4.1 Accident, two ad hominems, all or nothing, equivocation and amphiboly



Consider the following argument:

Most homicides of females in their 20's are committed by someone they know or with whom they are in a current relationship, or a person with whom they have had a relationship in the recent past.

Susie Gordan, a 24 year old female, was found dead and the evidence clearly points to homicide but the evidence also indicates it was done by a local homeless man who has schizophrenia.

But that is probably wrong, since most homicides of females in their 20's are committed by people who have been in a relationship with the victim or are known to the victim, and the homeless person was unknown to the victim

Notice that the conclusion that the homicide was committed by a homeless man with schizophrenia is dismissed in favor of a general rule which is true of most homicides. When this happens we say that the argument has committed the fallacy known as accident. Why this name? Since the time at least of the ancient Greek philosophers, to understand the nature of a thing was to understand its essential properties. Non-essential properties were known as accidental properties which can vary or change without changing the essential nature of the thing. For example, the nature of a circle is the set of all points the same distance from a distinguished point known as the center of the circle. An accidental property of a circle is that distance (known as the radius), hence one can change the radius and still have a circle, so the actual value of the radius is an accidental property. With this in mind, the accidental fallacy ignores important known accidental properties in favor of general properties of something. This fallacy is sometimes known as 'destroying the exception' since it ignores important exceptions to a rule in favor of a general rule.

accidental fallacy

Definition: When an inference is made based on a general rule applied to a particular case where it does not apply, the resulting error in reasoning is known as an accidental fallacy (or a fallacy of accident).


Ad hominem abusive and circumstantial

Two closely related types of logical fallacies occur when some aspect of a person is attacked, rather than the claim or subject under debate.

(a) Don't expect my opponent to be tough on crime, his parents were Quakers and pacifists.


(b) Mr. Smith is a convicted criminal, hence his stance on education reform can't be trusted.

The first argument presented attacks the circumstances of the opponent being born of Quaker parents, rather than the opponent's actual views on crime - while the second attacks in a negative or abusive way a person's past rather than the person's stance on educational reform. Both types of arguments are forms of a fallacy known as an ad hominem (Latin for 'against the person'), the first being an ad hominem circumstantial and the second being an ad hominem abusive. It seems almost too obvious for words that such arguments hold little relevancy to the subject matter under debate, but their proliferation in political ads is but one indication of their persistent use and effectiveness.

Dilbert comic

In the above Dilbert cartoon, the secretary attacks the newspaper columnist instead of disputing the argument that the use of the word 'dongle' was indeed correct. The newspaper columnist also commits an ad hominem abusive by accusing the secretary of being a nutbag, but at least gives an additional justification for the use of the word 'dongle'.


ad hominem (against the person) abusive and circumstantial

Definition: An argument which negatively attacks some aspect of a person making a claim rather than the claim itself is known as an ad hominem abusive fallacy. When some circumstance pertaining to a person's life is attacked rather than the claim the person is making the resulting fallacy is known as an ad hominem circumstantial.


All or nothing fallacy

Recall that one way we can show that an inference is not valid is to show it is possible for all premises to be true and at the same time the conclusion could be false. When considering such possibilities it turns out that not all possibilities work, and part of the informal way of showing an inference is invalid is to explore many until one works. This means that the exploration of other possibilities is an integral part of logical reasoning. Our next fallacy stems from a failure to consider other possibilities. Consider what is wrong with the following inference about car crashes

Since the cause of the car crash was not careless driving, it must be due to the driver being extremely intoxicated.


Edward Snowden is a traitor or a hero, hence any judicial decision must take into account the consequences of dropping all charges against a traitor or criminally indicting a hero.


Notice in the first case when one possibility is rejected another extreme possibility is taken to be the conclusion, but there are many other possible causes of car crashes, and hence other possible conclusions. In the second Edward Snowden is classified as either a traitor or a hero, when other options also exist (a person with good intentions that went beyond what was needed to expose illegal data collection, for example).

Dilbert presents his boss with a false dichotomy

The type of fallacy which makes inferences based on only two possibilities, as if they were the only ones, is known as the all or nothing fallacy, which is sometimes called the black-white fallacy or the false dichotomy fallacy.

all or nothing fallacy

Definition: When an inference is made based on two options (many times extreme) are given as if they were the only ones when other options exist (which are many times more probable than the two presented), then the resulting error in reasoning is known as the all or nothing fallacy.


Equivocation and ambiguity

In July of 2008 the Phoenix Mars Lander successfully landed on the planet Mars and began the start of a mission of sending data back to earth, which included the composition of some icy soil on the surface of Mars. William Boynton of the University of Arizona, lead scientist for the the Thermal and Evolved Gas Analyzer (TEGA) was then quoted as saying,

"We have water. We've now finally touched it and tasted it—and from my standpoint it tastes very fine1."

Upon hearing this on the news an acquaintance of mine quipped, "Who would ever put something in their mouth that has been on another planet, much less taste it?"

1. Handwerk, Brian. "Mars Water Discovered, "Tasted" by Lander -- A First." National Geographic. National Geographic Society, 1 Aug. 2008. Web. 06 Aug. 2016.

The acquaintance made an error in reasoning by misunderstanding the meaning of 'taste' in the original quote, and concluded that it is unwise to put any Martian substance in one's mouth. As funny as this example is, it denotes another class of fallacies based on misunderstanding the meanings of terms, which can happen by ambiguity in words or phrases or ambiguity in grammar. When the ambiguity results in words or phrases the fallacy is called equivocation, on the other hand when the fallacy rests on an ambiguity in grammar the fallacy is known as amphiboly, two examples of which are given below. In the first case, the word 'unsweet' is confused with 'sugar-free', in the second 'face-lift' is confused with a literal lifting of one's face.

Tim requested a coffee without sugar, but the employee prepared a coffee with the sugar-free substitute Stevia instead.

dilberts co-worker checks the wrong meaning of facelift


These two fallacies have the following characteristic properties.

the fallacy of equivocation / amphiboly

Definition: When an inference is made based on an ambiguous word or phrase, the resulting fallacy is called equivocation. If the error in reasoning is based on a grammatical ambiguity the fallacy is known as amphiboly.


Test your ability to recognize the above fallacies by taking the following quiz:

quiz: fallacies 1


Choose the correct fallacy