This is a fantastic resource from: http://papyr.com/hypertextbooks/comp1/logic.htm. Please visit their site and support what they are doing.

Using Logic in Composition

Introduction

A sound, well reasoned, compelling argument is one of the most persuasive communicative acts we humans can create. As writers, our goal is to learn enough about logic in the hope of allowing us to employ stronger arguments in our work. This page, however, is not complete discussion of logic as a science of reasoning, of different kinds of logic, or of all the different varieties of logical fallacies we humans commit. This page is merely a discussion of some of the uses of logic that writers employ in creating a persuasive or argumentative essay.1 Finally, let’s define terms here too before we proceed: argument here does not mean to fight, squabble, yell, or brow-beat. Here argument refers to the process of reasoning by advancing proof. Argument, as we will use the term in this course, has its roots in logic.

Logic as an academic discipline focuses on the science of reasoning, inference, and proof. Those are different goals from the uses of logic in composition. When writers employ logic in composition, the emphasis seems to be on determining if the reasoning behind an argument is valid or invalid, and then using those determinations to support or reject a thesis. Although the goals are different, some familiarity with logic and the structure of well-formed arguments and reasoning can help writers (a) construct valid arguments/reasoning in support of their theses and (b) evaluate and refute invalid arguments/reasoning used to support others’ theses. Therefore, here we will examine the simple basics of logical argument, some of the types of argument, and finally some of the mistakes we are likely to see when we use logic incorrectly (called fallacies or fallacious reasoning).

The Basics of Argument

Logical arguments start with propositions2. A proposition is a statement which is either true or false, for example:

“Ankara is the capital of Turkey.”
“Humans are the only animals to use language.”
“Christopher Columbus was the first European to sail to the New World.”

When we use propositions, we are either asserting the truth of the statement or denying the truth of the statement. Note that this is a technical meaning of “deny,” not the everyday meaning. To deny in this context means to gather evidence to show that the proposition can not be true, not just that it is wrong. What’s more, it’s the meaning of the proposition that we assert of deny, not the particular arrangement of words or the use of a particular word. Propositions themselves are open to debate and definition. Consider (2) above, for example: for many people language is synonymous with any communication system. Under such an interpretation, people might deny proposition (2). For others, however, language is one specific kind of communicative system, with traits and features not found in any other animal communicative system. Therefore, others might assert proposition (2) as true. Precise definitions and and supporting evidence are still important in an argument, since the writer will have to justify the assertions.

Propositions serve as the foundational elements to the three parts of an argument — the premises, the inferences, and the conclusions.

Propositions as Premises

A writer begins an argument by making a proposition. One or more propositions are necessary for the argument to continue. They must be stated explicitly and are called the premises of the argument. They are the grounds (or reasons) for accepting the argument and its conclusions. The writer must have evidence to support the assertion. (If a writer fails to explicitly state his/her premises, the audience is likely to be suspicious about the strength of the writer’s supporting evidence and thereby less likely to give any credence to the writer’s argument.)

Premises (or assertions) are often indicated by phrases such as because, since, obviously and so on. Words like obviously, certainly, surely are especially troublesome in an argument. (As a group, they are sometimes known as the language of certitude.) The language of certitude can be used to fool others into accepting dubious premises simply by trying to convince the readers that the premise is true beyond question through the use of intimidation, a fear of questioning the “certainty” of a premise for fear of looking foolish, ill-informed, or ignorant. It is the fear of embarrassment that intimidates some people into not questioning a premise that is asserted to be “obvious,” and that use of intimidation is how the language of certitude works.

Propositions as Inferences

A writer then uses the premises of the argument to derive further propositions, called inferences. Inferences are the propositions that are entailed (i.e., logically must follow) if the premises are true. Below, we will look at inferences and entailment (also called implications) in more detail, and we will examine the rules of implicature for deriving valid inferences (sometimes called a “truth table”). Phrases such as implies that, thus, or leads us to are indicative of inferences.

