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.
ogic 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).
ogical 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."
hen 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.
ropositions serve as the foundational elements to the three parts of an argument the premises, the inferences, and the conclusions.
Propositions as Premises
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.)
remises (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
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
inally, 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.
raditionally, 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.
n 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.
inally, 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.
aving 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.
econdly 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).
lso, 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?)
hirdly, 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.
ourth, 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."
he 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.
inally, 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 examine and analyze the opposing premises, inferences, and conclusions systematically, 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.
e need to remember these five points if we truly wish to write a valid argument rather than "pseudo-arguments."
arlier, 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
n 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.
o 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|
|T F F|
|T T T|
o 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.
f 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.
aving 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.
et'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.
f 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."
"We should support those governments that support our policies."
arlier, 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
f 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.
f 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
f 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
f 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
f 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
f 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
rgumentum 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.
or 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.)
awyers 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.
f 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."
o 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
rgumentum 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."
his 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
f 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
f 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
riters 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
he 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
f 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
f 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
f 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
ometimes, 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
f 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
ften 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
riters 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
f 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
f 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
f 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
f 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
f 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.
f 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
f 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
f 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
f 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?
f 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."
f 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
f 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.
f 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
f 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
f 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?"
See also the complex question.
f a writer throws in irrelevant material to distract readers from the real issues, then s/he is introducing a red herring into the argument. By diverting attention away from the premises and the inferences of the argument to an irrelevant issue (the red herring), the writer know that s/he might be able to sneak a weak or unsound argument onto the readers.
Shifting the burden of proof
riters always have the burden of proof for validating any assertion or proposition they make. Shifting the burden of proof, a special case of argumentum ad ignorantiam, means putting the burden of proof on the anyone who denies or questions the assertion being made. Like argumentum ad ignorantiam, this fallacy rests on the assumption that something is true unless proven otherwise.
"I am sure that Elvis, like Kennedy and Marilyn Monroe, is alive and living on a desert island in the South Pacific. However, some say Elvis isn't alive. Can they prove that?"
Slippery slope argument
f a writer suggests that accepting one idea automatically entails that we must accept any other related idea as well, then s/he is using the slippery slope argument.
"If we ban assault rifles, then we would have to ban hunting rifles and handguns as well, and we'll lose our Second Amendment rights. Therefore, we should not ban assault rifles or other automatic weapons."
"If we allow legal abortions, then soon we will also allow euthanasia. Then it's not a far step till we are legalizing the killing of the elderly or the ill simply because they are no longer useful. And why not simply kill any baby that is born with some tragic birth defect? But why kill only babies that are undesirable because of a birth defect? Why not kill a baby only because its hair color or sex is not the choice we want? So we must not allow abortion to remain legal."
ocial identification is the fallacy of excluding people from a discussion (or argument) on the basis of some socially distinguishing feature, such as ethnicity or race or gender or membership in some social group, etc. For example, I once witnessed two women sitting at a restaurant table in the company of a man. The women were arguing about abortion. One was adamantly pro-life, and the other was equally adamantly pro-choice. During this argument, that man sat quietly between them. At one point in their heated (and rather loud) debate, the man started to speak, and both women, simultaneously, turned on him and nearly said in unison:
"Shut up! What do you know about this problem? Men have no right to make laws or to debate the abortion issue: it's a woman's issue alone. Only women can get pregnant, only women can bear children, so only women should make the decisions about abortion rights."
It seemed to me that both women were guilty of fallaciously excluding the man from the debate on the basis of some socially identifying mark his gender. It is perfectly possible that a man might have something constructive to contribute to that discussion, but that man was not allowed an opportunity to participate on the basis of social identification. He was not part of the "group" as defined by the women.
For another example, consider:
"What do you Americans know about the strife in Northern Ireland? You're not Irish, so you should keep out of this struggle and let the Irish settle this among themselves."
We can think of the fallacy of social identification as a generalized ad hominem attack.
riters who misrepresent an opponent's position so that it is easier to refute the opposition are guilty of presenting a straw man argument. This is unfair and fallacious since the writer truly fails to refute the real arguments that the opponent has made.
f a writer resorts to the "Oh yeah? Well, you too!" rhetorical strategy as a response to a challenge, the writer has succumbed to the tu quoque fallacy. The underlying assumption here is that an action is acceptable because the other party has done it as well. Thus, a precedence is established. For instance:
"You've hit me before."
"So? You've hit me too."
Many rhetoricians see this as variety of personal attack and therefore classify it as a special case of argumentum ad hominem. I am not sure about that, however. It seems to me that the "Oh yeah? Well, you too!" fallacy is really a kind of circular reasoning.
1 Some rhetoricians make a distinction between argumentative and persuasive writing: argumentative writing uses rational appeal alone, while persuasive writing uses all three Aristotelian appeals.
An exercise allowing you to write a glossary and definitions of key terms for your study is available on the Logic and Logical Fallacy: Glossary and Definition page.
Copi, Irving M. Introduction to Logic. Upper Saddle River, N.J.: Prentice Hall, 2002.
Reed, David H. C. Letter to the New York Times, January 13, 1983, p. 14.
Rottenberg, Annette T. The Structure of Argument. New York: Palgrave Macmillan, 1994.
