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A Common Logical Fallacy I

Updated on July 4, 2014

The Fallacy

Ann Coulter proudly attacked world-popular sport soccer, taking it as a "proud American" attitude to defenestrate a game that lacks historical roots or popular appeal in US cultural history. One suspects that soccer's undeniable popularity among new immigrants, Latinos for one, is another thorn in conservative Coulter's side.

In her essay (cf., we read the following: "The prospect of either personal humiliation or major injury is required to count as a sport. Most sports are sublimated warfare." These are premises in an argument. An argument always has a conclusion, by definition. In an enthymematic argument, premises and/or conclusion may not be stated as the competent user of language can be counted on to discern them. An additional premise in the above argument would assert that soccer is not the kind of sport that gives sufficiently ample scope to injury-resulting violence and to personal humiliation; it is more of a team-based sport and, as such, the columnist implies, it is un-American in its communitarian, anti-individualist, and relatively non-violent properties. The intended conclusion of the author's argument is that soccer does not really make it to being a genuine sport. The essayist is confused in her logic. Let us construct the above argument and see what is wrong with it.

  1. Premise 1: Prospect of major injury or serious personal humiliation makes a game count as a sport.
  2. Premise 2: Soccer does not have the above feature.
  3. Conclusion: Therefore, soccer should not count as a sport.

The argument commits a formal fallacy. As constructed, the argument is deductive. The author's emphasis on requirements and the assertive fashion in which she builds toward the implied conclusion suggest an intend to present a deductive argument. So does the reference to types and definitions ("sport" as a type and what should and should not count as a sport.) The formal fallacy committed renders the argument invalid. Even if the argument passed the validity test, it would not make it through the soundness test because it does not have true premises. For one, if sports are to be thought of as games, Wittgenstein argued persuasively that there are no overarching typical or essential features which a game must have to count as a game. (Don't count on a populist narcissist to invest time and effort in reading the demanding writings of Wittgenstein, especially if she can spend her time more profitably in reading texts by such stalwarts as Reagan or Bush Jr..) Additionally, there are many accepted sports that lack the features she muses over. The second premise is also false. Soccer poses risk of serious individual injury and humiliation. The argument is helpless - it is frightening that the majority of readers do not realize this. Let us return to the validity check. Without passing this check, a deductive argument is worthless - it does not even matter if it does or does not have true premises.

Validity of a deductive argument is a matter of the logical form or structure or pattern the argument has. Extrapolation of logical form, in propositional logic, works like this: take a sentence like "it is raining and the game is not on." Logic depends on certain key words, the logical connectives of a language. "And" and "not" are among those logical connectives or logical constants. Cut the above sentence so that the constants are kept fixed: ".... and not ____." You have the logical form of the proposition expressed by the sentence. We could use propositional variables that are letter, as is done in introductory textbooks: "p and not-q." What matters is that any conjunction of a statement and a negation of another statement is true/false in exactly the same way that any other such conjunction is: p has to be true and q false for the whole to be true; there is no other way.

An argument is, by definition, a string of statements one of which is privileged in a certain way: it is put down as presumably being supported by the other statements - this is the conclusion. Support means this: there is no logical possibility that the premises are true and the conclusion false. This is the definition of validity which is a characteristic only of arguments known as deductive. Any deductive argument that is not valid is invalid. Invalid arguments have fallacious - invalid - logical forms. Valid arguments, and only valid arguments, have valid logical forms. Here are, below, some examples of valid argument forms of the standard propositional logic. You can put ANY statements for p, q, r: it does not matter, you always get a valid argument. This means that, IF the premises of such an argument are true, the conclusion is guaranteed to be true.

  1. p and not-q /.. Therefore, not-q
  2. If p, then q /.. Therefore, q
  3. If p, then q; if q, then r /.. Therefore, if p, then r
  4. If p, then if q, r ; if p, then q /.. Therefore, if p, then r
  5. If p, then if q, r /.. If p and q, then r

The following argument form is invalid. See that this is the logical form of Coulter's argument. Invalidity is not a matter of opinion. An invalid argument is invalid in the way the statement expressed by the sentence "a triangle has four angles" is false; if someone who utters it believes it to be true is immaterial. The falsehood of the statement is logically or analytically necessary; it is a matter of the meanings of the words in the statement. Similarly, a logical form is necessarily invalid, if it is invalid, as a matter of the meanings of the logical connectives (words like "and" and "if/then" and "not") in the form.

Here is the invalid form of the argument who have examined here. This is a formal fallacy that has the appropriate name "denying the antecedent."

if p then q; not-p /.. not-q

If Coulter were to say, instead that personal injury and humiliation are necessary conditions (not sufficient, as exemplified above), then the argument would be valid - although it would still be unsound since the premises are not true, as indicated above.

The reformulated argument would have it that "only if there is a risk of personal injury/humiliation, is something a sport." The logical form now is valid. Nevertheless, this formulation brings out, again, the absurdity in this position; ample counterexamples are available in which something counts as a sport even though it does not pose such risks. We should notice that what is being discussed does not involve a definition of "sport" although Coulter may not have been clear about this. A lexical definition would not help Coulter's case. Nor would her position benefit from using an extensional definition (a definition by enumeration of all games that count as sports). Perhaps, she should be charitably taken to be venturing a theoretical or stipulative definition (about what the necessary and sufficient conditions are for something to count as a sport, or as an American sport rather...) Nevertheless, the overall theory within which this definition could function would be open to similar objections like the ones made above.

Here is the valid argument form (known as Modus Tollens.)

if p, then q; not-q /... Therefore, not-p

Fallacy Test

Is the following argument valid or invalid? If you look like Ann Coulter, you look gorgeous; but, you don't look like her: therefore, you don't look gorgeous.

See results

© 2014 Odysseus Makridis


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    • villyvacker profile image

      Billy Turnock 

      4 years ago from Manchester England

      There's a line you can follow when trying to attract someone's's usually associated with getting the attention of the opposite sex...and it is....if you want to attract someone's attention take an opposing view of something they say. They will not be able to ignore you and you now on their radar....this is what Coulter has done, but on a more cataclysmiccally massive scale. She has chosen one of the most popular sports in the world...taken an opposing view to the rest of the worlds population with a veiled scientific explanation...and gets the attention of everyone. Job done...publicity stunt success.


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