Propositions as Conclusions

Finally, we arrive at the conclusion of the argument, yet another proposition. The conclusion derives from the premises and the inferences together, and its validity rests in the validity of the underlying premises and inferences. Conclusions are often indicated by phrases such as therefore, in sum, it follows that, we conclude and so on.

Types of Argument

Traditionally, rhetoricians recognized two types of argument, deductive and inductive3. A deductive argument provides conclusive proof of its conclusions by presenting all the supporting evidence and reasoning for the premises and the inferences. The idea is that if the premises are true, then the conclusion must also be true as well. In the process of deduction, we derive the conclusion by reasoning: the conclusion follows necessarily from (and is entailed by) the (general or universal) premises. The truth of the premises guarantees the truth of the conclusions.

If capital punishment does deter further crime, then it is justified as a form of punishment. (premise and inference)
Capital punishment does not in fact deter crime. (premise)
Therefore, it is not justified as punishment. (inference and conclusion)

The writer begins with a general statement (the premise) and then draws specific conclusions (by the processes of implicature and entailment). On the basis of the evidence and the reasoning which derives the implications, we judge a deductive argument as either valid or invalid.

An inductive argument is one in which the premises are supposed to support the conclusion in such a way that if the premises are true, it is not likely that the conclusion would be false. Inductive reasoning relies on the probability that the truth of the premises apply to the concluding proposition. Thus, if the premises and inferences are true, then probably the conclusion is as well. Consider, for example:

Aristotle was Greek. (premise)
Most Greeks eat lamb. (premise)
Aristotle probably ate lamb. (conclusion)

Inductive arguments (through the method of reasoning known as induction) develop their conclusions by inference, and those conclusions are not true or false, but rather probable or improbable. Writers use words and phrases like probably, improbably, plausible, implausible, likely, unlikely, and reasonable to conclude when making inductive arguments. Inductive arguments are not valid or invalid, but we can talk about whether they are stronger or weaker than other arguments, meaning that they have substantial or little supporting evidence.

Finally, we should note that the conclusion of one argument might be a premise in a different argument. A proposition can only be called a premise, an inference, or a conclusion with respect to its particular argument, to that particular context.

Composing an Argument: Five Points

Having looked at the three basic parts of an argument and the two traditional forms that arguments take, we can now look at how writers use argument in their work. The first point we should emphasize is that writers do not have to present or develop arguments in their essays using exactly the patterns as outlined above. Writers might choose to state the conclusions first (as a thesis statement perhaps) and then detail the premises and inferences later in support of the conclusion. This is perfectly acceptable.

Secondly we must recognize that arguments are harder to write than just the premises or conclusions alone. Simply stating the conclusions is not the same as writing an argument. Sometimes writers litter their essays with all sorts of assertions without ever producing anything which we might call an argument. In such cases, the writer simply asserts that some proposition is true (in other words, offers a conclusion) without ever bothering to present the premises or inferences from which the conclusions derive. Sometimes, writers do this because the arguments seem so clear in their own minds that they feel they need not write out the details of the argument, thinking that such is unnecessary for the readers. Sometimes, the writer is pressed for time and tries to shorten the argument to the conclusions alone. Sometimes, the writer hasn’t strong premises or inferences and simply wants to “push” the conclusion on the unsuspecting readers anyway. None of these are valid arguments (either in the formal or informal senses of the term).

Also, sometimes writers manage to make statements that do look like arguments but are not really. For example:

“If evolution is accurate, Darwin must either have been insane or a genius.”

However, that is not an argument; it is a conclusion (in the form of a conditional statement that does look a little like an argument). This statement does not assert its premises, does not make its inferences explicit. It merely presents its conclusion. (Even if we add the assertions, it still suffers from at least one other logical flaws, the bifurcation/false dilemma issue of either “insane” or “genius.” Might not Darwin have simply been a keen observer of the natural world, collecting data leading him to his conclusion?)

