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In philosophy, a formal fallacy (also called deductive fallacy or logical fallacy) is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic.[1] It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion.[2] Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. However, this may not affect the truth of the conclusion since validity and truth are separate in formal logic. For example, there could be a correlation between the number of times it rains and whenever a day is Tuesday, which could lead one to believe that "Tuesdays are days when it rains." However, in this case one would commit the ad hoc fallacy because there is no causal link between a day of the week and how often it rains. So, although it may be true in one's own perception it is impossible to validate using logic.

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.

"Fallacious arguments usually have the deceptive appearance of being good arguments."[3] 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. Recognizing fallacies can develop reasoning skills to expose the weaker links between premises and conclusions to better discern between what appears to be true and what is true.

Argumentation theory provides a different approach to understanding and classifying fallacies. In this approach, an argument is regarded as an interactive protocol between individuals that attempts to resolve their disagreements. The protocol is regulated by certain rules of interaction, so violations of these rules are fallacies.

Fallacies are used in place of valid reasoning to communicate a point with the intention to persuade. Examples in the mass media today include but are not limited to propaganda, advertisements, politics, newspaper editorials and opinion-based “news” shows.

A special case is mathematical fallacy, an intentionally invalid mathematical proof, often with the error subtle and somehow concealed. Mathematical fallacies are typically crafted and exhibited for educational purposes, usually taking the form of spurious proofs of obvious contradictions.



The standard Aristotelian logical fallacies are:

Other logical fallacies include:

In philosophy, the term logical fallacy properly refers to a formal fallacy—a flaw in the structure of a deductive argument, which renders the argument invalid.

However, it is often used more generally in informal discourse to mean an argument that is problematic for any reason, and thus encompasses informal fallacies as well as formal fallacies—valid but unsound claims or poor non-deductive argumentation.

The presence of a formal fallacy in a deductive argument does not imply anything about the argument's premises or its conclusion (see fallacy fallacy). Both may actually be true, or even more probable as a result of the argument (e.g. appeal to authority), 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.

In contrast to informal fallacyEdit

Formal logic is not used to determine whether or not an argument is true. 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 that 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 street is wet.

This argument is valid and, if it did rain, it would also be sound.

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

  1. If Albert Einstein 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 someone 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 is true that quantum mechanics is deterministic.
  3. Therefore, a scientist has made a statement about it.

Common examplesEdit

"Some of your key evidence is missing, incomplete, or even faked! That proves I'm right!"[4]

"The vet can't find any reasonable explanation for why my dog died. See! See! That proves that you poisoned him! There’s no other logical explanation!"[5]

"Adolf Hitler liked dogs. He was evil. Therefore, liking dogs is evil."[6]

A Venn diagram illustrating a fallacy:
Statement 1: Most of the green is touching the red.
Statement 2: Most of the red is touching the blue.
Logical fallacy: Since most of the green is touching red, and most of the red is touching blue, most of the green must be touching blue. This, however, is a false statement.

In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of a nonexistent principle:

  1. Most Rimnars are Jornars.
  2. Most Jornars are Dimnars.
  3. Therefore, most Rimnars are Dimnars.

This is fallacious. And so is this:

  1. People in Kentucky support a border fence.
  2. People in New York do not support a border fence.
  3. Therefore, people in New York do not support people in Kentucky.

Indeed, there is no logical principle that states:

  1. For some x, P(x).
  2. For some x, Q(x).
  3. Therefore, for some x, P(x) and Q(x).

An easy way to show the above inference as invalid is by using Venn diagrams. In logical parlance, the inference is invalid, since under at least one interpretation of the predicates it is not validity preserving.

People often have difficulty applying the rules of logic. For example, a person may say the following syllogism is valid, when in fact it is not:

  1. All birds have beaks.
  2. That creature has a beak.
  3. Therefore, that creature is a bird.

"That creature" may well be a bird, but the conclusion does not follow from the premises. Certain other animals also have beaks, for example, an octopus has a beak. Errors of this type occur because people reverse a premise.[7] In this case, "All birds have beaks" is converted to "All beaked animals are birds." The reversed premise is plausible because few people are aware of any instances of beaked creature besides birds—but this premise is not the one that was given. In this way, the deductive fallacy is formed by points that may individually appear logical, but when placed together are shown to be incorrect.

See alsoEdit


  1. ^ Harry J. Gensler, The A to Z of Logic (2010) p. 74. Rowman & Littlefield, ISBN 9780810875968
  2. ^ Labossiere, Michael (1995). "Description of Fallacies". The Nizkor Project. Retrieved 2008-09-09. 
  3. ^ 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 
  4. ^ "Master List of Logical Fallacies". 
  5. ^ Daniel Adrian Doss; William H. Glover, Jr.; Rebecca A. Goza; Michael Wigginton, Jr. (17 October 2014). The Foundations of Communication in Criminal Justice Systems. CRC Press. p. 66. ISBN 978-1-4822-3660-6. Retrieved 21 May 2016. 
  6. ^ "Hitler Ate Sugar". TV 
  7. ^ Wade, Carole; Carol Tavris (1990). "Eight". In Donna DeBenedictis. Psychology. Laura Pearson (2 ed.). New York: Harper and Row. pp. 287–288. ISBN 0-06-046869-6. 

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