Logically Fallacious: The Ultimate Collection of Over 300 Logical Fallacies (Academic Edition) (Dr. Bo's Critical Thinking Series)

by Bo Bennett

There are those who say that we are living in a “post-truth world.” This is the idea that the truth no longer matters. People back up their personal religious beliefs by stating “it’s true to me, and that’s all that matters.” People support their political candidate despite lie after lie by finding a way to derive a kernel of truth from their candidate’s lies. The media sells us their “version” of the truth based on the media empire’s ideological position—and we buy it, hook, line, and sinker. But guess what, the concept of truth has not changed; what has changed is our willingness to sacrifice our intellectual integrity for information that supports our beliefs, personal values, and ideologies.

Good, rational discourse should neither be a competition nor hostile; it should be seen as a partnership in order to get closer to the truth.

While virtually all humans past the age of two or three are capable of reasoning, an alarmingly small percentage of us are really any good at it.

Academically and logically, an argument is an attempt to persuade someone of something by offering reasons to accept a given conclusion.

Deduction is a form of reasoning and argument in which the conclusion follows necessarily from the premises.

If the premises are true, then the conclusion must be true. That is what makes an argument deductive. This is also referred to as a formal argument.

Arguments where the conclusion is merely based on probability, not necessity, are considered inductive arguments. These are usually constructed through inductive reasoning, which is the process of making general conclusions from specific instances.

A belief is defined as the psychological state in which an individual holds a proposition or premise to be true. Beliefs are formed in many different ways, which is outside the scope of this book, but it will suffice to say that many beliefs are not formed by reason and critical thinking.

Beliefs can often be stated explicitly as beliefs, stated as opinions, implied, or arrogantly stated as fact.

Beliefs can be wonderful, as in believing that humanity is overall good. Beliefs can be benign, as in believing the Red Sox are better than the Yankees. Beliefs can also be devastating, as in believing your god wants you to fly planes into buildings. But no matter how good a belief makes us feel or how good the potential outcome of a belief can be, it does not affect the truth of the belief. Although we are focusing on arguments, this book will help you find the truth of beliefs by examining any fallacious reasoning you may have used to form your beliefs.

One of the earliest academic discussions of logical fallacies comes from the book Elementary Lessons in Logic: Deductive and Inductive, published by MacMillian and Co. in 1872 where the modern definition of logical fallacies is used: “the modes in which, by neglecting the rules of logic, we often fall into erroneous reasoning.” Today, this basic definition is still used, and often abbreviated to just “an error in reasoning.” It is not a factual error.

First, unless one is involved in formal debate, we rarely see one present a formal syllogism that is subject to a formal fallacy. What we find in real life is a bunch of words that need to be parsed into an argument. We often find when there is a flaw in the logical structure of the argument (i.e., a formal fallacy), there is also one or more problems with the content (i.e., informal fallacies). It is good to know these two general classifications, but don’t expect to spot formal fallacies in everyday situations.

I would say that more often than not, cognitive biases do not lead to logical fallacies. This is because cognitive biases are largely unconscious processes that bypass reason, and the mere exercise of consciously evaluating an argument often causes us to counteract the bias.

Therefore, we will define a logical fallacy as a concept within argumentation that commonly leads to an error in reasoning due to the deceptive nature of its presentation. Logical fallacies can comprise fallacious arguments that contain one or more non-factual errors in their form or deceptive arguments that often lead to fallacious reasoning in their evaluation.

As you might have guessed, those who are acting unreasonably and irrationally are either incapable or unwilling to accept that their arguments are fallacious, if in fact, their arguments are fallacious. In these cases, you can come down to their level, appeal to their emotions, and exploit their cognitive biases—but this takes some manipulative talent, and I would argue that it is not very ethical. You can simply give up and refuse to argue any further, which I have done at times. Or, if possible, you can show how their arguments and beliefs are inconsistent with other beliefs they hold. This is my preferred strategy because it is not patronizing, nor does it reflect my frustration.

