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Key Concept: There are many types of arguments that violate logic and/or seek to use misleading rhetoric to convince people of cases that they cannot make (or at least do not choose to make) on logic, reason, and evidence alone. Being able to recognize these logical fallacies is important for proper critical examination of propositions, such as scientific arguments.

From the Greek logos, word, logic can be defined as the study of principles and rules to arrive at correct reasoning. It works primarily by the reasoning together of and statement of arguments. NOTE: popular use of the term to the contrary, in logic and rhetoric an "argument" is NOT simply contradiction, the "automatic gainsaying of any statement the other person makes." Instead, an argument is a connected series of statements intended to establish a proposition.

In other words, to "argue" is to "state one's case".

There is a vast field of formal logic with its own sets of technical terminology, symbols, etc. What we will present is greatly reduced.

The each individual statement in the "series of statements intended to establish a proposition" is called a premise. An argument might have a single premise, although many have a series of premises. In a properly constructed argument, the premise(s) should support a conclusion, the proposition which you were trying to establish.

Logic is used (or at least is used in principle) in nearly every field of human endeavor: science and other academic fields (history, etc.), of course, but also politics, business, advertising; indeed, anytime that someone is trying to convince other people about some proposition.

However, not all arguments are well-constructed. Logical fallacies can be unintentional (due to, among other things, Kida's 6 basic mistakes we make in thinking), or they can be quite deliberate. In the latter case, they are used as rhetorical devices to convince others instead of using correct, sound, valid reasoning.

The following is a sampling of some of the more commonly-encountered logical fallacies. There are many, many more. Also, some of the ones listed below go by many different names (in fact, most of these have Latin names as well). Additionally, some of these shade into each other. We've grouped these into general categories.

