NOTES ON LOGICAL FALLACIES, ETC.  (Click on what you want)

Two Logical Virtues for Good Arguments                      To main menu
One Practical Virtue for Good Arguments
What Fallacious Reasoning Is
Explaining Fallacies
Five Things About Fallacies
Eight Fallacies
    Affirming the Consequent and Denying the Antecedent
    Hasty Generalization
    False Alternatives
    False Cause
    Argument from Ignorance
    Ad Hominem
Handy Fallacies Summary



1) True reasons. This is an ideal, and for serious real-life arguments it usually can only be approximated. Approximations might be: the reasons are plausible although not certain; or, to the best of our knowledge there are no serious objections to them.

2) Reasons are properly related to conclusions. There are two kinds of proper relations between reasons and conclusions:

  a) Validity: If the reasons were true (regardless of whether they really are true), then the
       conclusion would necessarily have to be true also. In other words, the reasons, if they were
       true, would absolutely guarantee the truth of the conclusion.

  b) Strength: If the reasons were true (regardless of whether they really are true), then the
      conclusion would not necessarily have to be true, but it would probably be true. Strength is a
      matter of degrees, and it applies to arguments that are not valid. Arguments can be very strong,
      medium strength, weak, very weak, etc. Most serious real-life arguments are not valid, but have
      some degree of strength (or weakness).

These two logical virtues are independent of each other. Valid arguments and strong arguments can and often do have false reasons, and arguments with true reasons are often invalid and also weak.



A good argument should be persuasive for the intended audience.

A persuasive argument is one that does in fact succeed in convincing the audience that the conclusion is at least probably true. Logically bad arguments are sometimes very persuasive!  And logically good arguments can fail to be persuasive!

In other words, this (practical) virtue, like the two logical virtues, is independent; it may be present (or absent) regardless of whether either of the two logical virtues is present (or absent).

A really good argument, one that fulfils its function well, posesses all three virtues!

Whether an argument is persuasive depends a great deal on the audience to which it is directed. A logically naive audience, or a prejudiced audience, can often be persuaded by a logically bad argument; and logically good argument may fail to persuade even an open-minded or sophisticated audience.

Logically Good but not Persuasive:

How might an argument be logically good, but not persuasive?  Here are some ways:

o Dull and boring.       o Poorly organized.         o Too complicated for the audience.

o Includes remarks offensive to the audience.     o The audience will not listen, is not open-minded.

o Though the reasons are (probably) true, the audience doesn't know or doesn't believe that they
   are; they need to be given reasons for the reasons!

The ideal is an argument that has both the two logical virtues and the practical virtue of being persuasive for the intended audience. The ideal is difficult to achieve, and this is largely due to the fact that there is so much variation among audiences. A logically good argument may persuade some people but not others. An argument that is boring for one audience may be interesting to another. Some audiences are pretty open-minded, others aren't. What is too complex for some people is just right for others. And so on. When designing and organizing how to present an argument, it is important to assess the nature of the audience!

Persuasive but Bad:

There are many arguments that are persuasive but bad (in that they lack at least one of the two logical virtues). Why might a persuasive argument be logically bad? There are just two main possibilities (which can occur together):

o The reasons aren't true, but the audience is unaware of this.

o The reasons and conclusion aren't properly related, but the audience thinks they are.

There are some general types or patterns of arguments that have a definite tendency to fool and mislead people, and thus to be logically bad but nonetheless persuasive: fallacious arguments.



A fallacious argument is one that meets two conditions:

1) It lacks at least one of the two logical virtues. Thus fallacious arguments are often divided into two kinds: those that are mistaken because they don't meet the truth-of-reasons requirement (or, virtue), and those that are mistaken because they don't meet the properly-related-to-conclusion requirement (or, virtue).

2) It is of a fairly commonplace type. Some persuasive but bad arguments involve mistakes in reasoning that are somewhat unusual. Such arguments are not often categorized as fallacious. Fallacies involve mistakes in reasoning that are more or less everyday occurrences, because they have a definite tendency to fool people.

Familiarity with a few types of fallacies will reduce the chances that you will be fooled by the fallacious arguments of others, and it will also make it less likely that you will engage in fallacious reasoning yourself.

Fallacies, like argument forms, are types or patterns of reasoning. But with fallacies the patterns are not nearly so clear and well-defined as with argument forms. Be prepared for some unavoidable fuzziness in the study of fallacies. Some types or patterns of reasoning (in a vaguer sense of "pattern" than with argument forms) can be used either well or poorly. Use them well, and your reasoning is good; use them poorly, and your reasoning is fallacious.