People like simplicity and would often rather keep simplicity at the cost of rationality.

When others verbally attack you, take it as a compliment to the quality of your argument. It is usually a sign of desperation on their part.

Exception: Be very careful not to confuse “deferring to an authority on the issue” with the appeal to authority fallacy. Remember, a fallacy is an error in reasoning. Dismissing the council of legitimate experts and authorities turns good skepticism into denialism. The appeal to authority is a fallacy in argumentation, but deferring to an authority is a reliable heuristic that we all use virtually every day on issues of relatively little importance. There is always a chance that any authority can be wrong, that’s why the critical thinker accepts facts provisionally. It is not at all unreasonable (or an error in reasoning) to accept information as provisionally true by credible authorities. Of course, the reasonableness is moderated by the claim being made (i.e., how extraordinary, how important) and the authority (how credible, how relevant to the claim).

Exception: It has been stated elsewhere that “agree to disagree” falls under the appeal to closure. This is not the case because agreeing to disagree does not mean that either party is accepting the evidence of the other, in fact, it’s the opposite. People can agree to “move on” or “table the issue,” for many logical reasons. This is similar to negotiation and compromise. When people compromise, they usually do not agree to accept evidence they wouldn’t otherwise accept. For example, if an atheist and theist are debating the existence of the Biblical God, they wouldn’t say, “Okay, I’ll agree that some kind of creator god exists if you agree that this god does not currently interfere in the universe.”

Appeal to Common Belief argumentum ad populum (also known as: appeal to accepted belief, appeal to democracy, appeal to widespread belief, appeal to the masses, appeal to belief, appeal to general belief, appeal to the majority, argument by consensus, authority of the many, consensus fallacy, bandwagon fallacy, appeal to the number, argumentum ad numerum, argumentum consensus gentium, appeal to the mob, appeal to the gallery, consensus gentium, mob appeal, social conformance, value of community, vox populi) Description: When the claim that most or many people in general or of a particular group accept a belief as true is presented as evidence for the claim. Accepting another person’s belief, or many people’s beliefs, without demanding evidence as to why that person accepts the belief, is lazy thinking and a dangerous way to accept information. Logical Form: A lot of people believe X. Therefore, X must be true.

Appeal to Consequences argumentum ad consequentiam (also known as: appeal to consequences of a belief, argument to the consequences, argument from [the] consequences, appeal to convenience [form of], appeal to utility) Description: Concluding that an idea or proposition is true or false because the consequences of it being true or false are desirable or undesirable. The fallacy lies in the fact that the desirability is not related to the truth value of the idea or proposition. This comes in two forms: the positive and negative. Logical Forms: X is true because if people did not accept X as being true then there would be negative consequences. X is false because if people did not accept X as being false, then there would be negative consequences. X is true because accepting that X is true has positive consequences. X is false because accepting that X is false has positive consequences. Example #1 (positive): If there is objective morality, then good moral behavior will be rewarded after death. I want to be rewarded; therefore, morality must be objective. Example #2 (negative): If there is no objective morality, then all the bad people will not be punished for their bad behavior after death. I don’t like that; therefore, morality must be objective. Explanation: The fact that one wants to be rewarded, or wants other people to suffer, says nothing to the truth claim of objective morality. These examples are also begging the question that there is life after death. Examp...

