Logical Fallacies

qxz9524

Definition: The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.
Examples:
(i) All Texans are Americans, and no Californians are Texans, therefore, no Californians are Americans.
The predicate term in the conclusion is 'Americans'. The conclusion refers to all Americans (every American is not a Californian, according to the conclusion). But the premises refer only to some Americans (those that are Texans).
Proof: Show that there may be other members of the predicate category not mentioned in the premises which are contrary to the conclusion.
For example, from (i) above, one might argue, "While it's true that all Texans are Americans, it is also true that Ronald Regan is American, but Ronald Regan is Californian, so it is not true that No Californians are Americans."
Copi and Cohen: 207

Fallacy of Exclusion

Definition: Important evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the "principle of total evidence".
Examples:
(i) Jones is Albertan, and most Albertans vote Tory, so Jones
will probably vote Tory. (The information left out is that
Jones lives in Edmonton, and that most people in Edmonton
vote Liberal or N.D.P.)
(ii) The Leafs will probably win this game because they've
won nine out of their last ten. (Eight of the Leafs' wins came
over last place teams, and today they are playing the first
place team.)
Proof: Give the missing evidence and show that it changes the outcome of the inductive argument. Note that it is not sufficient simply to show that not all of the evidence was included; it must be shown that the missing evidence will change the conclusion.
Davis: 115

Fallacy of Drawing an Affirmative Conclusion From a Negative Premise
Definition: The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative.
Examples:
(i) All mice are animals, and some animals are not dangerous, therefore some mice are dangerous.
(ii) No honest people steal, and all honest people pay taxes, so some people who steal pay pay taxes.
Proof: Assume that the premises are true. Find an example which allows the premises to be true but which clearly contradicts the conclusion.
Copi and Cohen: 210

Existential Fallacy
Definition: A standard form categorical syllogism with two universal premises has a particular conclusion.  
The idea is thatsome universal properties need not be instantiated. It may be true that 'all trespassers will be shot' even ifthere are no trespassers. It may be true that 'all brakelesstrains are dangerous' even though there are no brakelesstrains. That is the point of this fallacy.
Examples:
(i) All mice are animals, and all animals are dangerous, so some mice are dangerous.
(ii) No honest people steal, and all honest people pay taxes, so some homest people pay taxes.
Proof: Assume that the premises are true, but that there are no instances of the category described. For example, in (i) above, assume there are no mice, and in (ii) above, assume there are no honest people. This shows that the conclusion is false.
Copi and Cohen: 210

Fallacies of Explanation
********************
An explanation is a form of reasoning which attempts to answer the question "why?" For example, it is with an explanation that we answer questions such as, "Why is the sky blue?"
A good explanation will be based on a scientific or empirical theory. The explanation of why the sky is blue will be given in terms of the composition of the sky and theories of reflection.

qxz9524

Subverted Support
Definition : An explanation is intended to explain who some phenomenon happens. The explanation is fallacious if the phenomenon does not actually happen of if there is no evidence that it does happen.
Examples
(i) The reason why most bachelors are timid is that their mothers were domineering.
(This attempts to explain why most bachelors are timid. However, it is not the case that most bachelors are timid.)
(ii) John went to the store because he wanted to see Maria.
(This is a fallacy if, in fact, John went to the library.)
(iii) The reason why most people oppose the strike is that they are afraid of losing their jobs.
(This attempts to explain why workers oppose the strike. But suppose they just voted to continue the strike, Then in fact, they don't oppose the strike. [This sounds made up, but it actually happened.])
Proof : Identify the phenomenon which is being explained. Show that there is no reason to believe that the phenomenon has actually occurred.
Cedarblom and Paulsen: 158
Non-Support
Definition :An explanation is intended to explain who some phenomenon happens. In this case, there is evidence that the phenomenon occurred, but it is trumped up, biased or ad hoc evidence.
Examples
(i) The reason why most bachelors are timid is that their mothers were domineering.
(This attempts to explain why most bachelors are timid. However, it is shown that the author bases his generalization on two bachelors he once knew, both of whom were timid.)
(ii) The reason why I get four or better on my evaluations is that my students love me.
(This is a fallacy when evaluations which score four or less are discarded on the grounds that the students did not understand the question.)
(iii) The reason why Alberta has the lowest tuition in Canada is that tuition hikes have lagged behind other provinces.
(Lower tuitions in three other provinces - Quebec, Newfoundland and Nova Scotia - were dismissed as "special cases" [again this is an actual example])
Proof : Identify the phenomenon which is being explained. Show that the evidence advanced to support the existence of the phenomenon was manipulated in some way.
Cedarblom and Paulsen: 160
Untestability
Definition: The theory advanced to explain why some phenomen occurs cannot be tested.
We test a theory by means of its predictions. For example, a theory may predict that light bends under certain conditions, or that a liquid will change colour if sprayed with acid, or that a psychotic person will respond badly to particular stimuli. If the predicted event fails to occur, then this is evidence against the theory.
A thoery cannot be tested when it makes no predictions. It is also untestable when it predicts events which would occur whether or not the theory were true.