Thirdly, consider this next example, which too looks like an argument at first glance but is not:

“Your country supported you; therefore, do your duty to your country.”

The clause do your duty to your country is a command. Commands can not be true or false, only indicative sentences can be true or false. Therefore, since we can not test the validity of a command, a command can not be a proposition, and that sentence can not be an argument.

Fourth, writers sometimes compose statements of causality that are confused for arguments. For example, consider the following two statements of the form A because B.

“My car will not start because there is something wrong with the spark plugs.”
“There must be something wrong with the spark plugs, because the car will not start.”

The first statement is a statement of causality, really, not an argument, and the writer is asserting as truthful that a known problem with the spark plugs is the reason the car will not start. The second sentence appears to mean the same as the first at first glance, but it does not. The second statement is an argument. In the second statement, the writer is concluding that the spark plugs are at fault because of a particular premise (the car will not start). That conclusion might be valid or invalid. (Or the car might simply be out of gas!) In sentence (2), we are arguing for A, offering B as evidence. This is then an argument. A subtle difference, indeed.

Finally, when composing an argumentative essay, it is not enough that we present a valid, sound argument in favor of our thesis. We also need to compose a counter-argument showing why the opposition’s reasoning and arguments are unsound and invalid. The counter-argument requires us to systematically examine and analyze the opposing premises, inferences, and conclusions, explaining the inconsistencies and errors we find as we analyze. The counter-argument is a crucial step that the writer must take to convince a reader that his/her point of view on an issue is the best point of view.

We need to remember these five points if we truly wish to write a valid argument rather than “pseudo-arguments.”

Propositions as Inferences: More on Implication

Earlier, when discussing propositions as inferences, we briefly mentioned that we would examine the rules of implicature for deriving valid inferences. And so we shall. When we think about inferences and implicature, we need to remember one very important point: the fact that a deductive argument is valid does not necessarily entail that its conclusion holds, or the fact that a deductive argument’s conclusion is true does not necessarily mean that its premises are true as well. This odd state of affairs derives from the often counter-intuitive nature of implicature.4

In the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion. That seems logical. However, it can happen that an argument can reach a true conclusion based on one or more false premises.

Stars exist in outer space. (premise)
Comets are stars. (false premise)
Therefore comets exist in outer space. (conclusion)

What’s worse, an argument might even be entirely valid if it contains only false propositions. For example:

All fish have stripes. (false premise)
Whales are fish. (false premise)
Therefore all whales have stripes. (false conclusion)

Here, the conclusion is not true because the argument’s premises are false. If the argument’s premises were true, however, the conclusion would be true. The argument is thus entirely valid in the technical sense. As strange as all that may seem, at least we can count on one outcome that cannot happen: we can not reach a false conclusion derived via true inferences from true premises.

So based on those examples, and others, logicians have created a “truth table” for implicature5 that matches premise to conclusion via inference. In the table below, the symbol “=>” denotes implication; A is the premise, B the conclusion. T and F represent true and false respectively.

A Truth Table for Implicature
Premise Conclusion Inference A B A=>B
F F T F T T	If the premises are false and the inference valid, the conclusion can be either true or false.
T F F	If the premises are true and the conclusion false, the inference must be invalid.
T T T	If the premises are true and the inference valid, the conclusion must be true.

To conclude, let us make one last distinction: there is a (technical) difference between a valid argument and a sound argument. A valid argument is an argument whose conclusions follow from its premises, but it is an argument whose conclusions might not be true (as we have seen above) because its premises might not be true. A sound argument, on the other hand, is a valid argument whose premises are true. A sound argument therefore arrives at a true conclusion. Logicians and rhetoricians are careful not to confuse sound arguments with valid arguments.

Of course, when we read the works of others, we do think about more than the mere soundness of an argument. Arguments are always presented as part of a larger context, a context in which the author has some particular purpose or objective in mind. These hidden arguments (as they are sometime called) are part of the persuasive nature of writing as well as these explicit arguments we compose. As well as evaluating the argument itself, we should also evaluate the ethical and emotional appeals as well as the intent of the argument.