• Formal Logical Fallacies (so called because the "form" [structure] of the argument is problematic):
  • The FORMAL Non sequitur: This is Latin for "It doesn't follow." The formal version of this is the result of improperly structured arguments. Here are some classic formulations of non sequitur arguments (you aren't responsible for knowing the particular names, which refer to the part of the structure which is incorrect):
    • Affirming the consequent: "If A is true, then B is true. B is true. Therefore, A is true." But this does not follow; the premises do not show that B is true ONLY if A is true. For example, "Humans are mammals. Inky is a mammal. Therefore, Inky is a human." (It does not follow that ALL mammals are humans from the premises. For instance, Inky might well be a cat.)
    • Denying the antecedent: "If A is true, then B is true. A is false. Therefore, B is false." But this does not follow; again, the premises do not establish if B is true if and only if A is true. Example: "If this object is an oak tree, it is a plant. It is not an oak tree. Therefore, it is not a plant."
    • Affirming a disjunct: "A is true or B is true. B is true. Therefore, A is not true." But this only follows if and only if WHEN A is true B is false. It might be that both A and B can be true at the same time. Note that the first statement is NOT "Either A is true or B is true", but it is intended to mislead you into thinking this is the case. Example: "I like ice cream or I like cats. I like cats. Therefore, I do not like ice cream." (In fact, one might very well like both!)
    • Denying a conjunct: "It is not the case that both A is true and B is true. B is not true. Therefore, A is true." This fails to consider the possibility that both A and B are false. Example: "I cannot be at home and in the city. I am not at home. Therefore, I am in the city"
• Premises are not actually related to the conclusion:
  • The colloquial Non sequitur: Unlike the formal fallacy, most people use the phrase non sequitur simply for statements there the final part is unrelated to the first part. Examples: "Mary bakes the best cakes in town. She should run for mayor." "I got sick after eating pizza. Roast chicken is the best."
  • Red Herring: Introducing a second argument in response to the first one to draw attention away from the original topic of discussion. Example: "If you want to complain about the dishes I leave in the sink, what about the dirty clothes you leave in the bathroom?" Many of the "appeals to emotion rather than reason" fallacies listed below are specific types of red herrings.
• Appeals to Non-Evidence:
  • Appeals to Ignorance: Not all events or phenomena are well-understood. In cases where we do not have evidence supporting or rejecting a particular claim, the appropriate logical response is to withhold judgment. However, the Argument from Ignorance uses the following: "We do not know what is going on in a particular event or phenomenon; therefore, MY claim is the correct one." Often formulated as "because claim A has not been demonstrated to be false, claim A must be true."
  • Argument from Personal Incredulity: This argument boils down to "I personally can't imagine how claim A could be true, so therefore claim A cannot be true" even when clear lines of evidence support claim A. Distinct from the Appeals to Ignorance in that in this case the actual phenomenon or event is understood by other parties, but the person making the argument claims or chooses not to accept that explanation.
• Appeals to Emotion rather than Reason:
  • Ad hominem: Ad hominem means "at the person." Ad hominem arguments are those that say a claim should be rejected (or supported) based on some attribute of the person making an argument rather than on the argument itself.
    • A special case of ad hominem is the Tu quoque fallacy. From the Latin "and you also", it says that the other person is making the same error or bad behavior as you are, so therefor it is justified for me to make the same error or bad behavior. But as the old saying goes "two wrongs don't make a right"; just because the opponent is also guilty of the bad thing doesn't make it a good (or even excusable) thing.
  • Argument from Authority: The idea that we should adopt (or reject) an idea because some respected person tells us to. The logical problem here is that the truth of a claim doesn't change based on whether a respected person supports it or not; the authority may have no expertise in the particular subject, or they might be mistaken. If the respected person has actual evidence for the claim, that evidence is what is used to support it, not the person themselves. A short form of this argument (seen by Dr. Holtz on the bathroom wall his first semester of freshmen year in college): "Ideas by Merit, Not by Source."
    A special case is the argument from false authority: this is extremely common in advertising, where a spokesperson is chosen to advocate a product on the basis of popularity or fictional expertise.
  • Argument from the People (aka the Bandwagon): "If many believe it so, it must be so." In fact, while examining whether the relative support for a claim might be useful in some contexts (e.g., finding out how many people support a claim...), it has no bearing on the validity of that claim. For example, the more people in a community that believe in fire-breathing dragons does not make the fire-breathing dragons more real (phrased differently, their belief is not evidence for the reality of the dragons.)
  • Arguments from Adverse Consequences: These are arguments in which one is asked not to accept a position because doing so would require them to accept unpleasant consequences that stem from it. Of course, in reality the truth of a claim is independent of whether it produces adverse affects.
    [NOTE: don't mix this up with a much more reasonable argument form, namely that one should probably not do something because it has bad consequences. The argument from adverse consequences is an argument about the truth claim, not about the consequences themselves.]
  • Slippery slope: An unreasonable reluctance to accept a sound argument because of the fear of being drawn from it to accept a similar but less sound argument, and so on until you have been persuaded, after many iterations, to accept a completely fallacious argument.
  • Straw Man: A weak parody of it (the "straw man") of an opponent's actual argument is proposed, and then dispatched. If the deception is successful, listeners never notice that the substitution occurred and imagine that the original opposing argument was defeated.
• Flawed Observations:
  • Observational selection: Also called cherry-picking. Noticing only the observations that tend to form the patterns that one wants to see and ignoring those observations that either don't fit or form undesirable patterns. Often summarized as "Counting the Hits and Ignoring the Misses."
  • Statistics of small numbers: Attempting to infer a large pattern from too few observations. Sometimes summarized as "Hasty Generalization".
• Flawed Interpretations:
  • Non-comprehension of statistics: Like it says.
  • Correlation equals Causation: It's easy to be convinced that because two things happen simultaneously, one must cause the other. This is not something we can assume. The hypothesis of non-correlation has to be tested.
  • Post hoc ergo propter hoc: This is Latin for "it came after so it was caused by..." This is a special case of the "correlation = causation" fallacy in which when one event follows another it is claimed to have been caused by it. While having one event precede another is the first step in showing a causal relationship, it is ONLY the first step; additional evidence is needed in order to establish an actual relationship between the two.
  • Special Pleading: Artificial resuscitation for an argument that has already been falsified by some reasonable standard. This usually assumes the form of an argument that the special circumstances surrounding a particular situation invalidate the falsification. [NOTE: don't confuse with the "Straw Man" argument! In the Straw Man, you create a weak parody of your opponent's argument to make them look bad; in Special Pleading you change your argument to make you look good.]
    • "No True Scotsman": A special case of Special Pleading. When a general claim has been made about some situation, and a clear exception has been demonstrated that falsifies that claim, assert that the exception wasn't actually part of the category being discussed rather than acknowledging the falsification of the claim. (The name comes from the following simple version: Person A: "No Scotsman puts sugar on his porridge." Person B: "I am Scottish, and I put sugar on my porridge." Person A: "Then you are not a true Scotsman.")
  • The Disregarded Middle or Excluded Middle (aka False Dichotomy): In the real world, there is often a broad spectrum of possible opinion on many topics. A serious fallacy is to assume there are only two possible positions (often, but not always, presented as the two extreme positions.)
    The Holmes Fallacy: Related to the Disregarded Middle, named after the famous dictum of Sir Arthur Conan Doyle's character Sherlock Holmes: "When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth." In some situations, you might be able to know what all the potential possible scenarios might be, and thus eliminate some until you are down to the best supported outcome. But in most cases, there are far too many possible scenarios to be able to practically assess them all. So people will invoke Holmes' dictum as a way of justifying a False Dichotomy argument (or at least one where only a small fraction of the potentially infinite possible scenarios are considered.)
• Playing with Language:
  • Equivocation: Using the different meanings for the same word to make an argument without justification. Many words have multiple different but equally valid meanings. For instance, "faith" for "a particular religion" (e.g., the Catholic faith), or for trustworthiness (e.g., "I have faith that my parents will send me the books I left at home"). If a person's argument uses the different meanings interchangeably in order to state their case (e.g., "You cannot trust a non-religious person, as they are without faith"), that person is using the fallacy of equivocation. This is related to Special Pleading and to Straw Man. Another case: "A woman does not need to fear a man-eating tiger." (Equivocating on "man" as "adult male human" and "man" as synonym for "human being.")
  • Weasel words: When a forthright statement is more likely to offend than persuade, it is sugar-coated by the coining of new terminology: e.g., "Ethnic cleansing" goes down easier than "Mass murder." Whereas Equivocation uses different meaning for the same word, Weasel Words is using different words for the same meaning.
• Playing with the Nature of Argumentation Itself:
  • Fallacy fallacy: Just because someone used a fallacious argument to come to a conclusion does not mean that their conclusion is invalid! It is not enough to simply identify that someone is using a logical fallacy in order to show that they are wrong; you must also establish that their conclusion is incorrect.
  • "Gish Gallop": Named after evolution-denier Duane Gish to describe his argumentation technique, but by no means original to him or to science denialism. Attempt to overwhelm the opponent with as many arguments as possible, without regard to the accuracy, validity, or strength of the arguments. People who use the Gish gallop can then claim their opponent's failure to account for one or more of these means that they have won. When this is done as a propaganda technique, it is called "firehosing."