Much (but not all) fallacious arguing involves the quick, oversimplified use of a type of reasoning that, if used in a more careful and sophisticated manner, could be quite respectable.



When you criticize an argument by saying that it involves a fallacy, you should be able to give a good explanation of why that fallacy is present in the argument. If you merely say that an argument involves a certain fallacy, but you don't give a good explanation why that fallacy is present, the suspicion arises that you're just guessing!  So, for each fallacy below, there will be both a discussion of what the fallacy is, and some comments on how to give a good explanation that will show that the fallacy is present in a particular argument.

WARNING: You will never get credit for a fallacy explanation of this sort:

---> "Just because [here you put a summary of a reason or two] doesn't prove that [here you put
        a summary of the conclusion]."

This isn't really an explanation at all. It just says that the reason(s) don't prove the conclusion. It doesn't explain WHY they don't!!! Pay particular attention to the guidelines below for how to give acceptable fallacy explanations.


Five Things About Fallacies:

1)  It is quite possible for an argument to have more than one fallacy in it. This is different from argument forms, for an argument does not at the same time fit more than one of the argument forms presented earlier.

2)  Sometimes fallacious arguments are "borderline cases" -- they could just about equally well be classified as involving either of two different fallacies. Fallacies aren't as neat and precise as the argument forms.

3)  There are two ways for an argument to be bad: false (or suspicious) reasons, and improper relation between reasons and conclusion. All but one of the fallacies below involve improper reason-to-conclusion relations. In other words, they are about arguments that would be bad even if the reasons were true (the one exception is the False Alternatives fallacy).

4)  Important issues are often complicated. Fallacious reasoning is typically an attempt to resolve a complex issue quickly and simply. Sometimes a simple argument that is fallacious can be expanded into a good argument by the provision of additional reasons; and sometimes it can't be. The only way to find out is to consider the complications.

5)  Showing or giving a good explanation why an argument is fallacious does not show that the argument has a false conclusion!!!  Fallacious arguments, which are almost always invalid arguments, may well have true conclusions. Fallacious arguments fail to prove that their conclusions are true (or, probably true).  That's very different from positively proving that their conclusions are false!



Affirming the Consequent (AC) and Denying the Antecedent (DA)

Arguments that fit these two invalid argument forms are considered fallacious, because they each meet the two main requirements for a fallacy: 1) They are commonplace types of reasoning, and 2) they are likely to fool people. You are likely to be fooled by AC (which is invalid) because if you aren't careful you will mistake it for AA (which is valid). And you are likely to be fooled by DA (also invalid) because if you aren't careful you will mistake it for DC (which is valid).

When you encounter an AC or DA argument, to explain how you know it is fallacious, draw the diagram, correctly identify the argument form, write "fallacy-invalid," and then describe circumstances that would make the reasons both true but the conclusion false.  For AC and DA you should always be able to do this!

Note.  It is quite possible for AC or DA to be parts of a longer, more detailed argument that is not fallacious, and that is actually a very strong argument (although it wouldn't be valid). But if an argument consists of nothing but a simple DA or AC argument, with no further information or qualifications, it's fallacious.


Fallacy of Hasty Generalization (HG)

Terminology:  A generalization is a statement about a lot of things. The more things the statement is about, the more general it is; the fewer things it is about, the more specific it is.  Don't confuse generality with vagueness.  Vagueness contrasts with precision, not with specificity.  The law of gravity is about a lot of things (all massive objects), and it also provides a very precise formula for calculating the force with which massive objects attract each other.  So the law of gravity is both very general and very precise!   Now consider this statement:  Joe's new pickup truck is awfully big and heavy.  This is a very specific statement because it's about just one thing, Joe's truck.  But it's also very vague (imprecise): just how big, and how heavy is his truck?

Definition of HG: A conclusion about a population (a large group of things) is reached on the basis of a sample (a subgroup of the large group) which is 'way too small. Typically the fallacy involves a subgroup of only one to three things.

Example HG argument: EKU students are all so friendly and helpful. I'm sure of this because just last week I got lost on the campus and a very helpful and friendly student got me all straightened out.

Explanation: HG because just one student who happens to be helpful and friendly is used as a basis (a sample) for concluding that all EKU students are helpful and friendly. That's a sample of one student out of thousands, which 'way too few to support the conclusion.

Note 1.  In an HG argument the reason(s) are about the sample; the conclusion is about the population.  If the conclusion isn't about a lot of things, HG cannot be present!

Note 2.  Some sample-type arguments are good, strong (but invalid) arguments.  HG is only present when the sample is much too small.


