Formal fallacy

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In philosophy, a formal fallacy (also called deductive 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] An argument that contains a fallacy is invalid. 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 invalid because one or more premises are false.

"Fallacious arguments usually have the deceptive appearance of being good arguments."[2] 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.

In contrast to informal fallacy

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 examples

"Some of your key evidence is missing, incomplete, or even faked! That proves I'm right!"[3]

"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!"[4]

"Adolf Hitler liked dogs. He was evil. Therefore, liking dogs is evil."[5]

See also


  1. ^ Harry J. Gensler, The A to Z of Logic (2010) p. 74. Rowman & Littlefield, ISBN 9780810875968
  2. ^ 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 
  3. ^ "Master List of Logical Fallacies". 
  4. ^ 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. 
  5. ^ "Hitler Ate Sugar". TV 
  • Aristotle, On Sophistical Refutations, De Sophistici Elenchi.
  • William of Ockham, Summa of Logic (ca. 1323) Part III.4.
  • John Buridan, Summulae de dialectica Book VII.
  • Francis Bacon, the doctrine of the idols in Novum Organum Scientiarum, Aphorisms concerning The Interpretation of Nature and the Kingdom of Man, XXIIIff.
  • The Art of Controversy | Die Kunst, Recht zu behalten – The Art Of Controversy (bilingual), by Arthur Schopenhauer
  • John Stuart Mill, A System of Logic – Raciocinative and Inductive. Book 5, Chapter 7, Fallacies of Confusion.
  • C. L. Hamblin, Fallacies. Methuen London, 1970.
  • Fearnside, W. Ward and William B. Holther, Fallacy: The Counterfeit of Argument, 1959.
  • Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
  • D. H. Fischer, Historians' Fallacies: Toward a Logic of Historical Thought, Harper Torchbooks, 1970.
  • Douglas N. Walton, Informal logic: A handbook for critical argumentation. Cambridge University Press, 1989.
  • F. H. van Eemeren and R. Grootendorst, Argumentation, Communication and Fallacies: A Pragma-Dialectical Perspective, Lawrence Erlbaum and Associates, 1992.
  • Warburton Nigel, Thinking from A to Z, Routledge 1998.
  • Sagan, Carl, The Demon-Haunted World: Science As a Candle in the Dark. Ballantine Books, March 1997 ISBN 0-345-40946-9, 480 pp. 1996 hardback edition: Random House, ISBN 0-394-53512-X

External links

  • The Fallacy Files by Gary N. Curtis – real examples posted regularly
  • ESGE Logical Fallacies – European Society for General Semantics
  • Logical Fallacies .Info
  • Stephen Downes Guide to the Logical Fallacies
  • Marilyn vos Savant explains Logical Fallacies
  • Overview of fallacies
  • Logic: An Invalid Approach [1]
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