Schick, Theodore and Lewis Vaughn. How to Think About Weird Things: Critical Thinking for a New Age, 2nd ed., Mayfield, 1998.
Related Sites on the Web
Downes, Stephen. "Fallacies" <http://onegoodmove.org/fallacy/index.htm>
The Internet Encyclopedia of Philosophy. "Deductive and Inductive Arguments" <http://www.utm.edu/research/iep/d/ded-ind.htm>
The Internet Encyclopedia of Philosophy. "Fallacies" <http://www.iep.utm.edu/fallacy/>
Labossiere, Michael C. "Fallacies" <http://www.nizkor.org/features/fallacies/>
Mathew. "Logic & Fallacies" <http://www.infidels.org/library/modern/mathew/logic.html>
Logical Argumentation & the Art of Critical Thought
Footnotes are at the end of the paper
Before you begin, and if you have not already done so, you may want to read the page titled Commonplace Nonsense
"No man who is indifferent to argument and to evidence can claim to be concerned for truth." - Antony Flew (1975), Thinking About Thinking, p. 14.
"The challenge to think better is a challenge to our integrity." - Antony Flew, Ibid, p. 113.
Logic, according to the Oxford dictionary, is the science of reasoning, proof, thinking, or inference. It describes the relation between language and the world, in its most systematic outline. Logic was first given formal expression by Aristotle, the famous Greek philosopher, almost 2500 years ago. In his well-known treatises, he described the way we try to discover the truth - observing the world, selecting impressions, making inferences and generalizing. In this process Aristotle identified two forms of reasoning: induction and deduction. Both forms, he realized, are subject to error. Our observations may be incorrect or insufficient, and our conclusions may be faulty because they have violated the rules governing the relationships between statements.
Logic allows us to analyze a piece of reasoning and determine whether it is correct or not (valid or invalid). It is an attempt to provide a theory of what makes an argument good. Two factors can make an argument bad: if the assumptions it starts from are ambiguous, unclear, or simply false, or if it reasons from these assumptions in the wrong way. For example, one of the most common errors in reasoning is the introduction of an irrelevant issue, one that has little or no direct bearing on the development of the argument.
When people make statements, they may offer evidence to support them or they may not. A statement that is supported by evidence is the conclusion of the argument, and logic provides the tools for the analysis of arguments. Logical analysis is concerned with the relationship between a conclusion and the evidence given to support it and with methods for distinguishing those arguments that are logically sound from those which are not.
Of course, one does not need to study logic in order to reason correctly; nevertheless, a little basic knowledge of logic is often helpful when constructing or analyzing an argument. In ordinary usage, the term "argument" signifies a dispute but in logic it does not have that connotation. As we use the term, an argument can be given to justify a conclusion, whether or not anyone openly disagrees. However, intelligent disputation - as opposed to the sort of thing that consists of loud shouting and name-calling - does involve argument in the logical sense. You may have seen the Monty Python skit in which a man enters a room and asks, “Is this the right room for an argument?” The occupant answers, “I already told you once”, to which the first man replies, “No, you didn’t”, and is told, “Yes, I did”. They then begin shouting at one another, hurling the same charges back and forth again and again. This is not what logicians have in mind when they talk about “arguments”.
Hence, for one who is interested in seeking an intelligent, reasonable resolution to a disagreement, it is an occasion for providing evidence and appealing to the rules of logic. Arguments are often designed to convince, and this is one of their important and legitimate functions; however, logic is not concerned with the persuasive power of arguments. Arguments that are logically incorrect often do convince, while logically impeccable arguments often fail to persuade. A person may be persuaded by an abominable argument; just as he may remain unconvinced by considerations which he certainly would accept if he were more rational, or more honest, or both. Roughly speaking, then, an argument is a group of statements standing in relation to its supporting evidence. More precisely, an argument consists of one statement that is the conclusion and one or more supporting statements of supporting evidence. The statements of evidence are called premises.
Note that no claim is being made here about whether logic is universally applicable. The matter is very much open for debate. This paper merely attempts to explain how to use logic, given that you have already decided that logic is the right tool for the job. Certainly there is an important place in life for passion, compassion, humour and commitment and it is important to understand that rationality and emotion are not logical opposites or mutually exclusive entities. But these emotions should not be allowed to inhibit one's objectivity, judgement and ability to get at the truth.
Propositions (or statements) are the building blocks of a logical argument. A proposition is a statement that is either true or false; for example, "It is raining" or "Today is Tuesday". Propositions may be either asserted (said to be true) or denied (said to be false). Note that this is a technical meaning of "deny", not the everyday meaning. The proposition is the meaning of the statement, not the particular arrangement of words used to express it. So "God exists" and "There exists a God" both express the same proposition. To be able to say correctly that a statement is true, one must be able to: (1) know what the statement means (i.e., its propositional content). However, as Immanuel Kant has pointed out over 200 years ago, knowing what X means or having a concept of X does not allow one to necessarily conclude that X exists. For example, we have a concept of a unicorn, but we cannot infer from this that unicorns exist, (2) know how to verify the statement and (3) have good reasons and evidence for believing the statement - psychological, emotional or practical reasons (i.e., motives) for believing a statement are irrelevant to the question of whether or not the statement is true.
An argument is, to quote the Monty Python sketch, "a connected series of statements to establish a definite proposition". An argument consists of three stages.