Fallacies

Having completed this all too brief overview of the traditional structure of argument, we can now look at some of the ways that argument is misused in writing or debate. What follows below are brief summaries of some of the common pitfalls and fallacies we should avoid when constructing an argument.

Let’s begin with another point of clarification: the term fallacy in ordinary usage refers to mistaken beliefs as well as to the faulty reasoning. However, in logic, the term is generally used to refer only to a form of technically incorrect argument, especially if that argument appears to be valid or convincing. So here we also define a fallacy as a logical argument or rhetorical device that appears to be sound but is truly unsound when examined more closely. By studying fallacies, we avoid being misled by them. (The unscrupulous study fallacies to pick up more techniques with which to fool the unwary.) Below is a list of some common fallacies, and also some rhetorical devices, often used in argumentative essays6.

Accent

If a writer attempts to change the meaning by changing the emphasis (the focus or the accent), the writer is committing a fallacy of reasoning. Accent is the attempt to persuade by shifting meaning and focus away from one issue to another issue. For example, compare:

“We should support those governments that support our policies.”

Ad hoc

Earlier, when talking about causality, we discussed one of the differences between argument and explanation. Ad hoc fallacies arise when writers try to give after-the-fact explanations for conclusions, rather than present premises and inferences that lead to those conclusions.

“Although we said we had proof that weapons of mass destruction existed, and although we found no evidence that they really did, the war was still justified because the leader was a tyrant.”

Affirmation of the consequent

If a writer composes an argument of the form A implies B; B is true; therefore A is true, the writer may have committed the fallacy of affirming the consequent. It is possible to reach a correct, true conclusion despite false premises. See the truth table for implication given earlier. Therefore, it is fallacious to argue that if B is true, A must be true as well.

Amphiboly

If a writer uses ambiguous, vague, or unclear premises, then s/he is guilty of amphiboly. It is hard for the readers to test and judge the merits of an argument if the premises are ambiguous or unclear.

Appeal to humor

If the writer tries to sway the readers through the use of humor, in place of premises, inferences, and evidence, the writer is guilty of using an appeal to humor. Humor has the interesting ability of allowing us to see the world from the humorist’s point of view. For example, if a couple happen to be watching a comedian on the television, and the comedian makes a sexist joke, and the man laughs, one can understand why the woman would be upset: for the man to laugh at the sexist joke must mean that the man shared the sexist world view with the comedian briefly. This can happen even if the man has shown no other signs of sexist attitudes or behaviors before. So if the writer can humorously construct an proposition, s/he might be able to attract readers to that perspective without the need to supply evidence or premises at all.

Argumentum ad antiquitatem / Appeal to tradition

If the writer argues for the merits of a proposition simply because it is the accustomed or traditional position to take, then the writer is guilty of the appeal to tradition. Sometimes we do things for good reasons; sometimes we do things simply because we have always done them. Such is the nature of appeal to tradition. The following argument appeared in a letter defending the membership policy of the Century Club, an all-male club established in New York in 1847, which was under pressure to admit women in the 1980s. The following was written by a Presbyterian minister who opposed the admission of women:

“I am totally opposed to a proposal which would radically change the nature of the Century …. A club creates an ethos of its own over the years, and I would deeply deplore a step that would inevitably create an entirely different kind of place.

A club like the Century should be unaffected by fashionable whims….”7

Argumentum ad baculum / Appeal to force

If the writer ever uses coercion, intimidation, or even the hint of a threat or potential of fear, then that writer is using the appeal to force to manipulate the readers into accepting the writer’s conclusion. It is often used in politics and can be seen in such phrases as “might makes right.” Appeal to force can be done directly or indirectly, for example:

“… the terrorists said we had to supply the money or they would harm the hostages.”

“We must learn to live together peacefully and cooperatively. Otherwise we will never be able to control the global problems and resource shortages that will inevitably kill the human race.”

