Trivium Pursuit

Formal and Informal Fallacies

Logical Fallacies

A fallacy is a defect in an argument which misleads the mind. The defect may be intentional or unintentional. If the defect is intentional, we sometimes call it a sophism. One’s understanding of fallacies may be used for good — in order to avoid or expose error; or it may be used for evil — in order to subtly deceive.

Ethics of Fallacy Detection

Being mislead by another's reasoning may lead one to be persuaded to follow a foolish and harmful course of action. As Christians are to be as wise as serpents, so they ought to be aware of the false reasonings which are common to man ever since the initial deception by the serpent in the garden. One should sense some moral obligation to be aware of faulty reasonings in order to protect himself from the misleadings of others, and to protect others from being mislead by himself. Above all, it is to the glory of God that we reason correctly, for without correct reasoning we cannot understand His Word, and without understanding we cannot fully and properly obey.

Detection of a fallacy in another's reasoning does not necessarily imply that it is proper to point it out. One can become obnoxious and offensive if he continually picks apart what others say. There are more gracious ways to avoid errors than simply pointing them out frankly, candidly and bluntly. To be sure, there are times to be brutally honest, but such times are less frequent than practiced. One's goal should be to win another to sound reasoning, and winning another often involves more than naked reason — it involves courtesy, consideration, and gentle coaxing. Also, one ought to approach such matters with humility, for fallacy is a malady so common to man that it is certain that the corrector himself is to be found at fault from time to time.

Formal Fallacies

A formal fallacy is one which involves an error in the form, arrangement or technical structure of an argument. The question in view is not whether a conclusion is true or false, but whether the form of the argument is correct or incorrect — valid or invalid.

The concluding statement of an argument may be objectively true, though the argument is formally invalid; or the concluding statement may be objectively false, though the argument is formally valid. Here are some examples:

Formally Valid Arguments:

1. True and Valid:
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.

2. False but Valid:
All men are green.
Socrates is a man.
Therefore Socrates is green.

Formally Invalid Arguments:

3. False and Invalid:
Some men are green.
Socrates is a man.
Therefore Socrates is green.

4. True but Invalid:
Some men are mortal.
Socrates is a man.
Therefore Socrates is mortal.

In example 2, the first statement is false, but the form or structure of the argument is correct or valid. (If all men were green; then Socrates would be also.)

In examples 3 and 4, the first statement says something about some men, not about all men. One could correctly reason from this first statement that Socrates might possibly be green or mortal, but he could not correctly reason that Socrates necessarily is green or mortal.

Formal fallacies are therefore invalid arguments — arguments where the concluding statement does not necessarily follow from the statements preceding it. The concluding statement may actually be objectively true, but it's truth does not depend on or follow from the other statements.

A change in the actual terms used in an argument may affect the actual truth value of the argument, but a change in terms will not affect the validity or invalidity of the argument. All men including Socrates are truly mortal; but all men including Socrates are not truly green. If all men were green, then Socrates would be also! But if only some men were green, then Socrates would not necessarily be green.

Because the terms themselves do not affect validity, we can substitute symbols for the terms.

All men are mortal. All a are b.
Socrates is a man. c is a.
Therefore Socrates is mortal. Therefore c is b.

No matter what terms you may put in the place of a, b, and c, if all a are members of the class called b, and c is a member of the class called a, the c must necessarily be a member of the class called b.

Because there are only a small number of possible relationships between the terms, these relationships can also be represented by symbols. When this is done, the whole form of an argument can be written in symbols. This is called symbolic logic, which is a special branch of the study of formal validity.

Informal Fallacies

Correct reasoning involves clear expression and valid form. Formal fallacies are a matter of invalid form. Informal fallacies are a matter of unclear expression. Formal fallacies deal with the logic of the technical structure, while informal fallacies deal with the logic of the meaning of language. The word "informal" does not here mean it is inferior, casual or improper. It only means that our focus is not on the form of the argument, but on the meaning of the argument.

An informal fallacy involves such things as: the misuse of language — words or grammar, misstatements of fact or opinion, misconceptions due to underlying presuppositions, or just plain illogical sequences of thought.

We encounter both formal and informal fallacies every day, but unlike formal fallacies, we cannot reduce informal fallacies to symbolic formulas. We can, however, compile a list of characteristic profiles of informal fallacies, and arrange them into general categories.

I. Informal Fallacies of Ambiguity

The first general category of informal fallacies we will examine is that which involves the imprecise use of language. Each language has its own "logic" — the way the written symbols or the spoken symbols are arranged to convey certain meanings. When a word or an expression is used in an imprecise manner, a door is opened for a misunderstanding — a fallacy.

A. Equivocation

A word may have more than one distinguishable meaning. An argument may be constructed around the ambiguity of the meaning of that word. If you use one meaning of the word in a premise; then another meaning of the word in another premise, or in the conclusion, you may appear to have proved something.

Example:
Logic teaches you how to argue.
People argue entirely too much.
Therefore we don't need to teach people Logic.

In this "argument" the word "argue" is used in two entirely different senses. In the first line, the word "argue" is used to mean only the process of arranging propositions to flow logically from a premise to a conclusion. In the second line, the word "argue" is used to include such meanings as a heated discussion, a bitter disagreement, a contentious altercation, a dispute or a controversy. A logical argument may sometimes lead to a dispute, or it may sometimes settle a dispute; but there is no necessary connection between teaching logical argument and encouraging people to bitterly argue.

Often a person does not recognize that he is using a term in two senses because the two senses are often very close — yet distinguishable. A gracious way to approach someone whom you think has equivocated is to ask him to define his use of the word in each proposition. If he does not recognize any difference, you may point out the differences — often subtle — which you notice. If he still does not catch on, you may wish to offer an example of your own equivocation in order to humble yourself and thereby disarm any "defense" mechanism which may be kicking in and blinding him. Another possibility which you must consider is that you have invented the equivocation in your mind — it is not real. If you are still satisfied that he has equivocated, you must determine whether the conversation can continue around the point, possibly returning later to the point after other things have been discussed and clarified.

B. Amphibology or Semantic and Syntactic Ambiguity

A variation on the above is when a word, phrase or grammatical construction is used which can be understood more than one way.

  • Example: Lots for sale. (Semantic Ambiguity: Allotments of land or numerous things?)
  • Example: Laurie calls her mother when she's alone. (Syntactic Ambiguity: Who is alone, Laurie or her mother?)

A Semantic Ambiguity can be removed by defining the ambiguous word or by offering a synonym. A Syntactic Ambiguity can be removed by reconstructing the sentence.

Some Amphibologies may be deliberate.

  • Example: "What I have written, I have written." (John 19:22)

Pilate states a fact, that he had written the inscription of condemnation on the cross; then he declares his intention, that he was not going to change the inscription.

The www.christianlogic.com has more on logic.