Fallacy of False Alternatives

Definition of FA: The reasons of an argument mention two (sometimes, more than two) alternatives, but there is pretty obviously at least one other alternative that the arguer should have considered, but didn't; this failure to consider a plausible alternative produces an incorrect conclusion.

Terminology: In an FA argument, it is false that the alternatives mentioned in the reasons are the only  alternatives. This is the only one of the fallacies presented here in which the mistake is that the argument has a false reason. For all of the other fallacies considered here, it doesn't matter whether the reasons are true or false, because the problem is with the relationship between the reasons and the conclusion.

Example FA argument:  Senator Blather was either telling the truth, or he was lying, and we know that what he said wasn't true. Therefore he was lying.

Explanation: FA because telling the truth and lying are not the only two alternatives that should have been considered. The Senator might have made an honest mistake (which isn't lying because lying has to be deliberate), or he might have been misinformed by his staff.

FA explanations: To give an acceptable explanation of why an argument involves the FA fallacy, you must include the following: 1) state the the two (or more) alternatives are that are mentioned in the argument, and 2) say that there is another alternative that should have been considered, and describe that missing alternative!  Of course the missing alternative is not in the argument you are criticizing -- you have to think it up for yourself.  It should be a reasonable, plausible alternative, not a wild or extremely unlikely one. If you can't write out a reasonable missing alternative, then you have no basis for saying that the FA fallacy is present.

Note.  FA often fits the DD argument form, and in such cases it is valid!  The mistake in FA arguments of the DD form is that they have an obviously false reason due to omitting one or more alternatives from the "or" reason.  So, sometimes a fallacious argument can be valid.


Fallacy of False Cause

Terminology: A causal (not casual!) statement is simply a statement that says that one type of event causes another to happen.  The word "false" in "false cause" should not be taken literally.  It doesn't mean that any statement is literally false.  It just means that the (causal) conclusion has been derived incorrectly.

Definition of FC: A causal conclusion is reached on the basis of very inadequate reasons.  There are two common ways of giving inadequate reasons for causal conclusions, and so there are two main versions of the FC fallacy:

1. The Post Hoc version of False Cause ("post hoc" is Latin for "after this"):

The fallacious reasoning goes like this: one event happened soon after another event. Therefore, the first event caused the second one to occur.

Example Post Hoc FC argument: The farm bankruptcy rate reached 20% just two years after Reagan became President. Thus, this high bankruptcy rate among farmers was due to Reagan being President.

Explanation: FC because merely pointing out that the high farm bankruptcy rate occurred after Reagan became President is inadequate for concluding that his election is what caused the rate to reach 20%.  Other things that occurred before the rate got so high may have been what caused it, such as: low prices for farm products, or high prices for farm supplies, or high interest rates for loans to farmers.

Note that the explanation mentions other possible causes! That second sentence in the explanation is needed for the explanation to be adequate!

2. The Association version of the FC fallacy:

The fallacious reasoning goes like this:  Two types of events are associated; that is, they frequently occur together.  Therefore, one of them causes the other to occur.

Example:  All the really prosperous countries in the world are democratic. So, their prosperity resulted from democracy.

Explanation:  FC because merely noting that democracy and prosperity occur together (are associated) is inadequate for concluding that democracy causes prosperity.  Maybe some countries were prosperous before they were democratic, in which case being democratic couldn't have caused their prosperity.  Or more likely, there are many factors that cause a country to become prosperous: good natural resources, staying out of wars, other countries wanting to buy their products, and so on. (Note the mention of other possible causes, which is needed for a good explanation!)

Note 1.  For FC to be present, the conclusion of the argument must be a causal statement; it must say that one thing, A, causes (or caused) another thing, B.  Remember that words like "produce", "result from", "bring about", "leads to", "due to", etc. are often used to express causal statements.

Note 2.  Some arguments with causal conclusions are good arguments, and they completely avoid both of the versions of FC.  They have reasons which give more information than merely saying that one thing happened before another, or merely saying that two things are associated. If the reasons of a causal argument mention "happened before" or association along with some other information, then think carefully -- it may not be fallacious!


Fallacy of Argument from Ignorance

Terminology: The root-meaning of the word "ignorance" is "I don't know."  Ignorance = lack of knowledge.  Thus the name "Argument from Ignorance" means "an argument based on lack of knowledge".

Definition of IG:  Concluding that something is true, merely because it hasn't been proved (or known, or shown, etc.) that it is false; or, concluding that something is false, merely because it hasn't been proved (or known, or shown, etc.) that it is true.