Argumentum ad crumenam

If the writer argues that money or success is proof of a propositions merit, s/he is guilty of argumentum ad crumenam, the belief that those with more success are more likely to be right.

“Gates is the richest man in the world obviously because his software is the best in the world.”

“Windows is the best operating system because Microsoft is the largest, most affluent, most profitable software company.”

Argumentum ad hominem

Argumentum ad hominem literally means an “argument directed at the man,” not at his ideas, evidence, arguments, or beliefs. Argumentum ad hominem usually occurs when the writer attacks the person or group of people making the assertion, rather than attacking the person’s evidence, assumptions, premises, inferences, or conclusions. Not only is this faulty logic, since the validity and soundness of an argument does not depend on the personal characteristics of the person who makes it, it is also a poor rhetorical strategy because it is so easy to beat.

For example, I once remember seeing a talk show that featured a guest who was trying to argue that some races of man were genetically inferior to other races of man. This guest had all sorts of charts and graphs reporting the findings of various tests by independent research programs into general intelligence, mathematical skills, creative thinking, genetics, hereditary, and the like. These tests, the guest argued, proved that some races where genetically inferior. Not long after the guest finished his presentation, members of the audience would begin to shout epithets at the speaker, calling him “racist,” a “bigot,” and worse. The speaker, however, would simply say, “You can call me whatever you like, but you haven’t done anything to disprove my argument.” With that one line, he could fool the gullible and deflect the ad hominem attack, looking that much better in the process. (The real way to approach this speaker would be to attack his evidence, to show that the original data were not relevant to the conclusions he was trying to make, to show that the speaker has no credentials or expertise that would allow him to analyze and interpret the data accurately anyway, to show that in some cases the data were corrupted and invalid in the first place.) For another example of ad hominem, consider:

“Atheism is an evil philosophy. It is practiced by Communists and murderers.”

There is no direct connection between the arguments of atheism and the people who propose those arguments. It is fallacious, therefore, to reject an argument simply because we reject the people who make the argument. (This is similar to social identification.)

Lawyers will sometimes cast doubt upon the testimony of a witness in a court of law by showing, for example, that s/he is a known perjurer. This is not truly an ad hominem attack. Rather, it is a valid way of reducing the credibility of the testimony given by the witness; however, it does not demonstrate that the witness’s testimony is false. To think that it does is to fall victim to argumentum ad ignorantiam.

If a writer uses some fact of the opponent’s particular situation, then then that writer is guilty of using the circumstantial form of argumentum ad hominem. For example:

“It is perfectly acceptable for a person to steal food if s/he is poor. How can you argue otherwise since you’re quite wealthy?”

“Of course you would argue that pornography is not a bad thing. You’re a man.”

To dismiss the opponent’s argument solely because of the particular circumstances of his/her life is unfair. (Again see also social identification.)

Argumentum ad ignorantiam

Argumentum ad ignorantiam means “argument from ignorance.” If a writer is trying to argue that something must be or might be real simply because there is no evidence to the contrary, then the writer is using argumentum ad ignorantiam. This fallacy asserts the truthfulness of a proposition simply on the basis that there is no evidence to the contrary:

“Of course UFOs are real. Nobody can prove otherwise.”

“Ghosts and other psychic phenomena might very well be real. No one yet has shown any proof that there is no after-life.”

This fallacy does not apply in a court of law, where one is generally assumed innocent until proven guilty. Therefore, we never ask a defendant to prove s/he’s not guilty. Also, in science, if it is known that an some event would produce specific evidence of its having occurred, the absence of such evidence can validly be used to infer that the event did not occur. See also shifting the burden of proof

Argumentum ad lazarum

If the writer suggests that a proposition by someone who is poor is sounder or more virtuous than a proposition put forward by someone who is wealthier, then that writer is using Argumentum ad lazarum, the opposite of the argumentum ad crumenam.