qxz9524

Examples:
(i) Aircraft in the mid-Atlantic disappear because of the effect of the Bermuda Triangle, a force so subtle it cannot be measured on any instrument.
(The force of the Bermuda Triangle has no effect other than the occasional downing of aircraft. The only possible prediction is that more aircraft will be lost. But this is likely to happen whether or not the theory is true.)
(ii) I won the lottery because my psychic aura made me win.
(The way to test this theory to try it again. But the person responds that her aura worked for that one case only. There is thus no way to determine whether the win was the result of an aura of of luck.)
(iii) The reason why everything exists is that God created it.
(This may be true, but as an explanation it carries no weight at all, because there is no way to test the theory. No evidence in the world could possibly show that this theory is false, because any evidence would have to be created by God, according to the theory.)
(iv) NyQuil makes you go to sleep because it has a dormative formula.
(When pressed, the manufacturers define a "dormative formula" as "something which makes you sleep". To test this theory, we would find something else which contains the domative formular and see if makes you go to sleep. But how do we find something else which contains the dormative formula? We look for things which make you go to sleep. But we could predict that things which make you sleep will make you sleep, no matter what the theory says. The theory is empty.)
Proof :Identify the theory. Show that it makes no predictions, or that the predictions it does make cannot ever be wrong, even if the theory is false.
Cedarblom and Paulsen: 161
Limited Scope
Definition :The theory doesn't explain anything other than the phenomenon it explains.
Examples
(i) There was hostility toward hippies in the 1960s because of their parents' resentment toward children.
(This theory is flawed because it explains hostility toward hippes, and nothing else. A better theory would be to say there was hostility toward hippies because hippies are different, and people fear things which are different. This theory would explain not only hostility toward hippies, but also other forms of hostility.)
(ii) People get schizophrenia because different parts of their brains split apart.
(Again, this theory explains schizophrenia - and nothing else.)
Proof :Identify the theory and the phenomenon it explains. Show that the theory does not explain anything else. Argue that theories which explain only one phenomenon are likely to be incomplete, at best.
Cedarblom and Paulsen: 163
Limited Depth
Definition : Theories explain phenomena by appealing to some underlying cause or phenomena. Theories which do not appeal to an underlying cause, and instead simply appeal to membership in a category, commit the fallacy of limited depth.
Examples
(i) My cat likes tuna because she's a cat.
(This theory asserts only that cats like tuna, without explaining why cats like tuna. It thus does not explain why my cat likes tuna.)

