1. Formal Fallacies
   The term formal fallacy is generally applied to invalid argument forms which resemble valid argument forms. They are fallacies of form or logical structure, not of content.
   1. Affirming the Consequent
      This fallacy has the form p > q, q, p. An example of this fallacy is the following. "If Bob went to the show, then Betty went to the show. Betty went to the show. Therefore, Bob went the show."

   2. Denying the Antecedent
      This fallacy has the form p > q, ~p, ~q. An example of this fallacy is the following. "If Bob went to the show, then Betty went to the show. Bob did not go to the show. Therefore, Betty did not go to the show."

   3. Incorrect Generalization
      An example of this fallacy is the following. Each person's happiness is a good to that person. Therefore, the general happiness is good for all persons. This argument attempts to generalize from the fact that a's happiness is a good to a (in symbols Gaa) and b's happiness is a good to b (Gbb), and so forth, to the conclusion that everyone's happiness is a good to everyone [in symbols, (x)(y)Gxy]. But all that can be concluded is that given any person, his own happiness is a good to that one, or in symbols (x)Gxx. That is from Gaa, Gbb, ... only (x)Gxx can be concluded. If one concludes (x)(y)Gxy, then that one has committed the fallacy of incorrect generalization.

   4. Undistributed Middle
      Any syllogism which violates one or more of the five rules of valid syllogism commits a fallacy. For instance any syllogism that violates the rule which requires the middle term to be distributed at least once is invalid and is said to have commited the fallacy of the undistributed middle. For example, the following syllogism fails to distribute the middle term "mortal". "All humans are mortal. Some mortals are not warmblooded. Therefore, humans are not warmblooded."

2. Informal Fallacies
   In general, informal fallacies are fallacies of content rather than of form or logical structure. Informal fallacies are divided into four types or forms.
   1. Linguistic Fallacies
      A linguistic fallacy is one that comes from the misuse of language.
      1. Equivocation
         This fallacy occurs when a key term in an argument is used ambiguously. There are many different kinds of the fallacy.
         1. Fallacy of Four Terms
            No valid syllogism has more than three terms. This fallacy violates this fact. A famous example of this fallacy is the following argument. "The end of a thing is its perfection. Death is the end of life. Therefore, death is the perfection of life." In this argument the word "end" is used ambiguously, equating it with "goal" in the first premise, and with "final event" in the second premise. Thus there are four terms in this syllogism, which can be seen by substituting the word "goal" for "end" in the first premise and the phrase "final event" for "end" in the second premise, and commits the fallacy of the four terms.

         2. Ambiguity of the verb "to be"
            In this fallacy the verb "to be" is used ambiguously. For example, "Knowledge is power. Some ignorant men have power. Therefore, some ignorant men have knowledge." If the word "is" occuring in the first premise is interpreted as identity (as in "Mark Twain is Samuel Clemens"), then the argument is valid, but unsound, since the first premise is false. Knowledge is not identical to power. But if the word "is" is taken in a metaphorical sense, or any other sense, then the argument is invalid.

         3. Use-mention Fallacy
            This fallacy occurs when words are confused with what they refer to. Quotation marks are often used in the English language to distinguish between talk about (or mention of) a word and the use of a word. For example, in talking about the state of Kansas, its English name is given without quotes; the word is used to talk about the state of Kansas. But in talking about the word which is the name of the state, the word, "Kansas", is put in quotes. The omission of the quotes can lead to confusion and to the use-mention fallacy of equivocation in an argument.

      2. Composition
         This fallacy is committed when an argument contains a premise in which a term is used collectively and a conclusion in which it is used distributively. A term is used collectively when it is used to refer to a class as a whole; a term in used distributively when it is used to refer to each member of a class. For example, "All men die at some time. Therefore, there will come a time when no men are living." As far as we know, each and every man will die at some time or other. But it does not follow that there will come at time when the species man will cease to exist.