“The Pope lives a simple, austere life, so he must be more spiritually attuned to hearts of the people.”

Argumentum ad misericordiam / Appeal to pity

If a writer is presenting the evidence so that it has the strongest emotional impact possible on the audience (regardless of the soundness or validity of the evidence), then this writer is appealing to the emotions in this fallacy, the appeal to pity, also known as special pleading. The writer uses the readers’ sense of pity to encourage the readers to accept his/her conclusion. For example:

“The right thing to do is to contribute substantially to our charity. The children in our orphanage will have little food and few toys without your donation.”

Argumentum ad nauseam

Writers sometimes feel that if they repeat a proposition often enough, the reader will accept it as fact. Of course, this is fallacious reasoning since repeating an assertion does not make it true, but it does seem to work that way psychologically for some people. Advertisers and children know this.

Argumentum ad novitatem

The opposite of argumentum ad antiquitatem, the writer asserts that a proposition is more likely to be correct simply because it is new or newer than the other propositions.

Argumentum ad numerum

If the writer attempts to persuade the readers by pointing to the sheer numbers of people who support a position, suggesting thereby that this is proof of the position’s validity or soundness, then that writer is guilty of argumentum ad numerum. This fallacy rests on the notion that the more people who support or believe a proposition, the more likely it is that that proposition is correct.

“The polls showed that the vast majority of Americans supported the President; therefore this proves the President was justified in going to war.”

This is much like argumentum ad populum.

Argumentum ad populum

If a writer attempts to persuade the readers by asserting that the majority of people feel a certain way on some issue, then the writer is guilty of argumentum ad populum, also known as appealing to the gallery or appealing to the people. Similarly, if the writer attempts to win acceptance of an assertion by appealing to the beliefs of a large group of people, that writer is using argumentum ad populum. Furthermore, this fallacy is often couched in emotive language. For example:

“Chevrolet — The Heartbeat of America”

“The Earth must be flat. Millions of people know that it is. Are you trying to tell them that they are all mistaken fools?” (Isabella to Columbus)

Argumentum ad verecundiam / Appeal to authority

If a writer uses the celebrity or the fame of others as proof for an assertion, s/he is guilty of appeal to authority. For example:

“George Foreman endorses this grill, so it must be good.”

“Ed McMahon wouldn’t be the spokesperson for this company unless it was a good company.”

This sort of argument, however, can be quite legitimate; for example, referencing an admitted authority in a particular field may be relevant to a discussion of that subject. This is why we have bibliographies. We cite the sources that are relevant and knowledgeable in a our field of research as a way of saying to the reader, “See reader; I have done my homework. I have learned my stuff; therefore, you can trust me when I come to a conclusion on this subject.” Citing a legitimate authority in a legitimate way builds ethical and rational appeal simultaneously.

Audiatur et altera pars

Sometimes, writers will not explicitly state all the premises and all the assumptions of their arguments. Traditionally, the rhetorical principle of audiatur et altera pars holds that all of the premises (all assumptions) of an argument should be stated explicitly. Though not strictly a fallacy, writers who ignore this principle run a risk: careful readers often feel that writers are trying to hide something if those readers see only implicit, rather than explicit, assumptions.

Begging the question

If a writer derives a conclusion from a premise that presupposes the conclusion, then s/he is begging the question, meaning that s/he has not truly addressed the issue under discussion, but rather has slipped around the real question fallaciously. This is a form of circular reasoning.

“Women are an important part of the church. But women shouldn’t be priests because Jesus was a man, the apostles were men, and so women should not be ordained as priests.”

Bifurcation / False Dilemma

Often referred to as the “either/or” fallacy, the writer tries to convince the reader to accept his/her proposition because s/he suggests that there are only two possibilities, one that is truly bad or the other less awful (the one likely to be favored by the writer). This is a false dilemma because usually other alternatives do exist but are not explored.

“Either you let me raise taxes, or I will have to lay off 100 police and fire fighters in order to balance the city’s budget.”