First of all, the propositions which are necessary for the argument to continue are stated. These statements, as has been previously mentioned, are called the premises of the argument. They are the evidence or reasons for accepting the argument and its conclusions. Premises (or assertions) are often indicated by phrases such as "because", "since", "obviously" and so on. (The phrase "obviously" is often viewed with suspicion, as it can be used to intimidate others into accepting suspicious premises. If something doesn't seem obvious to you, don't be afraid to question it. You can always say, "Oh, yes, you're right, it is obvious" when you've heard the explanation.)
Next, the premises are used to derive further propositions by a process known as inference. In inference, one proposition is arrived at on the basis of one or more other propositions already accepted. There are various forms of valid inference. The propositions arrived at by inference may then be used in further inference. Inference is often denoted by phrases such as "implies that" or "therefore".
Finally, we arrive at the conclusion of the argument ‑ the proposition that is affirmed on the basis of the premises and inference. Conclusions are often indicated by phrases such as "therefore", "hence", "thus", "consequently", "it follows that", "we conclude", and so on. The conclusion is often stated as the final stage of inference. For example:
Every event has a cause (premise)
The universe has a beginning (premise)
All beginnings involve an event (premise)
This implies that the beginning of the universe involved an event (inference)
Therefore the universe has a cause (inference and conclusion)
Note that the conclusion of one argument might be a premise in another argument. A proposition can only be called a premise or a conclusion with respect to a particular argument; the terms do not make sense in isolation. Sometimes an argument will not follow the order given above; for example, the conclusions might be stated first and the premises stated afterwards in support of the conclusion. This is perfectly valid, if sometimes a little confusing.
Recognizing an argument is much harder than recognizing premises or conclusions. Many people shower their writing with assertions without ever producing anything which one might reasonably describe as an argument. Some statements look like arguments, but are not. For example:
"If the Bible is accurate, Jesus must either have been insane, a pernicious liar or the Son of God."
This is not an argument - it is a conditional statement. It does not assert the premises that are necessary to support what appears to be its conclusion. (It also suffers from a number of other logical flaws, but we'll come to those later.)
"God created you; therefore do your duty to God."
The phrase "do your duty to God" is not a proposition, since it is neither true nor false (It is a command). Therefore it is not a conclusion, and the sentence is not an argument.
Finally, causal relationships are important. Consider a statement of the form "A because B". Here, event B is a cause that produces effect A. Causes are, as it were, the moving forces of the world. We refer to them in various ways: we may say that one event leads to another, produces it, brings it about, makes it happen, forces it, stops it, prevents it, stems it, increases it - the list goes on. No two or three terms can be depended on to cue causal arguments. You will have to judge whether a causal claim is involved, and if so, if the argument supporting the claim is a sound one. Errors in reasoning about cause-effect relationships are extremely common and can at times result in horrendous mistakes, made not only by members of the general populace, but by professional people as well. A recent case involved a discharged U.S. Marine who received an $850,000 severance cheque from the U.S. government as the result of a computer error. The ex-marine proceeded to spend over $400,000 of the money, and later argued that prior to receiving the cheque he had been praying to God that his "luck" would change - and his prayers were answered. Needless to say, the government was not impressed by this causal argument. A systematic account of causation and causal reasoning, however, is far beyond the scope of this paper. It should be pointed out that causation and causal inference are still hotly debated topics in philosophical and scientific circles. If we are interested in establishing the truth of A, and B is offered as evidence, the statement is an argument. If we're trying to explain or justify the truth of B when the truth of B is already taken for granted, then it is not an argument, but an explanation.
"There must be something wrong with the engine of my car, because it will not start." ‑‑ this is an argument.
"My car will not start because there is something wrong with the engine." ‑‑ this is an explanation.
Generally, an explanation is an attempt to indicate how or why an event occurred. Where explanation is appropriate, there is usually no question whether or not the event did occur. That much is either known to be true or accepted as true. The explanation is an attempt to make the event more intelligible or understandable. An argument, on the other hand, is an attempt to demonstrate that something is true. We employ arguments precisely when doubt exists about a statements truth. The difference between an argument and an explanation is clear enough in the abstract, but it can be very difficult to decide, in concrete instances, whether a passage is an argument or an explanation. In the example above, some confusion may result from the use of the word "because" - a word that often precedes a premise in an argument. Also, it is not possible for the same set of propositions to function simultaneously as an argument and an explanation.
There are two traditional types of argument, deductive and inductive. A deductive argument is one that provides conclusive proof of its conclusions ‑‑ that is, an argument where if the premises are true, the conclusion must also be true. A deductive argument is either valid or invalid. A valid argument is defined as one whereby if the premises are true, then the conclusion is true (Do not confuse "validity" with "truth" - validity refers only to the logical structure of an argument whereas truth is a property of propositions). Validity is a hypothetical or conditional characteristic; it assures us that the conclusion of the argument is true if the premises are true. An argument may be said to be valid in virtue of its form. For example, if (1) If everything is caused, then no one acts freely, and (2) Everything is caused, are both true, then it must also be true that (3) No one acts freely. We can represent the preceding argument in the following valid form, known as Modus Ponens.
If P, then Q Modus Ponens
Some other valid argument forms are:
Modus Tollens Disjunctive Syllogism
If P, then Q Either P or Q
Not Q Not P
Therefore, Not P Therefore, Q.