Some more thoughts on logical fallacies:

If you wish to explore these issues in a slightly longer format, here is the online Illustrated Book of Bad Arguments.

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Some additional thoughts about logic and argumentation:

• Understand (and when appropriate, avoid) "standard scripts" and strawmen: It is often easier to convert your own (or your opponent's) ideas and arguments into simplified slogans, mantras, and the like, and to render arguments into standardized scripts, than to address them at depth. There is some benefit to doing this (e.g., it may be easier to remember and recall them), but it comes with a major drawback. Specifically, what should be careful assessment of claims can become simply shouting slogans at each other. You need to understand the argument behind the slogan. And, if appropriate, try to avoid the mantra and simply state the argument itself. (As an observer of debates, you will find that in any given subject you will often hear the same arguments--even with the very same wording!--being used again and again. When you see this happening, it is quite likely that no one is going to be moved on either side, and thus there is no actual learning or decision-making).
• Listen to what people are actually arguing, not what you think they are arguing: Related to the above, be attentive to what people are saying. You might at first think that they are using a standard script (perhaps they used some of the key phrases from a slogan). Perhaps they are. But perhaps they are actually arguing some other case, or the same case with a different set of evidence or logic than normally presented. Give them and yourself the benefit of the doubt.
• A really, Really, REALLY important one: Understand your own argument, and why you hold it! Except in certain cases (e.g., for a class assignment; because you want to be perverse; etc.), you are probably only going to argue for a position you actually hold. Please evaluate why you hold that position. Consider an outsider looking at you: would they understand why you hold that position? Would you be able to reasonably convince them of your position in a fashion comparable to the manner you would expect someone else to convince you of their own position? To misquote Socrates:

  "The Unexamined Position is Not Worth Holding"

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Some Relevant Videos
"Critical Thinking", a 6-part series of very short videos by educational organization TechNyou.

"Part 1: A Valuable Argument" (2:21):

"Part 2: Broken Logic" (2:01):

"Part 3: The Man Who Was Made of Straw" (1:59):

"Part 4: Getting Personal" (2:05):

"Part 5: The Gambler's Fallacy" (2:57):

"Part 6: A Precautionary Tale" (2:53):

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Last modified: 3 October 2020