      3. Division
         This fallacy is committed when an argument contains a premise in which a term is used distributively and a conclusion in which it is used collectively Hence, it may be thought of as the "reverse" of the linguistic fallacy of composition.

      4. Amphiboly
         This fallacy concerns the ambiguity of grammatical construction, rather of words or phrases. For example, consider the following two sentences. (1) The Democrats say the Republicans are sure to win. (2) The Democrats, say the Republicans, are sure to win. The first sentence is ambiguous as the punctuation of the second sentence makes clear.

      5. Accent
         This fallacy results from the improper emphasis of a word or phrase in an argument. This fallacy is often committed by quoting a passage out of context. For example, suppose someone argued that Jefferson believed that only men, but not women, have equal rights by quoting Jefferson's statement that "All men are created equal with certain rights."

   2. Fallacies of Relevance (ignoratio elenchi)
      These fallacies are arguments in which the truth of the premises is irrelevant to establishing the conclusion. They are traditionally known as ignoratio elenchi (igoranace of what is required to establish or refute a conclusion). It is often difficult to determine whether presises are releveant to establishing a conclusion. But these fallacies are probably committed more frequently than any other type of fallacy. Since there are many ways to argue irrelevantly, only a few have been singled out and given names. The following are the traditional fallacies of relevance that occur more frequently.
      1. Argumentum ad hominem (argument to the man)
         An irrelevant or malicious appeal to personal circumstances; it consists in diverting an argument from sound facts and reasons to the personality of one's opponent, competitor or critic.

      2. The tu quoque (you too) fallacy
         This fallacy is a kind of argumentum ad hominem and is committed when one argues that his opponent holds (or held) the position that he now attacks, or engages (or engaged) in the activity that he now attacks. In other words, this fallacy is committed when one answers the charge by a similar countercharge. For example, it is committed when a senator defends his misuse of campaign funds by pointing out that his accusers have done the same thing. The fact that an opponent acts, or argues, in certain way is irrelevant to the charge that one now acts, or agues, incorrectly. Although this type of argument is an effective debating tactic, it does nothing to prove the truth of one's position or to refute the charges against one's position.

      3. Argumentum ad baculum (appeal to force or fear)
         This fallacy is committed whenever an argument appeals to intimiditation or fear instead of the evidence; it may contain, implicitly or explicitly, a threat.

      4. Argumentum ad misrecordiam (appeal to pity)
         This argument attempts to prove a point or to establish a line of reasoning by appealing to pity and related emotions.

      5. Argumentum ad ignorantium (argument from ignorance)
         This kind of argument purports to demonstrate a point or to persuade people by appealing to facts and reasons the falsity or inadequacy of which are not readily discerned; it is a misleading argument used in reliance on people's ignorance.

      6. Argumentum ad populum (appeal to people)
         This argument attempts to sway popular feeling or to win people's support by appealing to their sentimental weaknesses; it may appeal to patriotism, group interests and loyalies, and customary preferences, rather than to facts and reasons.

      7. Argumentum ad verecundum (appeal to authority)
         This argument appeals to human respect for great men, ancient customs, recognized institutions, and authority in general, in order to strengthen one's point or to produce an illusion of proof.

      8. Diversion
         This fallacy occurs when instead of trying to prove or disprove a conclusion, someone attempts to change the subject. Fallacies of this kind are frequent in debates.
         1. Appeal to Humor
            Diversion sometimes takes the form of an appeal to humor. It offten attempts to make an oppoent to appear to be ridiculous.

         2. Quibbling
            Diversion sometimes takes the form of quibbling, or arguing about insignificant details. For example, someone may argue about the meaning of a word when there is no reasonable doubt about the meaning of the word. Or he may argue about details and trivial points in such a way as to advoid or obscure the main and the more important issue. This diversion has given logic and debate a bad reputation as "hair-splitting," "nit-picking," or "logic-chopping."