Hypothetical Syllogism Constructive Dilemma
If P, then Q Either P or Q
If Q, then R If P, then R
---------------- If Q, then S
Therefore, If P then R ---------------------
Therefore, Either R or S
De Morgan’s Laws
(1) Not (P or Q) = Not P and Not Q: If a disjunction is false, then all its disjuncts are false and vice versa.
(2) Not (P and Q) = Not P or Not Q : If a conjunction is false, then at least one of its conjuncts is false, and vice versa.
Reductio ad Absurdum ("Indirect" proof)
To prove: P
Assume: Not P
From the assumption, derive an implication: Q
Show: Q is false (contradictory, inconsistent, silly, absurd)
The idea of a reductio ad absurdum is to establish a conclusion by refuting its opposite, and it is an especially attractive tactic when what you are attempting to refute is your opponent's position in order to prove your own.
An invalid argument form is called a formal fallacy. In such cases, the premises do not logically entail the conclusion - this error is referred to as a non sequitur, which means literally “it does not follow”. It is an unfortunate human tendency to believe much more than is actually warranted from the premises. Many informal fallacies fall under the rubric of irrelevancy, including appeals to authority and the ad hominem fallacy. These will be discussed later. Two common formal fallacies are:
Affirming the Consequent Denying the Antecedent
If P, then Q If P, then Q
Q Not P
Therefore, P Therefore, Not Q
An inductive argument is an argument relevant to one kind of assertion only; namely to empirical or factual claims and one in which the premises provide some evidence for the truth of the conclusion. Deductive reason is at the heart of Mathematical reasoning, whereas inductive reasoning is the logical underpinning for the Scientific Method. Inductive arguments are not valid or invalid; however, we can talk about whether they are better or worse than other arguments, and about how probable their premises are. An inductive argument is one whose conclusion is claimed to be more or less probable, but not certain. Inductive arguments can grow better or worse as new evidence comes in. There are degrees of strength or support. They are "justified" when they have enough good evidence to support their conclusion. Consider the following arguments, one deductive, and the other inductive:
Deductive: Every mammal has a heart
All whales are mammals
Therefore, every whale has a heart.
Inductive: Every whale that has been observed so far has a heart.
Therefore, every whale has a heart.
Consider the following two inductive arguments:
(1) Three hundred and fifty persons observed in a sample of 500 smokers have cardiovascular disease.
Therefore, smoking causes cardiovascular disease.
(2) All smokers have cardiovascular disease or will develop it during their lifetime.
Therefore, smoking causes cardiovascular disease.
The difference between arguments (1) and (2) is that of quantity or scope. The conclusion in each case is causative and the premise in (2) could quite easily have been a conclusion of the premise in (1). The conclusion reached in each of the arguments, which may or may not be warranted, could be a possible hypothesis or conjecture. A more cautious inductive inference from the premises might be: "Smoking is a factor in the cause of cardiovascular disease in some persons."
The deductive argument is designed to make explicit the content of the premises; the inductive argument is designed to extend the range of our knowledge. There are forms of argument in ordinary languages that are neither deductive nor inductive. However, we will concentrate for the moment on deductive arguments, as they are often viewed as the most rigorous and convincing. It is important to note that the fact a deductive argument is valid does not imply that its conclusion holds. This is because of the slightly counter‑intuitive nature of implication, which we must now consider more carefully. Obviously a valid argument can consist of true propositions. However, an argument may be entirely valid even if it contains only false propositions. For example:
All insects have wings (premise)
Frogs are insects (premise)
Therefore frogs have wings (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 a subtler manner, we can reach a true conclusion from one or more false premises, as in:
An elephant is bigger than a mouse (premise)
A mouse is bigger than a horse (premise)
Therefore, an elephant is bigger than a horse (conclusion)
On the other hand, an argument may have true premises and true conclusions and still be invalid. Consider:
The earth has one moon.
Snow is white.
Therefore, crows are black.
However, the one thing we cannot do is reach a false conclusion through valid inference from true premises. We can therefore draw up a "truth table" for implication.
The symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. "T" and "F" represent true and false respectively.
Premise Conclusion Inference
A B A=>B
F F T If the premises are false and the inference
F T T valid, the conclusion can be 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.
A sound argument is a valid argument whose premises are true. A sound argument therefore arrives at a true conclusion. Be careful not to confuse valid arguments with sound arguments.
An argument is sound if (i) its logic is good and (ii) the information in it is correct. A deductive argument is sound when it is both valid and contains only true propositions. An inductive argument is sound when it is both justified and contains only true propositions.
But determining the soundness of arguments is not a simple matter, for three reasons.
First, before we can assess an argument we must determine its precise meaning. It would be convenient if the meaning of arguments were always clear, but unfortunately this is often not so. An argument may be unclear because the meaning of one or more of its statements is unclear, or because the nature of the connection that is being asserted between the premises and conclusion is unclear. This means we have to learn how to interpret statements and arguments in a way that makes their meaning as clear as possible. The skills needed for this task are interpretive skills.
Second, determining the truth or falsity of statements is often a difficult task. Even when we are sure we know precisely what a statement means we may be unsure about its truth, and may even be unsure how to go about determining whether it is true or false. As we shall see, there are several different types of statements, and each type has its own method for determining truth and falsity. The skills needed for this task are verification skills.
