or reasons to persuade our readers, e.g.:

“As Aristotle also argues, because happiness is the work of a whole lifetime, and because it must include all goods, such as professional success, material wealth, physical and mental health, a loving family, a variety of trustworthy friends and successful children (and grandchildren), then we can say that a person’s level of happiness can only be judged after a completed life, that is, after a person’s death.”

3. Straw Man – misrepresenting an argument as a “false target” through misunderstanding or exaggeration, e.g.:

“Aristotle states that a person’s level of happiness can only be judged after their death. Therefore, according to Aristotle, if we die, we will become happy. Therefore Aristotle must have believed in heaven but not in hell, which is rather silly.”

1. Aristotle states that happiness requires a completed life.
2. Aristotle means that after people die, they become happy.
3. Dead people can only be happy in heaven.
________________________________________________
∴ Aristotle believed in heaven but not hell
Correction: Oh dear. Here, the student needs to pay closer attention to Aristotle’s meaning – Aristotle is talking about judgements made by living people about the happiness of the life a person has lived (“we can only call a man happy if …”). He is not talking about the afterlife at all in this section, so the student is criticizing him unfairly, as well as misinterpreting the original argument and inserting his own non-sequitur (“it does not follow”) about heaven.
The following language is useful for talking about fallacies and other logical relationships:
Although x is true, it does not follow that + fs
It is not the case that because [x is true], [y is true].
This leads to the x fallacy, in which + fs
This argument suffers from the x fallacy, in which + fs
The x fallacy occurs when + fs
It is a/n x fallacy to argue that + fs because + fs
The fallacy behind this argument is a/n x, because + fs
This argument is based on the x fallacy, because + fs
A commits the x fallacy when s/he argues that + fs
The x fallacy is the failure to take in to account that + fs
This argument is based on the common x fallacy that + fs
See also: