Explanation of Principles

I have tried to organize the fallacies on this website according to what I consider to be the actual structure of reasoning, not just according to arbitrary similarities. A warning to visitors is in order. This set of principles is rather idiosyncratic. Other logic teachers use other principles (or no principles at all). To justify my eccentricities, let me note that my approach to fallacies has been significantly influenced by the logical writings of Charles S. Peirce, in ways that will be obvious to those familiar with his work and probably won't matter to those who aren't.

This classification scheme is based on three principles.


1. There are three kinds of reasoning, not just two.

Using the syllogistic model, we can see that there are actually three types of reasoning. Most logic texts recognize only two. However, many logicians now follow Charles S. Peirce in recognizing hypothetical reasoning, which Peirce called Retroduction, as a third type of argument, not just a species of Induction. Peirce used the structure of the syllogism to explain his division.

Deduction Induction Retroduction
All humans are mortal.
Socrates is human.
Hence, Socrates is mortal.
Socrates is mortal.
Socrates is human.
Hence, all humans are mortal.
All humans are mortal.
Socrates is mortal.
Hence, Socrates is human.

For details on the three types of reasoning, click on the links.


2. Classification of fallacies should be based on where the fallacy occurs.

A fallacious argument contains an error of some kind. We can classify fallacies based on where this error occurs. Fallacies are traditionally divided into two groups, formal fallacies and informal fallacies. Formal fallacies are fallacious because there is an error in their form; informal fallacies are fallacious because they have a false premiss. With modifications, I accept this idea. I think there are two basic types of fallacies:

I. Fallacies of Soundness: arguments in which the premisses are unable to support their conclusion because one of the premisses is false. This is an error in the argument's content, rather than its form.

II. Fallacies of Circularity: arguments in which the premisses, whether true or false, are unable to support their conclusion because if the conclusion is under a shadow of doubt, the premisses are under the same shadow. This is an error in the argument's form, rather than its content.

Fallacies of Soundness may be further subdivided according to which of its premisses is false. To simplify (perhaps oversimplify) this idea, we will assume that all reasoning follows the basic pattern of the syllogism. A syllogism is an argument with two premisses leading to a conclusion. Each proposition in the argument has two terms, and in the course of the argument each term occurs twice, but never twice in the same proposition. The classic example of a syllogism is...

All humans are mortal.
Socrates is human.
Hence, Socrates is mortal.

The subject of the conclusion (Socrates) is called the minor term; the predicate of the conclusion (mortal) is called the major term. Hence the premiss in which the major term occurs (All humans are mortal) is called the major premiss; the premiss in which the minor term occurs (Socrates is human) is called the minor premiss. The basic idea is this: fallacies of soundness can be classified according to whether it is the major premiss or the minor premiss that is false. So Fallacies of Soundness may be divided into two categories:

A. Fallacies that afflict the major premiss.

B. Fallacies that afflict the minor premiss.

Fallacies of Ambiguities require some special consideration, but I believe they can also be subsumed under these two categories.


3. All fallacious reasoning is formally valid (for its type).

We must assume that not all of the premisses of an argument are necessarily stated. Often people offer arguments without stating all of the premisses that would be needed to make the argument formally valid. Usually they do so because the unstated premisses are obvious, and stating them would be boring and pointless. For example, someone who argued, "Socrates is mortal, since all men are mortal," would not be accused of reasoning in an invalid manner. He has merely treated the missing premiss, "Socrates is a man," as too obvious to require explicit statement--and he is surely not wrong to do so. However, if we are to treat incomplete arguments as valid, the critic of the argument must be responsible for unstated as well as stated premisses. Yet, any argument can be rendered valid by the addition of some premisses or other, provided we do not insist that those premisses be true. (This statement can be established through a rather trivial proof. Given any premiss, p, and any conclusion, q, a valid argument can be constructed by adding the premiss, 'If p then q'. Alternatively, we could construct a valid argument by adding 'q' as a premiss, rendering the argument circular, but valid.) This puts the critic in the position of being able to assume that any bad argument is valid. The object of the critique, then, is not to judge the validity of the argument, but only to expose the false or circular premisses that render the argument bad, even when (or perhaps especially when) those premisses have been left unstated.

An argument is fallacious when, in spite of its formal validity, there is a good reason why it should fail to persuade us.

Of course, many logic texts give a list of what they call "formal fallacies" which are supposed to be fallacious because they are not formally valid. Some examples include:

Affirming the Consequent: any argument of the form, "If p then q; and q. Therefore, p."

Denying the Antecedent: any argument of the form, "If p then q; but not p. Therefore, not q."

In syllogistic logic there are also some classical formal fallacies with names like "Illicit Major," "Illicit Minor," and "Undistributed Middle." Suffice it to say that these name syllogistic forms that fail the test for deductive validity, just as the above forms fail the test of deductive validity for propositional logic.

However, I do not recognize any list of "formal fallacies" (aside from the formally valid circularities). I don't because (in my view) failing to be deductively valid is not sufficient to make an argument a fallacy. Inductive arguments are not deductively valid and neither are Retroductive arguments. If failing to be deductively valid were, by itself, grounds for calling an argument fallacious, then all Inductive and Retroductive arguments would be fallacious simply by virtue of being Inductive or Retroductive rather than Deductive. Hence, if we are going to recognize forms of reasoning other than Deduction, we must not dismiss arguments as fallacious merely on the grounds that they fail to be deductively valid.

In fact, Inductive and Retroductive arguments often follow precisely the forms that are identified as formal fallacies. The name "Retroduction" actually refers to the tendency of the reasoning to move backward from consequent to antecedent (or from predicate to subject). That is, Retroductive reasoning typically follows the formal pattern labeled Affirming the Consequent. Likewise, since Inductive reasoning moves from evidence about a small group (the sample) to a generalization about a much larger group (the population), Induction typically follows the formal pattern labeled Illicit Minor.

Of course, just as a deductively valid argument may be fallacious (either by being circular of by having a false premiss), Inductive and Retroductive arguments may also be fallacious (either by being circular or by having a false premiss). There certainly are fallacious arguments that follow patterns described by the classical formal fallacies. However, such arguments are fallacious, not because they are bad Deductions, but because they are bad Inductions or bad Retroductions. Most of the arguments that a classical logician would label Affirming the Consequent are really Retroductions in which the causal principle to which the argument appeals is not the best explanation for the observation being explained. For example...

If alients visited the earth to teach humans the arts of civilization, then we should expect civilizations to spring up simultaneously in many different places. Civilizations did begin in many places at about the same time. Therefore the earth was visited by aliens who taught us the arts of civilization.

The argument follows the pattern labeled Affirming the Consequent, and this argument is undeniably fallacious. However, it is fallacious because it is an Arcane Explanation (appealing to the agency of entities not generally believed to exist), not because it affirms its consequent.


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