Third, assessing arguments is complex because there are several different types of inferences, and each type requires a different kind of assessment. It is necessary to learn how to recognize these different types of inferences and to become familiar with these different methods of assessment. For this purpose reasoning skills are needed.
These three types of skills ‑ interpretive skills, verification skills, and reasoning skills ‑ constitute what are usually referred to as critical thinking skills. Developing a mastery of them is important for several practical reasons.
First, we are inundated with information of all sorts, but this information is useless unless we know how to use it in our thinking to draw out its implications and consequences. Much of it is incomplete and one-sided in ways that are often not apparent, and if we are not on our guard we may be misled.
Second, we are constantly presented with arguments designed to get us to accept some conclusion that we would otherwise not accept. Politicians, preachers, advertisers, editorial writers, and special‑interest groups of all sorts spend a great deal of time, thought, and money attempting to persuade us to believe the things they want us to believe, and it is important to be on guard against arguments that fail to meet the appropriate logical criteria. This is partly a matter of our own self‑interest, for when others seek to make us believe things that are in their interest it is possible, or even likely, that our interests are not being well served.
Third, mastering critical thinking skills is also a matter of intellectual self‑respect. We all have the capacity to learn how to distinguish good arguments from bad ones and to work out for ourselves what we ought and ought not to believe, and it diminishes us as persons if we let others do our thinking for us. If we are not prepared to think for ourselves, and to make the effort to learn how do this well, we will always be in danger of becoming slaves to the ideas and values of others and to our own ignorance.
And finally, critical thinking skills can make it easier for us to persuade others to change their beliefs. Many beliefs are based more on emotion than on reason, although those holding them usually believe they are based on reason. In fact, it is rare to find a person, even a complete bigot, who does not believe that his or her beliefs have a rational basis. Critical thinking skills can often be effective in dislodging such beliefs, and persuading others to change their views.
This last point raises a number of moral questions. Like any skill, critical thinking skills can be used for good or ill. There are many ways in which they can be abused. They can be used to make a bad argument look much stronger than it really is, and to make an opponent's position look much weaker than it really is. They can be used to make us look wise, and to make others look foolish. They can be used to avoid having to respond to legitimate criticisms, and to persuade others to change their beliefs for inadequate reasons. Every day we find ourselves in situations in which we could use our critical thinking skills for such purposes, and sometimes we may be tempted to do so. Yielding to the temptation, however, is dishonest and hypocritical.
Consider these two valid arguments that have diametrically opposed conclusions, one of which must be unsound. Hence one or more of the premises of one of the arguments must be false. Which premises would you challenge?
(1) The world exhibits conclusive evidence of design.
(2) If the world exhibits conclusive evidence of design, then the world has a designer who is God.
(3) Therefore, God exists.
(1a) If God exists; there is an all-powerful, all-knowing, and perfectly good being who created the world.
(2a) If there is an all-powerful, all-knowing, and perfectly good being who created the world, then the world is free of evil.
(3a) The world is not free of evil.
(4a) Therefore, God does not exist.
To delve further into the structure of logical arguments would require a lengthy discussion of linguistics and philosophy. It is simpler and probably more useful to summarize the major pitfalls to be avoided when constructing an argument. These pitfalls are known as fallacies. In everyday English the term "fallacy" is used to refer to mistaken beliefs as well as to the faulty reasoning that leads to those beliefs. This is fair enough, but in logic the term is generally used to refer to a form of technically incorrect argument, especially if the argument appears valid or convincing. So for the purposes of this discussion, we define a fallacy as an argument which appears to be correct, but which can be seen to be incorrect when examined more closely or an argument that should not persuade a rational person to accept its conclusion. Inductive fallacies result from the wrong use of evidence: for example, the arguer leaps to a conclusion on the basis of an insufficient sample, ignoring evidence that might have altered her conclusion. Deductive fallacies, on the other hand, result from a failure to follow the rules of logic in a series of statements. Here the arguer neglects to make a clear connection between the various parts of her argument.
Below is a list of some common fallacies, and also some rhetorical devices often used in debate. Fallacies are difficult to classify, first, because there are literally dozens of systems for classifying, and second, because under any system there is always a good deal of overlap. Therefore, the following list is not intended to be exhaustive.
ARGUMENTUM AD BACULUM (APPEAL TO FORCE)
The Appeal to Force is committed when the arguer resorts to force or the threat of force in order to try and push the acceptance of a conclusion. It is often used by politicians, and can be summarized as "might makes right". The force threatened need not be a direct threat from the arguer. For example:
"... Thus there is ample proof of the truth of the Bible. All those who refuse to accept that truth will burn in Hell."
ARGUMENTUM AD HOMINEM
Argumentum ad hominem is literally "argument directed at the man". The abusive variety of Argumentum ad Hominem occurs when, instead of trying to disprove the truth of an assertion or the evidence for the argument, the arguer attacks the person's personality, character, circumstances, motives, qualifications, etc. This is invalid because the truth of an assertion does not depend upon the goodness of those asserting it. For example:
"Atheism is an evil philosophy. It is practised by Communists and dictators."
"Eric Hoffer knows nothing about philosophy. He's a longshoreman."