Appeal to Faith Description: This is an abandonment of reason in an argument and a call to faith, usually when reason clearly leads to disproving the conclusion of an argument. It is the assertion that one must have (the right kind of) faith in order to understand the argument. Even arguments that heavily rely on reason that ultimately require faith, abandon reason. Logical Form: X is true. If you have faith, you will see that. Example #1: Jimmie: Joseph Smith, the all American prophet, was the blond-haired, blue-eyed voice of God. Hollie: What is your evidence for that? Jimmie: I don’t need evidence—I only need faith. Explanation: There are some things, some believe, that are beyond reason and logic. Fair enough, but the moment we accept this, absent of any objective method of telling what is beyond reason and why anything goes, anything can be explained away without having to explain anything. Example #2: Tom: Did you know that souls (“Thetans”) reincarnate and have lived on other planets before living on Earth, and Xenu was the tyrant ruler of the Galactic Confederacy? Mike: No, I did not know that. How do you know that? Tom: I know this through my faith. Do you think everything can be known by science alone? Your faith is weak, my friend. Explanation: It should be obvious that reason and logic are not being used, but rather “faith.” While Tom might be right, there is still no valid reason offered. The problem also arises in the vagueness of the appeal to faith. Tom’s a...

One needs to ask, how do you know it is the will of God? Satan is said to be the great deceiver—he would only be great if those being deceived couldn’t tell the difference between God and Satan. In reality, appealing to Heaven, or God, is an abandonment of logic and reason, and as we have seen, potentially extremely dangerous.

Be loyal to truth and reason, even if it is seen as disloyalty to an ideology.

Appeal to Nature argumentum ad naturam Description: When used as a fallacy, the belief or suggestion that “natural” is better than “unnatural” based on its naturalness. Many people adopt this as a default belief. It is the belief that is what is natural must be good (or any other positive, evaluative judgment) and that which is unnatural must be bad (or any other negative, evaluative judgment). The appeal to nature fallacy is often confused with the naturalistic and the moralistic fallacies because they are quite similar. The appeal to nature, however, specifically references “natural” or “unnatural” and can also make a non-moral judgment such as “beautiful” or “destructive.” Logical Forms: X is natural. Y is not natural. Therefore, X is better than Y. That which is natural is good, right, beautiful, etc. X is natural. Therefore, X is good, right, beautiful, etc. That which is unnatural is bad, wrong, destructive, etc. X is unnatural. Therefore, X is bad, wrong, destructive, etc. Example #1: I shop at Natural Happy Sunshine Store (NHSS), which is much better than your grocery store because at NHSS everything is natural including the 38-year-old store manager’s long gray hair and saggy breasts. Explanation: I can appreciate natural food and products as much as the next granola-eating guy, but to make any claim of “betterness,” one needs to establish criteria by which to judge. Perhaps not paying almost twice as much for the same general foods is “better” for me. Perhaps...

Appeal to Popularity argumentum ad numeram (also see: appeal to common belief) Description: Using the popularity of a premise or proposition as evidence for its truthfulness. This is a fallacy which is very difficult to spot because our “common sense” tells us that if something is popular, it must be good/true/valid, but this is not so, especially in a society where clever marketing, social and political weight, and money can buy popularity.

Appeal to Ridicule reductio ad ridiculum (also known as: appeal to mockery, the horse laugh) Description: Presenting the argument in such a way that makes the argument look ridiculous, usually by misrepresenting the argument or the use of exaggeration. Logical Form: Person 1 claims that X is true. Person 2 makes X look ridiculous by misrepresenting X. Therefore, X is false.

Argument by Pigheadedness (also known as: argument by stubbornness, invincible ignorance fallacy) Description: This is a refusal to accept a well-proven argument for one of many reasons related to stubbornness. It can also be the refusal to argue about a claim that one supports. Logical Form: Argument X is well-argued. Person 1 has no objections to the argument, besides just refusing to accept the conclusion. Therefore, argument X is not true. Example #1: Dad: You are failing math since you moved the Xbox to your room. You have been playing video games for at least 6 hours each day since. Before that, you consistently got A’s and B’s. Don’t you think that the video games are the real problem here? Blake: No.

Argument by Repetition argumentum ad nauseam (also known as: argument from nagging, proof by assertion) Description: Repeating an argument or a premise over and over again in place of better supporting evidence. Logical Form: X is true. X is true. X is true. X is true. X is true. X is true... etc.