The way to avoid a false dilemma is to remember that often there are many different ways to resolve a problem, not just the two offered by the writer. In the example above, a city could raise revenues by increasing the taxes on gasoline, liquor, tobacco or by increasing the fees at its airports, harbor, parks, etc. We needn’t think that the only alternatives are raising property taxes and lay offs.

Circulus in demonstrando / Circular reasoning

Writers who use the same proposition as both a premise and a conclusion are guilty of circular reasoning. In such cases, the writer (and possibly the readers) will not notice the fallacy since the conclusion will be rephrased, allowing the fallacy to appear as a valid argument. For example:

“We must not allow homosexuals in the armed forces. If a member of the armed forces is found out to be homosexual, s/he will be discharged from service. And if homosexuals are in fear of losing their careers and their jobs, they are security risks since they will be open to blackmail if they are found out. Therefore, we should not allow homosexuals in the armed forces.”

Note that the argument is entirely circular; the premise is the same as the conclusion. Arguments like this have been the reason to ban homosexuals from the armed forces before Clinton’s “Don’t ask; Don’t tell” policy was instituted.

Complex question / Fallacy of interrogation / Fallacy of presupposition

If a writer presupposes a proposition within another question or statement, the writer is guilty of the fallacy of presupposition This is the opposite of begging the question. A classic example of this fallacy is the “loaded question”:

“When did you stop hitting your dog?”

The question presupposes the truthfulness of another assertion that has not even been established, or it might presuppose a positive answer to another question which has not even been asked. The goal of this trick is to suggest that something is true without having to support the proposition with evidence. Consider:

“Where did you put the books you took from me?”

“How long will America allow the United Nations to control its foreign policy?

Converting a conditional

If a writer tries to argue that a conclusion drawn from a specific condition also entails that we can conclude the specific condition by knowing the general situation, then s/he is converting a conditional. Argument using this fallacy take the form If A then B, therefore if B then A.

“If my cat is like all cats, then all cats are like my cat.”

Cum hoc ergo propter hoc

If a writer argues that two things are causally connected because they occurred at the same time, then the writer might be guilty of cum hoc ergo propter hoc, meaning “with this, therefore because of this.” See also post hoc ergo propter hoc. This fallacy ignores the possibility that the two things might be unrelated, having different causes, and that their simultaneous appearance was coincidence. This fallacy also ignores the possibility that the two things appeared at the same time for some yet unknown third cause, the common origin of both. Just because two things occur at the same time does not necessarily mean one caused the other. Coincidence does not prove causation.

“The accident happened at the same time the church bell rang: it must be a sign.”

Denial of the antecedent

If a writer argues that B must be false since A is false and A implies B, then s/he is guilty of denying the antecedent, meaning to deny the truth of that which went before. The fallacious argument takes the form A implies B, A is false, therefore B is false. The truth table for implicature above shows us that it is indeed possible for a false premise to still yield a true conclusion. That sort of thing happens all the time in the real world, and we marvel at such dumb luck. This fallacy is often confused with non causa pro causa.

Dicto simpliciter / Sweeping generalization / Fallacy of accident

If a writer applies a general rule to a particular situation even when the circumstances of the situation mean that the rule doesn’t apply, then s/he has made a sweeping generalization. A sweeping generalization is the opposite of a hasty generalization.

“Americans generally dislike eating tofu. You are an American, so you must dislike tofu.”

On occasion, a writer might use a general rule that ordinarily is applicable to a particular situation but at this moment, quite unexpectedly by some accident of chance, the rule doesn’t apply and the writer fails to notice the difference. This then is the fallacy of accident, employing a general rule to a particular case whose “accidental” circumstances mean that the rule is inapplicable.

All of these errors occur when the writer goes from the general to the specific.

Equivocation

If writers use the same term with different meanings in an argument, they are guilty of equivocation. This is unfair since the ambiguity of the key term makes it harder to evaluate the merits of the argument as a whole.