Sometimes in a court of law doubt is cast upon the testimony of a witness by showing, for example, that he is a known perjurer. This is a valid way of reducing the credibility of the testimony given by the witness, and not argumentum ad hominem; however, it does not demonstrate that the witness's testimony is false. To conclude otherwise is to fall victim of the Argumentum ad Ignorantiam (see elsewhere in this list).
The circumstantial form of Argumentum ad Hominem is committed when a person argues that his opponent ought to accept the truth of an assertion because of the opponent's particular circumstances. For example:
"It is perfectly acceptable to kill animals for food. How can you argue otherwise when you're quite happy to wear leather shoes?"
This is an abusive charge of inconsistency, used as an excuse for dismissing the opponent's argument. This fallacy can also be used as a means of rejecting a conclusion. For example:
"Of course you would argue that positive discrimination is a bad thing. You're white."
This particular form of Argumentum ad Hominem, when one alleges that one's adversary is rationalizing a conclusion formed from selfish interests is known as poisoning the well. "Poisoning the well" is also construed as an attempt to shift attention from the merits of the argument - the validity of the reasoning, the truth of the claims - to the source or origin of the argument. For example, the mere fact that Stalin or Hitler believed something does not show that the belief is false or immoral; just because some scoundrel believes the world is round, that is no reason for you to believe it is flat.
ARGUMENTUM AD IGNORANTIAM
Argumentum ad ignorantiam means "argument from ignorance" or "appeal to ignorance". This fallacy occurs whenever it is argued that something must exist or be true simply because it has not been proved false. Or, conversely, when it is argued that something must be false because it has not been proved true. The absence of evidence establishes nothing; what we don't know cannot be evidence for (or against) anything! Our ignorance is no reason for believing anything, except perhaps that we ought to try to undertake an appropriate investigation in order to reduce our ignorance and replace it with reliable information. (Note that this is not the same as assuming that something is false until it has been proved true, a basic scientific principle.) Examples:
"Of course God exists and the Bible is true. Nobody can prove otherwise."
"Of course ESP and other psychic phenomena do not exist. Nobody has shown any proof that they are real."
Part of the temptation to believe that proof by ignorance is real proof may stem from the fact that is some courts of law a defendant is presumed innocent until proven guilty. In other words, lack of evidence against someone is taken as proof, for the purposes of the court, that they did not commit the crime. However, as many cases of guilty people being freed because of a lack of evidence show, this in not really a proof, of innocence, but merely a practical, if imprecise, way of protecting innocent people from wrongful conviction.
Also, in scientific investigation if it is known that an event would produce certain evidence of its having occurred, the absence of such evidence can validly be used to infer that the event did not occur. For example:
"A flood as described in the Bible would require an enormous volume of water to be present on the earth. The earth does not have a tenth as much water, even if we count that which is frozen into ice at the poles. Therefore no such flood occurred."
In science, we can validly assume from lack of evidence that something has not occurred. However, we cannot conclude with certainty that it has not occurred.
ARGUMENTUM AD MISERICORDIAM
This is the Appeal to Pity, also known as Special Pleading. The fallacy is committed when the arguer appeals to pity or sympathy or "moralizes" for the sake of getting a conclusion accepted. It amounts to inconsistency in the sense that one finds reasons where his advantage lies but refuses to apply the same principle to others. For example:
"If I don't get an "A" in this course, I won't be on the honour roll."
"I really worked hard in this course, therefore I should get a pass."
"I'm 38 years old and out here busting my butt in this heat and you call the ball out. It was on the line!" (Jimmy Connors at the 1992 U.S. Open)
"I did not murder my mother and father with an axe. Please don't find me guilty; I'm suffering enough through being an orphan."
This fallacy is closely related to "wishful thinking" or "rationalization". It amounts to ignoring or refusing to look for evidence that we do not want to face or which might refute our position. Like the ostrich with his head in the sand, we ignore the facts. For example:
"He will recover from cancer, because he is a good man and good men deserve to live a lot longer than he has lived."
A subtler version of special pleading is the one closely associated with Voltaire’s famous statement: “Superstition is someone else’s religion.” Voltaire’s point is that most people who belong to one religion or another believe that their religion is the TRUE religion and all others are false. Their God, their Sacred Book and their Prophet are the genuine material whereas all others are bogus and mindless superstition. This fallacy is a form of self-righteousness and hypocrisy in the sense that if these same people applied the same rules of evidence to their own faith that they applied in rejecting the faith of others, they would have to reject their own as well.
ARGUMENTUM AD POPULUM
This is known as Appealing to the Gallery, or Appealing to the People. To commit this fallacy is to attempt to win acceptance of an assertion by appealing to the majority, to what is popular - mob appeal. It often amounts to arguing in order to arouse an emotional, popular acceptance of an idea without resorting to a logical justification of the idea. An appeal is made to such things as biases, prejudices, feelings, enthusiasms, and attitudes of the multitude rather than to rational support of the idea. This is the strategy of many demagogues - remember Mark Antony's speech in Julius Caesar? For example:
"Pornography must be banned. It is violence against women."
"The Bible must be true. Millions of people know that it is. Are you trying to tell them that they are all mistaken fools?"