qxz9524

(ii) Ronald Reagan was militaristic because he was American.
(True, he was American, but what was it about being American that made him militaristic? What caused him to act in this way? The theory does not tell us, and hence, does not offer a good explanation.)
(iii) You're just saying that because you belong to the union.
(This attempt at dismissal tries to explain your behaviour as frivolous. However, it fails because it is not an explanation at all. Suppose everyone in the union were to say that. Then what? We have to get deeper - we have to ask why they would say that - before we can decide that what they are saying is frivolous.)
Proof :Theories of this sort attempt to explain a phenomenon by showing that it is part of a category of similar phenomenon. Accept this, then press for an explanation of the wider category of phenomenon. Argue that a theory refers to a cause, not a classification.
Cedarblom and Paulsen: 164
Fallacies of Definition
*******************
In order to make our words or concepts clear, we use a definition. The purpose of a definition is to state exactly what a word means. A good definition should enable a reader to 'pick out' instances of the word or concept with no outside help.
For example, suppose we wanted to define the word "apple". If the definition is successful, then the reader should be able go out into the world and select every apple which exists, and only apples. If the reader misses some apples, or includes some other items (such as pears), or can't tell whether something is an apple or not, then the definition fails.
Too Broad
Definition : The definition includes items which should not be included.
Examples
(i) An apple is something which is red and round.
(The planet Mars is red and round. So it is included in the definition. But obviously it is not an apple.)
(ii) A figure is square if and only if it has four sides of equal length.
(Not only squares have four sides of equal length; trapezoids do as well.
Proof :Identify the term being defined. Identify the conditions in the definition. Find an item which meets the condition but is obviously not an instance of the term.
Cedarblom and Paulsen: 182
Too Narrow
Definition: The definition does not include items which should be included.
Examples
(i) An apple is something which is red and round.
(Golden Delicious apples are apples, however, they are not red (they are yellow). Thus they are not included in the definition, however, they should be.)
(ii) A book is pornographic if and only if it contains pictures of naked people.
(The books written by the Marquis de Sade do not contain pictures. However, they are widely regarded as pornographic. Thus, the definition is too narrow.

qxz9524

(iii) Something is music if and only if it is played on a piano.
(A drum solo cannot be played on a piano, yet it is still considered music.)
Proof : Identify the term being defined. Identify the conditions in the definition. Find an item which is an instance of the term but does not meet the conditions. Cedarblom and Paulsen: 182
Failure to Elucidate
Definition: The definition is harder to understand than the term being defined.
Examples:
(i) Someone is lascivious if and only if he is wanton.
(The term being defined is "lascivious". But the meaning of the term "wanton" is just as obscure as the term "lascivious". So this definition fails to elucidate.)
(ii) An object is beautiful if and only if it is aesthetically successful.
(The term "aesthetically successful" is harder to understand than the term "beautiful".
Proof : Identify the term being defined. Identify the conditions in the definition. Show that the conditions are no more clearly defined than the term being defined. Cedarblom and Paulsen: 184
Circular Definition
Definition : The definition includes the term being defined as a part of the definition.
(A circular definition is a special case of a Failure to Elucidate.)
Examples:
(i) An animal is human if and only if it has human parents.
(The term being defined is "human". But in order to find a human, we would need to find human parents. To find human parents we would already need to know what a human is.)
(ii) A book is pornographic if and only if it contains pornography.
(We would need to know what pornography is in order to tell whether a book is pornographic.)
Proof : Identify the term being defined. Identify the conditions in the definition. Show that at least one term used in the conditions is the same as the term being defined.
Cedarblom and Paulsen: 184
Conflicting Conditions
Definition :The definition is self-contradictory.
Examples
(i) A society is free if and only if liberty is maximized and people are required to take responsibility for their actions.
(Definitions of this sort are fairly common, especially on the internet. However, if a person is required to do something, then that person's liberty is not maximized.)
(ii) People are eligible to apply for a learner's permit (to drive) if they have (a) no previous driving experience, (b) access to a vehicle, and (c) experience operating a motor vehicle.
(A person cannot have experience operating a motor vehicle if they have no previous driving experience.)
Proof : Identify the conditions in the definition. Show that they cannot all be true at the same time (in particular, assume that one of the conditions is true, then show from this that another of the conditions must be false).
Cedarblom and Paulsen: 186