“Microsoft is proud of the fact that it gives away free software. Its Internet Explorer and Outlook Express programs have been free to anyone for years. That’s one of the reasons the company managed to build a monopoly in those sectors. However, now if computer users wish to continue to use the newest versions of Microsoft’s free software, they will have to buy Microsoft’s newest operating systems, since the newest versions of the free software will only come bundled on the new operating system.”

Fallacies of composition

If a writer concludes that a property of one of the parts applies to the whole, then s/he has committed the fallacy of composition.

“Aircraft are made entirely of lightweight alloys; therefore, they must be very lightweight machines.”

Similarly, if a writer argues that the properties of an individual are shared by the entire collection, then we see again the fallacy of composition from another perspective.

“A car creates less pollution than a bus. Therefore, cars are environmentally better than buses.”

Fallacy of division

If a writer assumes that a property of the whole is shared by all the parts, s/he has fallen victim to the fallacy of division. This is the opposite of the fallacy of composition.

“You come from an uneducated family. You must be uneducated.”

Likewise, a writer might also mistake a property of a collection to be identical with the properties of each item.

“Children are selfish. Therefore, this child is selfish.”

Fallacy of the undistributed middle / A is based on B fallacies / …is a type of… fallacies

If a writer argues that two or more things are similar without specifying how or why they are similar, then s/he is guilty of the fallacy of the undistributed middle.

“Aristotle is a mammal, cats are mammals, so Aristotle is a cat.”

“Poetry is a based on rhythm, and music is based on rhythm, so isn’t poetry a kind of music?

False analogy

If a writer uses a comparison that is very weak, inappropriate, or based on a misunderstanding, then s/he is using false analogy. An analogy (comparing something known to something unknown in order to explain or understand the unknown) is one of the most useful rhetorical devices a writer can employ. However, if the comparison is based on just a few similarities (ignoring heaps of differences) or if the comparison is based on a misunderstanding of a term or idea (ambiguity), we then have a false analogy.

“College is much like high school. Each has 50 minute classes. Each has a different teacher for different subjects. So there is no difference between them.”

Hasty generalization

If a writer derives a general conclusion on the basis of just a few examples that are not representative of all possible situations, cases, or scenarios, then s/he is guilty of hasty generalization. This fallacy is the opposite of the sweeping generalization.

“I once got a bad carton of milk from that store, so I’ll never shop there again.”

Non causa pro causa / Post hoc ergo propter hoc

If a writer argues that A caused B without actually showing the causal relationship, then s/he has the non causa pro causa fallacy, meaning, literally, “not proven to be the cause.”

“I took an aspirin and took a nap; then my headache disappeared. So the aspirin cured my headache.”

Naps too have been known to cure headaches.

Likewise, if a writer argues that A happened after B, therefore B must have caused A, then s/he might have the post hoc ergo propter hoc fallacy, meaning, literally, “after this, therefore because of this.”

“The Soviet Union collapsed after taking up atheism. Therefore we must avoid atheism for the same reasons.”

Together, these are often called the false cause fallacies.

Non sequitur

If a writer draws conclusions from premises that are not logically connected to the conclusion, then s/he has committed a non-sequitur.

“Smoking cigarettes is dangerous, but nearly everything in life has some danger, such as driving a car or crossing the street. So, if you are willing to drive a car, you should also be willing to smoke.”

Personification / Reification / Hypostatization

If writers present abstractions as if they were concrete entities, then they are guilty of reification, also known as hypostatization. occurs when an abstract concept is treated as a concrete thing. A special case of this rhetorical gaff is personification, in which the abstraction is imagined to have human qualities.

“Nature doesn’t like the way humans treat the environment.”

Plurium interrogationum / Many questions

If the writer demands or suggests that there is only one answer to a complex question, or insists on a single answer to a multi-part questions, then s/he is using the fallacy of many questions.

“Yes or no, Mr. Jones, did you throw away the items after you stole the merchandise?”