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"Genuine Havana," detail from Library of Congress, LC-USZ62-78340.Philosophy 103: Introduction to Logic
Enthymemes: The Elliptical Argument

Abstract:  Strategies for completing and evaluating incomplete syllogisms are discussed.

  1. An enthymeme is an argument in which one proposition is suppressed—i.e., it's missing for one reason or another.

    1. In some cases, the missing proposition is not stated because it is obvious.

      E.g., "You'll be fine, just follow your heart." The missing premiss is "All persons who follow their heart are persons who do fine."  (Note that the explicit statement of the missing premiss makes the argument somewhat dubious.)

    2. In other cases, if the missing proposition were present, the argument might lose rhetorical force.

      E.g.,"Mary does well because she pays attention." The missing premiss would be "All people paying attention are people who do well." (Note that it seems reasonable that some persons who pay attention might not do well.)

    3. Occasionally, the proposition is suppressed in an effort to conceal the unsoundness or the invalidity of the argument.

      E.g., "No cars with internal combustion engines are energy efficient, so no American-made cars are energy efficient."  (The missing premiss would be the false premiss, "All American-made cars are cars with internal combustion engines.)

  2. Note: many accounts define an enthymeme as an argument in which a premiss is missing. Nevertheless, some enthymemes omit the conclusion for rhetorical effect.

    E.g., "Self-absorbed people don't help charities and I know you not to be self-absorbed."  The missing conclusion would be, "So I'm sure you will help" and it has been left unstated in order to be effective on defensively motivated persons.

  3. To evaluate a syllogism effectively, we usually need to render the argument explicitly. To do so requires detective work based on a thorough understanding of the rules and fallacies for standard form categorical syllogisms

    1. By the principle of charity, we attempt to supply a missing statement that makes the argument valid unless there is contextual evidence present to the contrary.

    2. To supply the missing statement requires through knowledge of the rules for syllogisms and understanding the ideas of the individual advancing the argument.

    3. To supply intentionally a statement which makes the argument invalid is to commit the straw man fallacy.

  4. First, let us consider some example enthymematic arguments based on statement forms alone. To see if the elliptical argument is valid we must supply the suppressed proposition and test for validity. If necessary, we can go through the rule one by one until the appropriate missing statement is found.  The results of this strategy are summarized in the following examples.

    1. Example 1:

      Some M is not P.
      All M is S.
      ______________
      . . . . . . . . . . . . . . .

      1. By the syllogistic rules, we know that the conclusion must be negative or else the fallacy of an affirmative conclusion from a negative premiss would occur.

      2. We also know that the subject of the conclusion must be distributed or else the fallacy of the illicit process of the minor term would occur.

      3. Hence, the conclusion must be the O statement, "Some S is not P.

    2. Example 2:

      . . . . . . . . . . . . .
      Some S is M.
      ______________
      Some S is not P.

      1. By definition, the missing major premiss contains P, the major term, and M, the minor term.

      2. Since the middle term is undistributed in the minor premiss, M must be distributed in the major premiss or else the fallacy of the undistributed middle term would occur.

      3. Since the major term P is distributed in the conclusion, P must be distributed in the major premiss or else the fallacy of the illicit process of the major term would occur.

      4. Thus, the missing major premiss must have both terms distributed. The major premiss is an E statement: either "No M is P" or "No P is M" fits the bill.

    3. Try the following syllogism on your own. What is the missing premiss?

      No P is M.
      . . . . . . . . . . .
      ___________
      No S is P.
      Solution

  5. Second, let us consider an example from ordinary language.

    1. State Mutual of America reduces the rates of life insurance for nonsmokers. These are the reasons offered:

    2. "You see we're convinced that people who don't smoke cigarettes are better risks than people who do, and better risks deserve better rates."

      The conclusion is the missing statement:

      All better risks are persons deserving better rates.
      All nonsmokers are better risks.
      ___________________________________
      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
      Solution

Suggested Readings:

"Enthymeme," The Free Dictionary.com by Farlex.
"Enthymeme," The 1911 Edition Encyclopedia.
"The Enthymeme: An Interdisciplinary Bibliography," Carol Poster

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