Contemporary America seems prone to this fallacy and was referred to as early as 150 years ago by Alexis de Toqueville as the “tyranny of the majority” in his book Democracy in America. John Stuart Mill and Ralph Waldo Emerson were two other Eighteenth Century intellectuals who also pointed this out. That the majority of people believe a proposition does not imply its truth. Most people, for example, once believed the earth was flat. When one becomes aware of the pervasiveness of psychics, televangelists, self-help gurus and pseudo-scientific nonsense on television this state of affairs is not getting any better.
Bertrand Russell once wrote “The fact that an opinion is widely held is no evidence whatever that it is not utterly absurd; indeed, in view of the silliness of the majority of mankind, a wide-spread belief is more likely to be foolish than sensible.” (Marriage and Morals)
ARGUMENTUM AD NUMERUM
This fallacy is closely related to the argumentum ad populum. It consists of asserting that the more people who support or believe a proposition, the more likely it is that the proposition is correct. Or, an unreliable method of reasoning which treats majority opinion by voting as a source of truth or a reliable guide for action on every question (The Democratic Fallacy) On many issues one must appeal to an expert or recognized authority. Those who want to put every issue to a vote are often shirking their responsibility to make a decision. Democracy is of value only in certain contexts - what is desired is an informed majority, not just a majority.
"It must be a good book - it's on the best seller list."
"Since most people believe in God and all cultures have had some concept of God, he must exist."
“The pilot of the airliner polled the passengers and the majority concluded that an emergency landing was warranted, hence an emergency landing is the most rational course of action.”
ARGUMENTUM AD VERECUNDIAM
The Appeal to Authority uses the admiration of the famous to try and win support for an assertion. For example:
"Isaac Newton was a genius and he believed in God."
"Albert Einstein was a genius and he did not believe in God."
"We must obey the Ten Commandments - they are the will of God."
"Domino's Pizza is great - Wayne Gretzky says so."
"Abortion / Homosexuality is wrong because the Bible prohibits it."
This line of argument is not always completely bogus; for example, reference to an admitted authority in a particular field may be relevant to a discussion of that subject. For example, we can distinguish quite clearly between:
"Stephen Hawking has concluded that black holes give off radiation" and "John Searle has concluded that it is impossible to build an intelligent computer". Hawking is a physicist, and so we can reasonably expect his opinions on black hole radiation to be informed. Searle is a respected philosopher of mind, but it is arguable whether he is well‑qualified to speak on the subject of machine intelligence.
Arguing that something is true because it has practical effects upon people: it consoles them or makes them happier, easier to deal with, more moral, loyal, and stable. The prudential argument presented by Blaise Pascal in his famous "Wager" is tainted in this way. Pascal argued that one should believe in the proposition "God exists" because it is prudent to do so and has consolatory and salutary effects on the believer. Another similar example:
"One should believe in immortality because without such a concept people have nothing to live for. There would be no meaning or purpose in life and everyone would be immoral."
THE FALLACY OF ACCIDENT
The Fallacy of Accident is committed when a general rule is applied to a particular case whose "accidental" circumstances mean that the rule is inapplicable. It is the error made when one goes from the general to the specific. For example:
"Christians generally dislike atheists. You are a Christian, so you must dislike atheists."
Moralists and legalists who try to decide every moral and legal question by mechanically applying general rules often commit this fallacy. In the realm of ethics, philosophers refer to this error as casuistry. For example:
"Thou shalt not bear false witness [lie], therefore you should tell the rapist where your sister is hiding." or
"One should not break promises. Therefore I should not break the promise to play tennis with Ralph in order to save this drowning child."
The general requirement that promises should not be broken has a tacit qualification like "all things being equal" or "in the absence of an overriding obligation". When there is a drowning child, all things are not equal, because there is an overriding obligation to save the child. During the Nuremberg Trials, the oft-heard excuse of Nazi and Gestapo members in their treatment of Jewish people that they were only following orders of their superiors is a case in point. Although one has an obligation to obey one's superiors, the obligation is overridden by the obligation to respect the minimal human rights of other people.
CONVERSE ACCIDENT / HASTY GENERALIZATION
This fallacy is the reverse of the fallacy of accident. It occurs when one forms a general rule by examining only a few specific cases that are not representative of all possible cases. This fallacy is loosely related to "slanting" - the finding or looking only for evidence that supports a pre-determined (or a priori) conclusion. Rationalizations, the finding of bad reasons or evidence that support what one already believes or intends to believe anyway, are similar self-serving biases. For example:
"Jim Bakker, Peter Popoff and Jimmy Swaggart are insincere Christians. Therefore, all Christians are insincere."
"Both Socrates and Jesus Christ, two famous martyrs, accepted slavery and we know that slavery is wrong. Therefore, all martyrs are immoral."
SWEEPING GENERALIZATION / DICTO SIMPLICITER
A sweeping generalization occurs when a general rule is applied to a particular situation in which the features of that particular situation render the rule inapplicable. A sweeping generalization is the opposite of a hasty generalization. For example:
"I believe in the Golden Rule as an inherent duty to do unto others as I would have them do unto me. If I were unable to answer a question on an examination, I would want my neighbour to help me. So it is my duty to help the person sitting next to me who asked me to give her the answer to a question on this exam."