Argument by Selective Reading Description: When a series of arguments or claims is made and the interlocutor acts as if the weakest argument was the best one made. This is a form of cherry picking and very similar to the selective attention fallacy. Logical Form: Person 1 makes arguments X, Y, and Z. Argument Z is the weakest. Person 2 responds as if argument Z was the best person 1 has made.

Argument from Hearsay (also known as: the telephone game, Chinese whispers, anecdotal evidence, anecdotal fallacy/Volvo fallacy [form of]) Description: Presenting the testimony of a source that is not an eyewitness to the event in question. It has been conclusively demonstrated that with each passing of information, via analog transmission, the message content is likely to change. Each small change can and often does lead to many more significant changes, as in the butterfly effect in chaos theory. Hearsay is generally considered very weak evidence if it is considered evidence at all. Especially when such evidence is unfalsifiable (not able to be proven false). Logical Form: Person 1 told me that he saw Y. Therefore, I must accept that Y is true. Example #1: Lolita: Bill stole the money from the company petty cash fund. Byron: How do you know? Lolita: Because Diane told me. Byron: How does she know? Lolita: Julian told her. Byron: Did anyone actually see Bill steal the money? Lolita: I don’t know, we could ask Morris. Byron: Who’s he? Lolita: The guy who told Julian. Explanation: Lolita is making a bold claim about Bill, based on hearsay. Not only did Lolita not see Bill steal the money, but neither did Diane, Julian, and who knows about Morris. Example #2: There is life after death! I once heard this story from my friend’s sister, that her maid of honor’s niece knew this guy who had a friend who heard from his camp counselor a story where some guy was in a coma and saw hi...

Argument from Ignorance ad ignorantiam (also known as: appeal to ignorance, appeal to mystery [form of], black swan fallacy [form of], toupee fallacy [form of]) Description: The assumption of a conclusion or fact based primarily on lack of evidence to the contrary. Usually best described by, “absence of evidence is not evidence of absence.” Logical Forms: X is true because you cannot prove that X is false. X is false because you cannot prove that X is true. Example #1: Although we have proven that the moon is not made of spare ribs, we have not proven that its core cannot be filled with them; therefore, the moon’s core is filled with spare ribs. Explanation: There is an infinity of things we cannot prove—the moon being filled with spare ribs is one of them. Now you might expect that any “reasonable” person would know that the moon can’t be filled with spare ribs, but you would be expecting too much. People make wild claims, and get away with them, simply on the fact that the converse cannot otherwise be proven. Example #2: To this very day (at the time of this writing), science has been unable to create life from non-life; therefore, life must be a result of divine intervention. Explanation: Ignoring the false dilemma, the fact that we have not found a way to create life from non-life is not evidence that there is no way to create life from non-life, nor is it evidence that we will some day be able to; it is just evidence that we do not know how to do it. Confusing ignoran...

Explanation: The unwillingness to entertain ideas that one finds unbelievable when the ideas are mainstream ideas made by a reputable source, such as a NASA and the truthfulness of the moon landings, is fallacious. Exception: We can’t possibly entertain every crackpot with crackpot ideas. People with little credibility or those pushing fringe ideas need to provide more compelling evidence to get the attention of others.

Explanation: The reason this technique works so well, is because imagined reasons are often more persuasive than real reasons. If someone wants to be convinced, this technique works like a charm. However, to the critical thinker, this will not fly. Silence is not a valid substitute for reason or evidence.

Tip: Silence can be very powerful. In public speaking, knowing when to pause and let the audience digest what you said helps them comprehend your message. In argumentation, a pause after making a solid point can increase the odds your interlocutor(s) will accept the point.