      9. Strawman
         This fallacy occurs when an implausible, easily attacked, theory is substituted for one that is more plausible and less easily attacked. The following are its two most common forms.
         1. Oversimplification
            This fallacy occurs when an oversimplified theory that omits significant details and important qualifications is substituted for the theory being attacked. This fallacy is often unintentionally committed by beginning philosophy students who substitute what they think a philosopher said for what he actually said.

         2. Extension
            This fallacy occurs when a theory is extended in such a way as to make it apply to areas which it was never intended to cover in order to refute the theory.

      10. Non Sequitor
          The literal meaning of this phrase is "it does not follow." Thus, it strictly should be used to refer to formal fallacies only. But because the premises of some formal fallacies appear more relevant to their conclusion than the premises of others, the phrase is usually applied only to those formal fallacies in which there appears to be no relevant relationship whatever between the premises and conclusion. Thus a non-sequitor is wildly implausible argument.

   3. Fallacies of Begging the Question (petitio principii)
      These fallacies take several different forms. In each case, however, the fallacy of assuming as proven what one what one in attempting to prove.
      1. Circular Reasoning
         This fallacy is committed when it is argued that a proposition is true becasue it is true. Circular arguments are often appear plausible because (1) the premise and conclusion are worded differently, or (2) other premises intervene between a premise and its reaffirmation in the conclusion.

      2. Question Begging Expression
         This fallacy also presupposes that what is to be proven has already been proven. For example, to argue that any "right-thinking person" would agree that a certain conclusion is justified, or that a conclusion is "clearly" or "obviously" true may be to beg the question. No doubt a "right-thinking person" would accept only justified conclusions, but this is no way proves that the conclusion in question is justified. Nor does claiming that a conclusion is "clearly" or "obviously" true show that the conclusion is in fact true.

      3. Complex Question
         This fallacy occurs when a question is asked that presupposes an answer to another question that has not been asked. The classic example of this fallacy is "When are you going to stop beating your wife?" It assumes an affirmative answer to the question that has not been asked and not been answered, "Are you beating your wife?" Similarly, asking a jury "Are you going to let the defendant go free when your wife or child might be his next victim?" presupposes that the defendant has been proven guilty of the very thing it is intended to prove.

      4. Repeated Assertion
         This fallacy uses the techniques of repeated assertion; but repeating a proposition more than once in no way provides proof for the claim being made. These techniques are often used in advertising campaigns. And the classic example was Nazis propaganda of which Adolf Hilter once claimed that if one tells a big enough lie and tells it often enough, then people will come to believe it.

   4. Fallacies of Unwarranted Assumption
      These fallacies refer to arguments that contain a false premise or rests on a false assumption which is widely held and often leads to unsound arguments.
      1. Bifurcation (Black and White Fallacy)
         This fallacy occurs when it is assumed that only two alternatives are possible in a given situation when, in fact, more than two are possible. For example, this fallacy is committed when it argued that those who are not with us are against us, or that an action that is not moral is immoral. The first argument is fallacious because it is possible for people to be neutral, neither for nor against us. The second argument is fallacious because an action that is not moral need not be immoral; it may be amoral, that is, such that moral criteria do not apply at all. This fallacy often arises from a confusion of contraries with contradictories. Contradictory propositions are those such that if one is true the other is false. For example, "the box is black" and "the box is nonblack" are contradictories. Contrary propositions, on the other hand, are those such that both could not be true but both could be false. For example, "the box is black" and "the box is white" are contraries. For if "the box is black" is true, then "the box is nonblack" is false, but it can not be inferred from this that "the box is white" is true, because the box could be any color other than black. Black and white are contraries, not contradictories. When a pair of contraries is treated as a pair of contradictories the black-and-white fallacy is committed.

