Formal fallacy

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"Logical fallacy" redirects here. For other meanings, see Fallacy (disambiguation).

In philosophy, a formal fallacy is a pattern of reasoning that is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid. A formal fallacy is contrasted with an informal fallacy, which may have a valid logical form and yet be unsound because one or more premises are false.

The term fallacy is often used generally to mean an argument that is problematic for any reason, whether it is formal or informal.

The presence of a formal fallacy in a deductive argument does not imply anything about the argument's premises or its conclusion. Both may actually be true, or even more probable as a result of the argument, but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described. By extension, an argument can contain a formal fallacy even if the argument is not a deductive one; for instance an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

"Fallacious arguments usually have the deceptive appearance of being good arguments."[1] Recognizing fallacies in everyday arguments may be difficult since arguments are often embedded in rhetorical patterns that obscure the logical connections between statements. Informal fallacies may also exploit the emotional, intellectual, or psychological weaknesses of the audience. Having the capability to recognize fallacies in arguments is one way to reduce the likelihood of such occurrences.

A different approach to understanding and classifying fallacies is provided by argumentation theory. In this approach, an argument is regarded as an interactive protocol between individuals which attempts to resolve their disagreements. The protocol is regulated by certain rules of interaction and violations of these rules are fallacies.

Such fallacies are used in many forms of modern communications where the intention is to influence behavior and change beliefs. Examples in the mass media today include but are not limited to propaganda, advertisements, politics, newspaper editorials and opinion-based “news” shows.

In contrast to informal fallacy

Formal logic is not used to determine whether or not an argument is true or false. Formal arguments can either be valid or invalid. A valid argument may also be sound or unsound. A valid argument has a correct formal structure. A valid argument is one where if the premises are true, the conclusion must be true. A sound argument is a formally correct argument which also contains true premises. Ideally, the best kind of formal argument is a sound, valid argument.

Formal fallacies do not take into account the soundness of an argument, but rather its validity. Premises in formal logic are commonly represented by letters (most commonly p and q). A fallacy occurs when the structure of the argument is incorrect, despite the truth of the premises.

As modus ponens, the following argument contains no formal fallacies.

  1. If P then Q
  2. P
  3. Therefore Q

A logical fallacy associated with this format of argument is referred to as affirming the consequent, which would look like this:

  1. If P then Q
  2. Q
  3. therefore P

This is a fallacy because it does not take into account other possibilities. To illustrate this more clearly, substitute the letters with premises.

  1. If it rains, the street will be wet
  2. The street is wet.
  3. Therefore it rained.

Although it is possible that this conclusion is true, it does not necessarily mean it MUST be true. The street could be wet for a variety of other reasons that this argument does not take into account. However, if we look at the valid form of the argument, we can see that the conclusion must be true.

  1. If it rains, the street will be wet.
  2. It rained.
  3. Therefore, the streets are wet.

This statement is both valid and sound.

If statements 1 and 2 are true, it will absolutely follow that statement 3 is true. However, it may still be the case that statement 1 or 2 is not true. For example:

  1. If a scientist makes a statement about science, it is correct.
  2. Albert Einstein states that all quantum mechanics is deterministic.
  3. Therefore it's true that quantum mechanics is deterministic.

In this case, statement 1 is false. The particular informal fallacy being committed in this assertion is argument from authority. By contrast, an argument with a formal fallacy could still contain all true premises:

  1. If Bill Gates owns Fort Knox, then he is rich.
  2. Bill Gates is rich.
  3. Therefore, Bill Gates owns Fort Knox.

Though, 1 and 2 are true statements, 3 does not follow because the argument commits the formal fallacy of affirming the consequent.

An argument could contain both an informal fallacy and a formal fallacy yet lead to a conclusion that happens to be true, for example, again affirming the consequent, now also from an untrue premise:

  1. If a scientist makes a statement about science, it is correct.
  2. It's true that quantum mechanics is deterministic.
  3. Therefore a scientist has made a statement about it.

Common examples

Main article: List of fallacies

See also

References

Notes
  1. ↑ Damer, T. Edward (2009), "Fallacious arguments usually have...", Attacking Faulty Reasoning: A Practical Guide to Fallacy-free Arguments (6th ed.), Belmont, California: Wadsworth, p. 52, ISBN 978-0-495-09506-4, retrieved 30 November 2010  See also Wikipedia article on book 
Bibliography

External links

In propositional logic
In quantificational logic
Syllogistic fallacy
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