(last updated:  Jan 02, 2009)

This page tries to illustrate the many ways in which false or invalid arguments are made.  There are three general categories of invalid argument:
  1. Errors of Fact:  If the facts that are presented are incorrect, the argument could be wrong (but not necessarily - the facts could be irrelevant to the case, or not representative).
  2. Avoiding the Issue:  These are statements that do not really address the issue at hand.
  3. Errors of Generalization:  This is a more subtle and very common class of error, discussed in more detail below.

Avoiding the Issue has the following variants:

Ad Hominem To discredit an argument by questioning the motives or character of the person rather than dealing with the argument in question. Alternatively, to support an argument by appealing to the authority of the person making the argument.
Begging the Question The proposition to be proved is assumed implicitly or explicitly in one of the premises.
Non Sequitur An argument is a non sequitur if the conclusion does not logically follow from the premise.

Errors of Generalization fall into these categories:

Correlation implies Causation Two events that occur together are claimed to be cause and effect. In fact, the causation could be the other way, or there might be little actual relationship between them.
False Dichotomy, or Single Cause The false assumption that two hypotheses are mutually exclusive. Thus finding an error or an exception to one hypothesis is considered to be proof of the other.
Absence of Evidence Absence of evidence is not necessarily evidence of absence (ie. the falshood of the hypothesis). The question should be: Is there enough information available that we should expect to see certain evidence for the hypothesis.
Fallacy of Distribution: Composition or Unrepresentative Sample An argument that assumes what is true of some of the members is true of the entire class to which they belong.
Fallacy of Distribution: Division An argument that assumes what is generally true of a class must therefore be true of all members of that class.

A more detailed presentation of logical fallacies can be found in Wikipedia.  But I think it has far too many overlapping definitions.

A Simple Example

The different types of logical fallacies will be illustrated using this simple story line:  John has a child named "Junior", and a cat. A broken cookie jar is found in the kitchen. How did the jar get broken?

Logical Fallacy Example Argument Why the Argument is False
Error of FactJunior was not home that day, so he did not break the cookie jar.Assume Junior was in fact at home that day. That invalidates the argument. But the fact that this argument is false does not prove Junior did break the cookie jar, it is simply irrelevant.
Correlation implies Causation I saw Junior in the kitchen, so he must have broken the cookie jar.
Just being in the kitchen does not necessarily mean that Junior broke the jar. The jar might have been broken by someone else. Junior might have been in the kitchen because he was attracted by the noise of the breaking jar.
False Dichotomy, or Single Cause Junior was with me, so it must have been the cat. Even assuming that Junior being with you means he did not break the jar, it does not follow that the cat did it. There are other ways the jar could be broken.
Absence of Evidence I did not see the Junior break the jar. Unless you were watching Junior the entire time during which the jar could have been broken, this does not mean he is innocent.
Fallacy of Composition All kids are destructive, just like Junior. Even assuming Junior is guilty here, you cannot generalize from one child to all children.
Fallacy of Division Kids are destructive and often break things, so Junior must have broken the jar. Children are not all the same. Junior might be a more placid child than most. And even if Junior is a destructive child, he may not have broken the jar this time.
Ad Hominem John spoils Junior and will always protect him, so Junior must have broken the jar. The criticism of John's relationship with Junior is used as a substitute for the question of how the jar got broken.
Begging the Question Junior is a good kid and is very careful, so he could not have broken the jar. You are simply assuming in advance that Junior would not break the jar.
Non Sequitur Junior loves John, and John trusts Junior.  How could he have broken the jar? Love and trust have nothing to do with how the jar got broken.

Real World Examples

The following tables presents examples of typical fallacies in the areas of Racism and Culture, Climate Change, and Politics. In each case he premise may (or may not) be correct, but the argument made does not support it. There are often multiple fallacies used in a single argument.

Racism and Culture

Racism is the classic example of generalization. But opponents of racism are often guilty of flawed reasoning as well.

Statement Logical Fallacy
Black people are lazy, stupid and violent. 1) Fallacy of Composition:  There may (or may not) be a greater tendency for some of these characteristics in the black population, possibly due to historical injustice or other factors. To suggest it applies to all black people is totally invalid.
I don't want a black person living next to me. I see what they do all the time on the news. 1) Fallacy of Division:  Even assuming there is truth to the generalizations made above, it does not follow that they apply to every black person.
More people are questioning the need for society to accommodate all the religious or cultural beliefs of immigrants, so our society is becoming more bigoted and racist. 1) Fallacy of Composition:  Some people who hold this opinion may have racist views, but it does not follow that all people who question immigration policy are racist.
2) Non Sequitur:  Immigrants are of many races - racism is irrelevant to this question.
3) Ad Hominem:  By calling people you disagree with bigoted, you are attacking the person rather than considering the issue.
Islam is a religion of peace. Our local Imam said so, and he quoted a verse in the Koran that showed this is true. 1) Appeal to Authority:  The Imam knows his religion, but he may have an incentive not to tell you the entire truth about it.
2) Fallacy of Composition:  The Koran may contain peaceful verses, but it also contains many aggressive and violent verses. The Koran cannot be understood from a single verse.
The Islamic extremists are just a tiny minority. The Muslims that I know are very nice people. Islamic civilization achieved great things while Europe wallowed in ignorance. This whole thing is overblown by rightwingers trying to scare people.
1) False Dichotomy:  It is not accurate to divide Muslims (or any other group for that matter) into one distinct group called "extremists" (ie. those who actually carry out terrorist actions) and "moderates" (ie. everyone else).  There is a continuous range of opinion between these two extremes.
2) Fallacy of Composition:  The Muslims you know may not be representitive of the entire Muslim population.
3) Non Sequitur:  The historical situation one thousand years ago has little bearing on the situation today.
4) Ad Hominem:  The use of the term "rightwingers" is an attempt to avoid the question by calling into question the motives of those who question Islam.