It is obviously stupid to reason like this:  I don't know whether X is true or false; therefore, I conclude that X is true.  It would be just as stupid to conclude that X is false.  If you don't know, then you don't know whether X is true or not!  But when someone says "It has not been proved that X is true," that is just a way of saying that "We don't know whether X is true or not."

Example IG argument:  No one has proved that metal amalgam dental fillings are dangerous to your health; therefore, they are safe.

Explanation:  IG because the mere failure to prove that metal amalgam fillings are dangerous is inadequate for concluding that they aren't dangerous (i.e. that they are safe).  It may be that no one has even investigated whether they are dangerous.

Note 1.  The key point about IG is that merely failing to prove (or know, etc.) that X just leaves you ignorant of whether X is true or false, so it does not enable you to correctly conclude anything about X's opposite.

Note 2.  For IG to be present, the reason(s) must explicitly say "it has not been proved (or shown, etc.) that [. . X . .] ".  In other words, the arguer must explicitly use ignorance as a reason!

Note 3.  The word "merely" is important.  If an arguer provides other reasons in addition to failure to know (or show, etc.), then the argument may not be fallacious.  For example, if the above argument had added the information that there have been extensive tests of the safety of metal amalgam fillings, then the fallacy would not be present.  Looking carefully for evidence and not finding any is very different from simply not having any evidence!


Fallacy of Ad Hominem (AH)

Terminology: "Ad Hominem" is an old Latin phrase which literally means "against the person".  The basic idea is that an arguer is presenting reasons which are aimed at ("against") a PERSON, when the arguer should be presenting reasons that are aimed at ("against") a POSITION or a VIEWPOINT.

Background: Often arguments have conclusions which say that some position or viewpoint is mistaken, or should be rejected.  In order to support such a conclusion, the reasons should point out some problem(s) with that position -- they should be reasons aimed against that position (and NOT against a person who holds that position).  For instance, if an argument's conclusion is that a Senator's tax policy is no good, then the reasons should be criticisms of (against) the Senator's tax policy (and NOT criticisms aimed at the Senator himself).

Definition of AH:  An argument which has a conclusion in which some position is rejected and which has reasons which are NOT aimed against that position at all, but which instead are aimed against some person(s) who accepts that position.  This is bad reasoning because it is merely a way of diverting attention from the proper issues.

Example AH argument:  The people who favor the tax-increase bill will give you lots of reasons why they think it should be passed.  But in fact it is a lousy bill which should be defeated, for the simple reason that it is supported by Senator Whitney Berton.  You know him - the guy who is widely suspected of being guilty of tax evasion!

Explanation:  AH because the arguer rejects the tax-increase bill merely on the basis of a criticism (that he is suspected of tax evasion) of Senator Berton, who supports the bill. It gives no information at all about the strong or weak points of the bill itself.

Senator Berton's tax proposal might be a good idea even though he himself is a crook, and it might be a bad idea even though he himself has never violated any law.  His proposal should be evaluated on its merits, not on the basis of the Senator's personal life.  This argument has a reason that criticizes a person (Senator Berton), when it ought to have reasons that criticize the Senator's position concerning increased taxes.  Notice that this argument says absolutely nothing about the pros and cons of the tax-increase proposal itself!

Note 1.  In an AH argument the conclusion is that some "position" or "viewpoint" is false, or should be rejected.  So AH arguments have "negative" conclusions.  Sometimes the personal criticism stated in the reasons is very obvious, sometimes it is rather indirect.  A common variety of AH is to criticize someone for "not practicing what he preaches" and then rejecting what he preaches.

Note 2.  If the conclusion of an argument is about a person(s) character, then personal criticisms may be appropriate, and then AH would not be present. For instance, if in court a lawyer criticizes a witness for having a history of lying and concludes that the jury shouldn't believe the witness, then the lawyer has not committed the AH fallacy.  A witness's character is a very relevant and important consideration in court.

Note 3.  "Personal criticism" means "a criticism directed at a person (or group of people) by the arguer". It does not simply mean "a personal opinion".  It is, either directly or indirectly, a criticism of someone's character.

Note 4.  There could be a "positive" version of AH: a position or viewpoint is correct because someone who holds that position is a good person.  This is also fallacious reasoning, but it is not nearly so common as the negative version explained above.


Fallacy of Equivocation (EQ)

Terminology: "equi" means "equal".  "voca" means "call".  To equivocate literally means to say (to call) that two things are equal, when in fact they are NOT equal.  Thus it is to deceive or to mislead -- to say what isn't so!