NON CAUSA PRO CAUSA / POST HOC ERGO PROPTER HOC
These are known as False Cause fallacies. The fallacy of Non Causa Pro Causa often occurs when one identifies something as the cause of an event but it has not actually been shown to be the cause. For example:
"I took an aspirin and prayed to God, and my headache disappeared. So God cured me of the headache."
The fallacy of Post Hoc Ergo Propter Hoc occurs when something is assumed to be the cause of an event merely because it happened before the event. For example:
"The Soviet Union collapsed after taking up atheism. Therefore we must avoid atheism for the same reasons."
Statistical relationships often have nothing to do with cause and effect. For example:
"Very few automobile accidents occur when driving over 150 km/h. Therefore, one should drive over 150 km/h."
"People with large feet are better at mathematics than people with small feet. Therefore, having big feet is a reliable measure of one's mathematical ability."
Many superstitious beliefs are based on the post hoc fallacy. Accidents are attributed to walking under a ladder, breaking a mirror or a black cat walking across one's path. Many athletes are superstitious in this way - they wear a particular item of clothing before a contest and attribute this to their winning. When people read their horoscopes, which tend to be very general and universally applicable, they only look for evidence that confirms the horoscope prediction and ignore evidence to the contrary. The horoscope then becomes a self-fulfilling prophecy - which is particularly the case when the person is already a believer in Astrology. It is extremely alarming how many people believe in Astrology in spite of the fact that numerous scientific studies have shown Astrology to be false! Astrology is a pre-scientific cosmology (over 2000 years old) that attempts to predict the future and people's psychological make-up and predispositions based on the movements of the planets!! Of course, the mass media, particularly the newspapers, are extremely irresponsible in their promotion of this bogus belief system.
CUM HOC ERGO PROPTER HOC
This fallacy is similar to post hoc ergo propter hoc. It asserts that because two events occur together, they must be causally related, and leaves no room for other factors that may be the cause(s) of the events. For example:
"Sunday causes Monday."
“Mozart had a spine and heart and was a great composer; I have a spine and heart so I’ll probably turn out to be a great composer.”
PETITIO PRINCIPII / BEGGING THE QUESTION
This fallacy occurs when the premises are at least as questionable as the conclusion reached. It amount to circuitous reasoning - a logical "spinning of the wheels". For example:
"Murder is immoral because it is wrongful killing."
"The wealthy should be taxed heavily because they have a lot of money."
"The Universe has a beginning. Everything that has a beginning has a beginner. Therefore, the Universe has a beginner called God."
"Aristocracy is the best form of government because the best form of government is one in which there is strong aristocratic leadership."
This type of reasoning is often found in what are described as "closed systems" of thought. Closed systems bring out the worst kind of intellectual dishonesty and self‑righteousness. Moreover, closed systems are both self-fulfilling and self-defeating. Seeking to explain everything, they explain nothing. When defending their views, people frequently try to make their statements and arguments safe by reducing them to what philosophers call tautologies: that is, to the sort of statements that are necessarily true because the person making the assertions have made them true by definition or defend them against challenges by appealing to the truth of the system itself. For example, consider the following dialogue:
True Believer: "Do you know why you refuse to accept the truth of our religion? Do you know what your problem is? It's pride - sinful pride. And pride, my friend, is the work of Satan."
Skeptic: "I do not believe in Satan."
True Believer: "I understand, but that disbelief is itself the work of Satan. Don't you see how manipulative Satan can be?"
CIRCULUS IN DEMONSTRANDO
This fallacy occurs when one assumes as a premise the conclusion which one wishes to reach. Often, the proposition will be rephrased so that the fallacy appears to be a valid argument. For example:
"Homosexuals must not be allowed to hold government office. Hence any government official who is revealed to be a homosexual will lose his job. Therefore homosexuals will do anything to hide their secret, and will be open to blackmail. Therefore homosexuals cannot be allowed to hold government office."
Note that the argument is entirely circular; the premise is the same as the conclusion. An argument like the above has actually been cited as the reason for the British Secret Services' official ban on homosexual employees.
Another example is the classic:
True Believer: "God exists!"
Skeptic: "How do you know that God exists?"
True Believer: "It says so right here in the Bible."
Skeptic: "How do you know that what the Bible says is true.”?
True Believer: "It's the word of God."
COMPLEX QUESTION / FALLACY OF INTERROGATION
This fallacy is the interrogative form of “begging the question”. The question asked depends on a premise that has not been addressed. Those door-to-door proselytising evangelists such as the Jehovah Witnesses are notorious in committing this fallacy when they ask the question:
“What do you think God has planned for the human race?”
The hidden premise here is “God exists” and is precluded by the above statement.
Another example is the classic loaded question:
"Have you stopped beating your wife?"
The question presupposes a definite answer to another question that has not even been asked or creates the impression that a prior question has already been answered. It begs the question because it attempts to force a respondent to grant an assumption that is itself in need of proof. Lawyers in cross‑examination often use this trick, when they ask questions like:
"Where did you hide the money you stole?"
Or, a teacher might pose this question to a suspected cheater:
"Did you cheat by copying from your neighbour or by smuggling in your notes?"
Similarly, politicians often ask loaded questions such as:
"What are your views on the token effort made by the government to deal with this monstrous national debt?"
"Was it stupidity or through deliberate dishonesty that the administration hopelessly botched our relations with Japan?"