Logic: Argumentation and Fallacies

I. Sound Argumentation

A sound argument is one that is logically valid (the conclusion follows from the premises) with true premises.

II. Common Fallacies of Meaning

1. Circular: An argument is circular if it presumes the truth of what is to be proved.
2. Equivocation: An argument equivocates if it changes the meaning of a term or phrase within the argument.
3. Red herring: An argument is beside the point if it argues to a conclusion irrelevant to the issue at hand. Straw Man: A straw man argument misrepresents an opponent’s views.

III. Common Fallacious Argument Forms

1. Appeal to the crowd: Most people believe A. Therefore, A is true.
2. Genetic: We can explain why you believe A. Therefore, A is false.
3. Appeal to ignorance: No one has proved A.Therefore A is false. (and vice versa)
4. Post hoc ergo propter hoc: A happened after B. Therefore, A caused B.
5. Composition: This part is F. Therefore, the whole is F. (and vice versa)

IV. Fallacies with Non-Fallacious Forms

Appeal to authority 

Correct form:

1. X holds that A is true.
2. X is an authority on the subject.
3. The consensus of authorities agrees with X.
4. Therefore, there’s a presumption that A is true.

Incorrect forms omit premise 2 or 3, or conclude that A must be true.

Ad Hominem

Correct form:

1. X holds that A is true.
2. In holding this, X violates legitimate rational standards (for example, X is inconsistent, biased, or not correctly informed).
3. Therefore,  X isn’t fully reasonable in holding A.

Incorrect forms use factors irrelevant to rational competence (for example, X is a
member of a hated group or beats his wife) or conclude that A is false.
 
V. Misc Fallacies

1. Black-and-white thinking: Oversimplifies by assuming that one or another of two extreme cases must be true.
2. Hasty generalization: To assume that the members of a certain group are more alike than they actually are.
3. Trick question: A question that assumes the truth of something false or doubtful.

VI. Fallacies of Inconsistency

1. Self-refuting statement: A statement that makes such a sweeping claim that it ends up denying itself.
2. Universalizability: Whatever is right in one case also would be right in any exactly or relevantly similar case, regardless of the individuals involved.