Argument of the Beard (also known as: fallacy of the beard, heap fallacy, heap paradox fallacy, bald man fallacy, continuum fallacy, line drawing fallacy, sorites fallacy) Description: When one argues that no useful distinction can be made between two extremes, just because there is no definable moment or point on the spectrum where the two extremes meet. The name comes from the heap paradox in philosophy, using a man’s beard as an example. At what point does a man go from clean-shaven to having a beard? Logical Form: X is one extreme, and Y is another extreme. There is no definable point where X becomes Y. Therefore, there is no difference between X and Y. Example #1: Why does the law state that you have to be 21 years old to drink? Does it really make any difference if you are 20 years and 364 days old? That is absurd. Therefore, if a single day makes no difference, then a collection of 1095 single days won’t make any difference. Therefore, changing the drinking age to 18 will not make any difference.

Argument to Moderation argumentum ad temperantiam (also known as: appeal to moderation, middle ground, false compromise, gray fallacy, golden mean fallacy, fallacy of the mean, splitting the difference) Description: Asserting that given any two positions, there exists a compromise between them that must be correct. Logical Form: Person 1 says A. Person 2 says Z. Therefore, somewhere around M must be correct. Example #1: So you are saying your car is worth $20k. I think it is worth $1, so let’s just compromise and say it is worth $10k. (Assuming the car is worth $20k) Explanation: The price of $20k was a reasonable book value for the car, where the price of $1 was an unreasonable extreme. The fact is the car is worth about $20k—thinking the car is worth $1 or $1,000,000, won’t change that fact3. Example #2: Ok, I am willing to grant that there might not be angels and demons really floating around Heaven or hanging out in Hell, but you must grant that there has to be at least one God. Is that a fair compromise? Explanation: There is no compromise when it comes to truth. Truth is truth. If there are angels, demons, and God, there are angels, demons, and God. If there aren’t, there aren’t. Compromise and splitting the difference work fine in some cases, but not in determining truth.

Base Rate Fallacy (also known as: neglecting base rates, base rate neglect, prosecutor’s fallacy [form of]) Description: Ignoring statistical information in favor of using irrelevant information, that one incorrectly believes to be relevant, to make a judgment. This usually stems from the irrational belief that statistics don’t apply to a situation, for one reason or another when, in fact, they do. Example #1: Only 6% of applicants make it into this school, but my son is brilliant! They are certainly going to accept him! Explanation: Statistically speaking, the son may still have a low chance of acceptance. The school is for brilliant kids (and everyone knows this), so the vast majority of kids who apply are brilliant. Of the whole population of brilliant kids who apply, only about 6% get accepted. So even if the son is brilliant, he still has a low chance of being accepted (about 6%). Example #2: Faith healing “works,” but not all the time, especially when one’s faith is not strong enough (as generally indicated by the size of one’s financial offering). Unbiased, empirical tests, demonstrate that a small but noticeable percentage of people are cured of “incurable” diseases such as cancer. Explanation: This is true. However, what is not mentioned in the above is the number of cases of cancer that just go away without any kind of faith healing, in other words, the base rate of cancer remission. It is a statistical certainty that among those with cancer, there will be a perc...

Begging the Question petitio principii (also known as: assuming the initial point, assuming the answer, chicken and the egg argument, circulus in probando) Description: Any form of argument where the conclusion is assumed in one of the premises. Many people use the phrase “begging the question” incorrectly when they use it to mean, “prompts one to ask the question.” That is NOT the correct usage. Begging the question is a form of circular reasoning. Logical Form: Claim X assumes X is true. Therefore, claim X is true. Example #1: Paranormal activity is real because I have experienced what can only be described as paranormal activity. Explanation: The claim, “paranormal activity is real” is supported by the premise, “I have experienced what can only be described as paranormal activity.” The premise presupposes, or assumes, that the claim, “paranormal activity is real” is already true. Example #2: The reason everyone wants the new “Slap Me Silly Elmo” doll is because this is the hottest toy of the season! Explanation: Everyone wanting the toy is the same thing as it being “hot,” so the reason given is no reason at all—it is simply rewording the claim and trying to pass it off as support for the claim.