Climate Change

Statement Logical Fallacy
a) Global warming is not caused by increasing greenhouse gases because the IPCC is biased, and pushing scary scenarios leads to more funding for climate scientists.
b) Global warming skeptics are all funded by Exxon-Mobil so they cannot be believed.
1) Ad Hominem:  This argument attacks the motivation of the scientists rather than considering the validity of their arguments.
2) Fallacy of Composition:  Some scientists may have bias, but that does not mean they all do.
a) Al Gore's documentary "An Inconvenient Truth" contains several errors of fact and some exaggeration of evidence for global warming. Therefore we don't need to worry about global warming.
b) Al Gore won a Nobel Prize for his work, so global warming must be a serious issue.
1) Fallacy of Composition:  The existance of some errors, even if they are deliberate, does not necessarly invalidate the rest of the argument.
2) Appeal to Authority:  A Nobel Prize does not necessarily mean that the work is entirely correct, or relevant to the argument being made.
Hurricane intensity is not influenced by global warming because that was not mentioned in the official statement by the National Hurricane Center. 1) Appeal to Authority:  The National Hurricane Center may only represent one opinion among various scientitific groups.
2) Single Cause:  The fact that the NHC examined other causes of hurricanes does not mean global warming has no influence.
3) Non Sequitur:  The NHC may not have considered global warming at all in its report.
Global warming is causing climate change. There was a lot of flooding in Europe this year. Therefore the flooding was caused by global warming. 1) Correlation implies Causation:  There have always been floods, so global warming may have nothing to do with it. You need a lot more than one year of data to draw such a conclusion.
Global warming is causing forests to expand in the Arctic. Therefore it is no big deal if we cut down some rainforest, because the net forested area is increasing. 1) Fallacy of Distribution:  Not all forest is the same. The tropical rainforest being lost is very different from the new Arctic forests that might be gained.
2) Non Sequitur:  Forest area may not be a good measure of forest value.
If we can't predict the weather accurately a few days ahead, how can climate models predict what will happen in one hundred years? 1) Non Sequitur:  A climate model is not a weather model running for 100 years.
2) False Dichotomy:  The results of a climate model have uncertainty, but that does not make them entirely invalid.
The theory of Evolution is wrong because of all the missing links. Obviously, the more missing links there are, the more wrong Evolution is. Every time they find a new fossil, all that means is instead of one missing link, now there are two, one on each side of the new fossil. Therefore there are more missing links than before, and Evolution is even more wrong than it was before. 1) Absence of Evidence:  Missing links are expected because the fossil record is so sparse.
2) Fallacy of Division:  The class of "missing links" has variation in the significance of its members. A single group of organisms clearly not connected with the rest of life would call evolution into question. A large number of trivial "missing links" means nothing.


Statement Logical Fallacy
George Bush was an evil mam whow was a bad president. My opinion is the opposite of that of George Bush, therefore I am right. 1) Fallacy of Composition:  George Bush has a large number of characteristics, not all of which are necessarily "bad", even in your opinion.
2) Error of Fact:  For example, he believes that the sun rises in the morning and sets in the evening. In reality, you and he share most beliefs.
3) False Dichotomy: Even if what Bush believes is "bad", it does not follow that your beliefs are "good".  The "good" belief may be shared by neither of you.
"Lay down your arms," Oscar Romero [Catholic Archbishop in El Salvador in the 1970's] challenged soldiers from his cathedral pulpit. "Do not kill your own brothers and sisters any longer." That was 28 years ago today. The San Salvador archbishop had become a relentless peace activist, repeatedly calling for an end to the violence wracking his country.

Clearly, Romero's message of peace was way too subversive. Clearly, he had to go. Funny people, peace activists. On the surface, they seem nice enough, but they obviously possess some indefinable nagging little quality that drives other people stark, staring bonkers.

Some of those other people include your average, everyday warmongers, not all of them Salvadoran military men. In fact, some are actually pretty swell fellas -- guys like George W. Bush and Dick Cheney (who observed last week that the U.S. invasion of Iraq, with its death count of untold thousands of Iraqis and nearly 4,000 U.S. soldiers, has been a "successful endeavour" that "has been well worth the effort.")  [from here]
1) Fallacy of Composition:  The actions and beliefs of the individual Oscar Romero, who is widely admired, are being transferred to the entire category of "peace activists". In fact, there is no reason to believe Romero was a pacifist - he did not demand that the army disband, only that it stop killing civilians. Romero would probably disagree with many of the opinions of modern peace activists.

2) Non Sequitur:  The fact that many people have died does not necessarily mean that the Iraq war was wrong, or is a failure. Many more people died in World War Two - does that mean the Allies should never have fought it, or that the war effort was an even bigger failure than Iraq? The Iraq War should be judged on its objectives, and the results compared to what would have happened if it had not been fought. Maybe it was wrong, but this argument does not establish that.

3) Ad Hominem:  The sarcastic comment about "swell fellas" is another appeal to emotion rather than reason.

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