Logical Fallacies

Adapted from Classical Rhetoric for the Modern Student, 2nd ed., Edward P. J. Corbett, Oxford University Press, New York, 1971.

Fallacies of Matter

The burden of proof rests on the one who challenges the generally accepted view of things. ... We can call for and challenge the source of an individual's information, but we will most effectively undermine an assertion by adducing evidence that a claim is false. The next best thing to having the refutative information at our fingertips is to know where we might find the facts that will discredit our opponent's statement.

One point needs to be made very strongly here: mere assertion, on either side of an argument, does not constitute proof.

Half-truth: Everything that is said is true, that is, verifiable as a fact; but because not enough is said, the total picture is distorted. Such omission of details conceals or distorts the context of a situation.

Fallacies of Reasoning

All fallacies of reasoning, whether inductive or deductive, could be classified as non sequiturs -- that is, as conclusions or generalizations that "do not follow" from the premises. A logical fallacy is, at bottom, an instance of incoherence -- the chain of reasoning does not link together.

Induction, Deduction, and the Syllogism

In induction we proceed from the particular to the general. Hence in a scientific demonstration or in logic we arrive inductively at a generalization through observation of a series of particulars. The validity and truth of the generalization will be in direct proportion to the number of pertinent particulars studied. ...

The syllogism was a schematic device that Aristotle invented to analyze and test deductive reasoning. ... The syllogism reasons from statements or propositions. These propositions are called premises. The reasoning follows this course: if a is true, and b is true, then c must be true. [Or: x is y; y is z; therefore, x is z.] ...

The square of opposition presents schematically the four kinds of categorical propositions -- that is, propositions that either assert or deny something, without conditions or alternatives proposed.

The UA-proposition is a universal affirmative. The UN-proposition is a universal negative. The PA-proposition is a particular affirmative. The PN-proposition is a particular negative.

UA UN PA PN

A proposition has either universal or particular quantity and either affirmative or negative quality. The universal and particular propositions are at the top and bottom, respectively, of the square of opposition, and the affirmative and negative propositions are at the left and right, respectively.

• UA is contrary to UN and contradictory to PN.
• UN is contrary to UA and contradictory to PA
• PA and PN are subcontrary to each other.

The valid deductions we can make from the various propositions:

• If UA is true, PA is true; if UN is true, PN is true.
• If PA is true, no deduction can be made about UA; if PN is true, no deduction can be made about UN.
• If UA is true, UN is false; if UN is true, UA is false.
• If UA is false, no deduction can be made about UN; if UN is false, no deduction can be made about UA. [Contrary propositions cannot both be true, but they may both be false.]
• One of a pair of contradictory propositions (UA vs. PN or UN vs. PA) must be true and the other false.
• Subcontrary propositions (PA and PN) can both be true but cannot both be false.

(The law of contradiction is based on the principle that a thing cannot at the same time be and not be.)

Fallacies of Reasoning in Deduction

Equivocation: A term has more than one meaning, and therefore no conclusion can be validly drawn.

Undistributed middle term (y): The link in a chain of arguments is not supplied.

Illicit process: A term in the conclusion is used more generally than it is in the premise(s).

Conclusion from two negative premises: No relationship among all three terms in the syllogistic chain of reasoning is established, and therefore no conclusion can be drawn.

Affirmative conclusion from a negative premise: A negative premise excludes a relationship between terms, so the only conclusion that can follow is one that excludes a relationship between one of those terms and a third.

"Either/Or" fallacy ("black-or-white syndrome"): The alternative terms must be mutually exclusive to make a valid either/or argument.

Fallacy of affirming the consequent: The conclusion simply restates a hypothetical premise.

Fallacy of denying the antecedent: The conclusion simply restates the contrary of a hypothetical premise.

Fallacies of Reasoning in Induction

Faulty generalization ("jumping to a conclusion"): The evidence for the conclusion is inadequate, because the particulars may be irrelevant, unrepresentative, or not numerous enough or derived from an authority that is biased or prejudiced, incompetent, outmoded, misquoted, misinterpreted, or quoted out of context.

Faulty causal generalizations: In arguing from an effect to a cause, the cause may be inadequate or other causes may result in the same effect. In arguing from a cause to an effect, the operation of cause to effect may not be established or the cause may result in other effects.

Faulty analogy ("the analogy does not hold"): Analogies may concentrate on irrelevant, inconsequential similarities and overlook pertinent, significant dissimilarities. An analogy never proves anything; at best it persuades someone on the grounds of probability. It is the degree of probability that is susceptible to challenge.

Miscellaneous Fallacies

Begging the question (circular reasoning): The conclusion is assumed in the premise. Be on your guard whenever you meet expressions like "obviously," "of course," "as everyone knows," "really," "unquestionably."

Argument ad hominem ("to the man"): The argument is switched from a discussion of issues to a discussion of personalities. If we find that we cannot refute someone's argument, we might attack his or her character.

Argument ad populum ("to the people"): This is the tactic of appealing to irrational fears and prejudices in order to prevent audiences from squarely facing the issues. Honorific terms are used to stir up a favorable emotional climate; pejorative terms are used to arouse hostile reactions. None of these terms are "good" or "bad" in themselves. They become "weasel words" when they so color the emotional atmosphere of a discussion that people are disposed to accept as proven what has only been asserted. Appeals to emotions are legitimate -- in fact, rhetoricians maintained that people could not be moved to action unless their emotions were touched -- but appeals to emotions are reprehensible when they cloud the issue, when they anesthetize people's rational faculties, when they move people to do things or accept things which they would not do or accept if their conscience or reason were allowed to operate.

The "red herring" (changing the subject): This is another diversionary tactic of ignoring or avoiding the issue.

The complex question: This is a form of begging the question. A question implies an answer to another question that is not asked. Example: "When did you stop picking your nose?" Instead of answering that, you must insist on answering the implied premise first ("Are you or have you ever been a nose picker?").

See more logical fallacies.