Tip: Moral reasoning is difficult, and the consequences of making poor moral decisions can be traumatic, but the more experience you have with moral reasoning, the better you will get at it. Don’t allow an authority to rob you of this growth opportunity.

Bulverism Description: This is a combination of circular reasoning and the genetic fallacy. It is the assumption and assertion that an argument is flawed or false because of the arguer’s suspected motives, social identity, or other characteristic associated with the arguer’s identity. Logical Form: Person 1 makes argument X. Person 2 assumes person 1 must be wrong because of their suspected motives, social identity, or other characteristic associated with their identity. Therefore, argument X is flawed or not true. Example #1: Martin: All white people are not racists. Charlie: Yes they are. You just believe that because you are white. Explanation: Charlie is making two errors: 1) he is assuming that Martin must be wrong and 2) he is basing that assumption on an accidental feature of Martin—the amount of pigmentation in his skin.

Cherry Picking (also known as: ignoring inconvenient data, suppressed evidence, fallacy of incomplete evidence, argument by selective observation, argument by half-truth, card stacking, fallacy of exclusion, ignoring the counter evidence, one-sided assessment, slanting, one-sidedness) Description: When only select evidence is presented in order to persuade the audience to accept a position, and evidence that would go against the position is withheld. The stronger the withheld evidence, the more fallacious the argument.

Commutation of Conditionals (also known as: the fallacy of the consequent, converting a conditional) Description: Switching the antecedent and the consequent in a logical argument. Logical Form: If P then Q. Therefore, if Q then P. Example #1: If I have a PhD, then I am smart. Therefore, if I am smart, then I have a PhD. Explanation: There are many who could, rightly so, disagree with the first premise, but assuming that premise is true, does not guarantee that the conclusion is true. There are many smart people without PhDs. Example #2: If I have herpes, then I have a strange rash. Therefore, if I have a strange rash, then I have herpes.

Complex Question Fallacy plurium interrogationum (also known as: many questions fallacy, fallacy of presupposition, loaded question, trick question, false question) Description: A question that has a presupposition built in, which implies something but protects the one asking the question from accusations of false claims. It is a form of misleading discourse, and it is a fallacy when the audience does not detect the assumed information implicit in the question and accepts it as a fact. Logical Form: Question X is asked that requires implied claim Y to be accepted before question X can be answered. Example #1: How many times per day do you beat your wife? Explanation: Even if the response is an emphatic, “none!” the damage has been done. If you are hearing this question, you are more likely to accept the possibility that the person who was asked this question is a wife-beater, which is fallacious reasoning on your part. Example #2: How many school shootings should we tolerate before we change the gun laws? Explanation: The presupposition is that changing the gun laws will decrease the number of school shootings. This may be the case, but it is a claim that is implied in the statement and hidden by a more complex question. Reactively, when one hears a question such as this, one’s mind will attempt to search for an answer to the question—which is actually a distraction from rejecting the implicit claim being made. It is quite brilliant but still fallacious. Exception: It is n...

Conflicting Conditions contradictio in adjecto (also known as: a self-contradiction, self-refuting idea) Description: When the argument is self-contradictory and cannot possibly be true. Logical Form: Claim X is made, which is impossible as demonstrated by all or part of claim X. Example #1: The only thing that is certain is uncertainty. Explanation: Uncertainty itself cannot be certain by definition. It is a self-contradiction. Example #2: I don’t care what you believe, as long as your beliefs don’t harm others. Explanation: This is a contradiction. At first glance, “as long as” appears to be a condition for the assertion, “I don’t care what you believe,” but it’s not; the assertion has to be false in all cases. The arguer must always care if the person believes something that will harm others or not.