      2. False Dilemma
         A dilemma argument says that, given two conditionals and the disjunction of their antecedents, it can be inferred that the disjunction of their consequents. This argument requires more than two premises. It must consist of two conditionals and a disjunction, and the conclusion is a disjunction. Such arguments are designed to push one's opponents into a corner and to annihilate them. Methods have been invented to evade or refute the conclusion of a dilemma. These methods have given picturesque names, relating to the fact that a dilemma has two (or more) "horns." There are three ways of defeating or refuting a dilemma known as (1) "going (or escaping) between the horns," (2) "taking (or grasping) it by the horns," and (3) "rebutting it by means of a counterdilemma." These do not prove the dilemma invalid, but are ways of avoiding the conclusion of the dilemma. (1) The first method of escaping between the horns of a dilemma is by rejecting its disjunctive premise. This method is the easiest for, unless one half of the disjunction is the explicit contradictory of the other, the disjunction may very well be false. This is the fallacy of a false dilemma and its exposure is the way to escape between the horns of the dilemma. (2) The second method attempts to escape the conclusion of dilemma by showing at least one of the conditionals is false. (3) The third method attempts to rebute a dilemma with a counterdilemma that has been constructed so that its conclusion is opposed to the conclusion of the original. These last two methods do not involve the fallacy of the false dilemma.

      3. Slippery Slope
         There are two forms of this fallacy. One form of this fallacy occurs when it is assumed without warrant that slight differences or difference of degree are unimportant. For example, some argue that there is no need for them to vote in elections because their vote could not make difference in the outcome. But if no one were to vote, then there could not be an election; and if there were a tie, then one vote would decide the election. In the second form of this fallacy, it is argued that because slight differences or difference of degree are unimportant, there is therefore no significant or important difference between things that differ in degree only. This is like arguing that if a camel get his nose in the tent, then eventually the whole camel will be in the tent. This may be true, but on the other hand it might not be. It has even been argued that there is no difference between things that differ in degree only. Thus some have argued that there is not difference between sleeping and waking, hot and cold, or good and bad. Arguments of this type rest on the unwarranted assumption that because it is impossible to draw sharp distinction with regard to a subject matter, no distinction can be drawn at all. Finally, this fallacy may be committed when it is assume that slight difference or differences of degree are always important. While the difference of making 69 or 70 on the final exam can make difference whether one receives a D or C for the course, the difference in making 98 or 99 can make no difference in the final grade for the course, since either grade is sufficient for one to receive an A for the course.

      4. Composition
         This fallacy is committed when it is is reason that some property possessed by every member of a class (or every part of a whole) also is possessed by that class (or the whole). For example, this fallacy is committed when one reason from the shortness of each chapter of a book to the shortness of the book as a whole.

      5. Division
         This fallacy is the opposite of the fallacy of composition. This fallacy of division is commited when it is inferred that some property of a class (or whole) is a property of each of its members (or parts). For example, this fallacy is committed when one reasons from the great length of a book to the long length of each chapter, or from the difficulty of an exam to the difficulty of each question in the exam. The exam may be difficult because of too many questions or not enough time to answer them.

      6. Inconsistency
         This fallacy of inconsistency, or assuming contradictory premises, arises from the fact that any conclusion can be deduced from false premises. These arguments are valid but worthless. Similarly, any conclusion can be deduced from contradictory premises. This allows any action to be justified by appeal to inconsistent premises. For example, a school administrator may dismiss a teacher on the grounds that he is politically active, and another on the grounds that he is inactive in politics. As long as such an administrator's reasoning goes undetected or unchallenged, he is able to do whatever he pleases. Assuming contradictory premises or propositions such that it is logically impossible for them all to be true must be distinguished from assuming premises which as a matter of fact are not all true. For example, a politician who promises both to increase governmental services and to reduce taxes has probably promised something that cannot be done, but he has not contradicted himself.

3. Inductive Falllacies
   These fallacies usually involve one of the fallacies of insufficient evidence. These fallacies occur when the premises of an argument are relevant but are not themselves sufficient to establish the conclusion. In other words fallacies of insufficient evidence occurs when only part of the evidence relevant to establishing the conclusion is taken into consideration. Thus they are sometimes spoken of as fallacies of neglected aspect. The following are only a few of this type of fallacy.
   1. Hasy Generalization
      This fallacy is committed when one generalizes too quickly from one or a few instances. For example, when, on the basis of one or two short visits to Southern California in the winter, it is concluded that it rains a great deal in Southern California, one is committing this fallacy. This fallacy is not because it moves from particular instances to a generalization, but rather because it does so too quickly on too little evidence.