Sometimes an arguer will use the same word (or phrase) to mean two different things -- sometimes deliberately, sometimes without even realizing it.  In other words, there is a change in the meaning of a word or phrase within an argument.  In good arguments, key words and phrases should be used with the same meaning throughout.  If you, the reader or listener, do not notice the change in meaning, then you can be misled or deceived into thinking that a bad argument is a good one.

Definition of EQ:  An argument has an incorrect conclusion due to some word or phrase in the argument being used to mean two different things.  Usually the same word or phrase will be used two (or more) times in the argument -- but with different meanings.

You should be especially careful to think about the meanings of words that are used for comparing things ("relative terms") -- words like: big, small, rich, smart, important, expensive, short, old, etc. Exactly what they mean depends on what is being used for comparison.  Is Montana a BIG state? Well, it depends.  Do you mean big in total area, in population, in tobacco production, in wilderness areas, or what?

Example EQ argument:  All men are rational beings, and no man is a woman; thus no woman is rational.

Explanation:  EQ because the meaning of "man/men" shifts from "human" (in the first reason) to "male" (in the second reason).

Note: EQ explanations should include the two different meanings which are present in the argument. Put quote marks around your two different meanings.  The argument itself will not say what the two meanings are. You have to supply them for yourself!

Note.  You should NEVER use a word or phrase to explain the meaning of itself!  For instance, this would be WRONG: the meaning of "man" shifts from "man" to "male".


 About Inconsistency

Inconsistency is a relation(ship) between or among statements (not arguments).  Usually when discussing inconsistency we have only two statements under consideration, but occasionally there are more.

Definition.  Two (or more) statements are inconsistent with each other when it is impossible (unimaginable, inconceivable) that they could both (or, all) be true together.  "Together" means at the same time or place, or in the same circumstances, or with reference to the same people or things.  When it is possible that they could be true together, they are consistent.

Note that consistency/inconsistency concerns how statements relate to each other, not how they relate to the world, or to "facts."  When statements clash with each other, they are inconsistent with each other.  If they don't clash with each other, they are consistent with each other.

Examples.   1)  Today is Saturday.  Today is Sunday.
                     Comment: These statements can't both be true together, so they are
                        inconsistent.  If you're reading this on a weekend, then one of them is
                        literally true; otherwise, both of them are false.  But when consistency/
                        inconsistency is the issue, whether the statements are literally true is not
                        very relevant; it's how they relate to each other that counts!

                     2)  This year is 1995.  This year is 1996.
                     Comment: Obviously these are inconsistent, and they are both literally false.

                     3)  This year is 1995.  Next year will be 1996.
                     Comment: These are also both literally false, but they are consistent.  They
                         don't clash with each other, although they both are literally false.  So,
                         false statements can be either consistent or inconsistent; it depends on
                         how they relate to each other.

                     4)  China is in Asia.  Two multiplied by seven is fourteen.
                      Comment:  These are both actually true, so of course it is possible that  they
                        could both be true, because they are true!  So they are consistent, they do
                        not clash with each other.  "But they aren't even related!"  True, they aren't.
                        Unrelated statements are always consistent with each other, and so are
                        any statements that are literally true.  Because "inconsistent" means "can't
                        both be true."  If they both are true, then they can't be inconsistent!  If they
                        are unrelated, then they can't clash with each other!

                     5)  Sam is taller than Mary.  Mary is taller than Suzie.  Suzie is taller than Sam.
                      Comment:  Any two of these could be true, but there's no way all three could
                        be true together.  So this is an inconsistent trio of statements.

                     6)  If it's snowing, then the weather is cold.  The weather is warm.
                      Comment. These are consistent.  The conditional statement doesn't say
                        that it really is snowing, nor does it say that the weather is really cold.
                        The if-then could quite well be true even when the weather is actually warm.

                     7)  If it's raining, the streets are wet.  The streets are wet.  It isn't raining.
                      Comment:  A consistent trio of statements.  Could be the streets are wet
                        because it's recently been raining, or snow has just melted, etc.

                     8)  If it's raining, the streets are wet.  The streets are dry, and it's raining.
                       Comment:  An inconsistent trio.  Think about it.  No way these could all
                        be true together.

                     9)  If she studies the night before, she'll get an A on the test.  If she doesn't
                            study the night before, she'll get an A on the test.
                      Comment:  A consistent pair of conditional statements.  It might be that she'll
                        get an A whether she studies or not, so it's possible they could both be true.

Overall.  Consistency/inconsistency concerns how statements relate to each other.  If you can imagine some way in which they could both (or, all) be true together, then they are consistent.  If they are so inter-related that they can't possibly both (or, all) be true, then they are inconsistent.