Confusing Currently Unexplained with Unexplainable Description: Making the assumption that what cannot currently be explained is, therefore, unexplainable (impossible to explain). This is a problem because we cannot know the future and what conditions might arise that offer an explanation. It is also important to note that we cannot assume the currently unexplained is explainable. Logical Form: Claim X is currently unexplained. Therefore, claim X is unexplainable. Example #1: Teri: I don’t know why that stuffed animal flew off my dresser this morning. I guess some things in life will forever remain a mystery! Explanation: The fact that Teri could not explain something, does not make it unexplainable. Later, it might be revealed that a family member was playing a trick and tied a string to the stuffed animal. Maybe Teri will read about a slight earthquake that happened at the same time. Maybe Teri will later discover that there is a rat in her room that made a home in her stuffed animals. The point is, what is currently unexplained is not necessarily unexplainable.

Conjunction Fallacy (also known as: conjunction effect) Description: Similar to the disjunction fallacy, the conjunction fallacy occurs when one estimates a conjunctive statement (this and that) to be more probable than at least one of its component statements. It is the assumption that more specific conditions are more probable than general ones. This fallacy usually stems from thinking the choices are alternatives, rather than members of the same set. The fallacy is further exacerbated by priming the audience with information leading them to choose the subset as the more probable option. Logical Form: X is a subset of Y. Therefore, X is more probable than Y. Conjunction X and Y (both taken together) is more likely than a constituent X. Example #1: While jogging around the neighborhood, you are more likely to get bitten by someone’s pet dog, than by any member of the canine species.

Conspiracy Theory (also known as: canceling hypothesis, canceling hypotheses, cover-ups) Description: Explaining that your claim cannot be proven or verified because the truth is being hidden and/or evidence destroyed by a group of two or more people. When that reason is challenged as not being true or accurate, the challenge is often presented as just another attempt to cover up the truth and presented as further evidence that the original claim is true. Logical Form: A is true. B is why the truth cannot be proven. Therefore, A is true. Example #1: Noah’s ark has been found by the Russian government a long time ago, but because of their hate for religion, they have been covering it up ever since. Example #2: Geologists and scientists all over the world are discovering strong evidence for a 6000-year-old earth, yet because of the threat of ruining their reputation, they are suppressing the evidence and keeping quiet. Explanation: The psychology behind conspiracy theories is quite complex and involves many different cognitive biases and fallacies discussed in this book. In general, people tend to overlook the incredible improbabilities involved in a large-scale conspiracy, as well as the potential risks for all involved in the alleged cover-up. In the above examples, those who stick with a literal interpretation of the Bible often experience cognitive dissonance, or the mental struggle involved when one’s beliefs contradict factual claims. This cognitive dissonance causes p...

Denying a Conjunct Description: A formal fallacy in which the first premise states that at least one of the two conjuncts (antecedent and consequent) is false and concludes that the other conjunct must be true. Logical Forms: Not both P and Q. Not P. Therefore, Q. Not both P and Q. Not Q. Therefore, P. Example #1: I am not both a moron and an idiot. I am not a moron. Therefore, I am an idiot. Explanation: I might be an idiot, but the truth of both premises does not guarantee that I am; therefore, this argument is invalid—technically, the form of this formal argument is invalid. Being “not both” a moron and an idiot, only means that if I am not one of the two, I am simply not one of the two—we cannot logically conclude that I am the other. Example #2: I am not both a Christian and a Satanist. I am not a Satanist. Therefore, I am a Christian. Explanation: The truth of both premises does not guarantee that I am a Christian; therefore, this argument is invalid—the form of this formal argument is invalid. Being “not both” a Satanist and a Christian, only means that if I am not one of the two, I am simply not one of the two—we cannot logically conclude that I am the other.

Denying the Antecedent (also known as: inverse error, inverse fallacy) Description: It is a fallacy in formal logic where in a standard if/then premise, the antecedent (what comes after the “if”) is made not true, then it is concluded that the consequent (what comes after the “then”) is not true. Logical Form: If P, then Q. Not P. Therefore, not Q. Example #1: If it barks, it is a dog. It doesn’t bark. Therefore, it’s not a dog.