   2. Weak or Faulty Analogy
      An argument by analogy is one in which it is argued that because two or more things or types of things are similar in some respects, they are also similar in another respect or respects. This argument is subject to many abuses because many conditions must be fulfilled for a correct or strong analogy. To the degree that the properties cited as shared are relevant to establishing that the other property is shared, the probability that the conclusion is true is strengthened. In general, the presence of one property is relevant to establishing the presence of another only if the two are causally related. If the properties are not relevant, or if relevant differences have been overlooked, then the fallacy of faulty analogy has been committed.

   3. False Cause
      This fallacy has several different forms.
      1. Post hoc ergo propter hoc
         This Latin phrase means "after this, therefore, because of this". This fallacy is committed when it is argued that A is a cause of B simply because A occurs earlier than B. Reasoning of this type is the source of many superstitions, for example, that dancing or tom-tom beating can cause rain. The way to show that A is not a cause of B is to demonstrate that A can be present without B occurring.

      2. Chance Variation
         This fallacy occurs when a statistical correlation is taken without further evidence as a causal correlation. Although there may be a statistical correlation, say, between the price of eggs and the crime rate in New York City, does not entitle one to conclude that one of these is the cause of the other.

      3. Common Effects
         This fallacy arises when two phenomena, both of which are the result of some third phenomenon, are taken as cause and effect of each other. For example, a patient may have both a skin rash and a fever, but it does not follow that one is the cause of the other, for both may be caused by a third phenomenon.

      4. Reciprocal Effects
         This fallacy occurs when reciprocal effects, or phenomena that mutually influence one another, are taken as though the relation holds only in one direction. It does not follow from the fact that A is a cause of B, that B cannot be a cause of A.

      5. Confusion of Cause and Condition
         Every effect presupposes a set of conditions without which that effect would not occurred. When these conditions are considered to be the cause of the effect, this fallacy is committed.

      6. Confusion of Cause and Effect
         This fallacy is committed when a confusion of cause and effect occurs to think that an effect is a cause, or a cause an effect.

   4. Statistical Fallacies
      1. Small Sample
         This fallacy is committed when the results of a poll of a small sample that is not random is projected on the entire population from which the sample is taken.

      2. Data of differing Quality
         This fallacy is committed when the statistics is based on information of differing quality possibly due to variations in the quality of the data-gathering procedures at various places and times.

      3. Biased Statistics
         This fallacy is committed when statistic is drawn from a sample that is known (or should be known) not likely to be representative of the population being sample.

      4. Unknowable Statistic
         This fallacy is committed either when statistic are simply made up, or guessed at on the basis of little or no evidence, or when their approximate nature is masked in precision.

      5. Accident or False Correlation
         This fallacy consists in erroneously assuming that a correlation between two or more samples represents a causal correlation. The fallacy is committed when an accidental correlation is taken to be causal. It cannot be automatically assumed that accidental correlation are really causual. Most such correlations are not likely to continued in the future. If what might be called "background information" make it extremely unlikely that there is any causal connection of the kind suggested by the statistics, the correlation should be dismissed as accidental. Not to do so is to commit this fallacy.

   5. Accident
      This fallacy is committed when anyone argues that what is true as a general rule is also true to some special situation. Note that this fallacy does not consist in arguing from a generalization to a specific instance of the generalization, but in arguing from a generalization to some special or exceptional case which the generalization is not intended to cover.

   6. Special Pleading
      This fallacy is committed whenever anyone presents evidence of support of one conclusion, or one side, of an issue while ignoring or withholding evidence that would support another conclusion, or another side, of the issue.