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"Genuine Havana," detail from Library of Congress, LC-USZ62-78340. Enthymemes:
Analyzing Enthymematic Arguments

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

  1. An enthymeme is a particular means of expressing a syllogistic argument which has one proposition suppressed—i.e., one proposition (either a premiss or a conclusion) is not stated. [1]

    1. In ordinary language, nearly all syllogistic arguments are expressed as enthymemes. The missing proposition in these arguments is left implicit for ease of expression and is usually easily supplied by the listener. Often, if the missing statement were explicitly stated, the argument would lose rhetorical effectiveness and would be thought of as “stating the obvious.”

    2. In some cases, the missing proposition is not explicitly stated because the inference is only probable. It the missing premiss or conclusion were to be explicitly supplied, the argument would be seen to be formally invalid.

      1. The following enthymematic example is often mistakenly attributed to Alexis de Tocqueville: [2]

        ”America is great because she is good.”

        Implicitly, the conclusion “America is great” logically follows only if the doubtful premiss ”All good nations are great nations” is assumed and added to the given premiss “She (i.e. America) is good. Thus, when the argument is explicitly reconstructed, it becomes

          All good nations are great nations.
          America is a good nation
          America is a great nation.

        Note that in constructing the argument as valid, we necessarily were restricted to a false major premiss; consequently, the argument is unsound.

      2. Consider this second example:

        “You'll do fine, just follow your heart.”

        The missing premiss necessary for validity in the argument would be “All persons who follow their heart are persons who do fine.”

        Note that the explicit statement of the missing premiss makes the argument valid but unsound since the supplied premiss is clearly false. Some persons who follow their heart do not do well.)

          (All persons who follow their heart are persons who do fine.)
          You are a person who follows your heart.
          You are a person who does fine.

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

      E.g., “Mary does well because she pays attention.”

      Here, the suppressed premiss necessary for validity 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.) And so, the argument when stated explicitly becomes:

        (All persons paying attention are people who do well.)
        Mary is a person paying attention.
        Mary is a person who does well.

    4. Occasionally, a 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 necessary for validity here is the false premiss, "All American-made cars are cars with internal combustion engines.) The reconstructed argument, then looks like this:

        No cars with internal combustion engines are energy efficient.
        (All American-made cars are cars with internal combustion engines.)
        No American-made cars are energy efficient.

      In this case, again, the argument is valid, but unsound.

  2. Note: Some sources define an enthymeme as an argument in which a premiss is missing. Nevertheless, some enthymemes omit the conclusion in order to tweak a rhetorical effect.

    E.g., “Self-absorbed people don't help charities and I know you not to be self-absorbed.” In this psychologically manipulative reasoning, the import of the missing conclusion would be intended to be something like "So I'm sure you will help.” with the conclusion “You are a person who helps charities.”

    However, no conclusion validly follows from two negative premisses. Possibly in this case, the conclusion was left unstated both for the reason the argument is invalid and for the supposed rhetorically persuasive effect of appealing to one's vanity in order to obtain help. Reconstructing the full argument, we obtain the following syllogism:

      No self-absorbed people are persons who help charities.
      You are not a self-absorbed person. [Note this is an E statement.]
      (You are a person who helps charities.) [Note this is an A statement.]

    As mentioned above, this syllogism tests out invalid because of its exclusive premisses.

  3. In order to evaluate an enthymeme effectively, the argument needs to be explicitly stated. To do so requires detective work based on a thorough understanding of the rules and the fallacies for standard form categorical syllogisms.

    1. By the principle of charity, we should attempt to supply a missing statement that makes the argument valid unless the context of the passage explicitly prevents such an interpretation.

    2. To be able to supply the missing statement requires through knowledge of the rules for syllogisms and an understanding of the intention of the individual advancing the argument. In the beginning, it might be helpful to check off each syllogistic rule systematically in order to deduce the appropriate missing proposition. Later, once the rules and fallacies become familiar, systematically checking each syllogistic rule will seldom be necessary for disclosing the intended missing proposition.

    3. Normally, during argument reconstruction, if a proposition is intentionally supplied making the argument invalid, when such a proposition was not so intended by the individual advancing the argument, the straw man fallacy would be committed by the evaluator.

  4. First, let us consider some example enthymematic arguments based on statement forms alone. To see if these elliptical argument forms are valid we must supply the suppressed proposition in accordance with the rules for validity.

      • Example 1:

        Some M is not P.
        All MD is SD.
        . . . . . . . . . . . . . . .

      We can systematically check each rule and its related fallacy in order to determine the structure of the statement form necessary for validity as follows: [3]

      1. Rule 1: The syllogism must have exactly three terms. The argument form already has exactly three terms: S, P, and M, so this rule is being followed.

      2. Rule 2: The middle term must be distributed at least once in the premisses. The middle term is distributed in the subject of the minor premiss (as the subject of an A proposition), so this rule was not violated.

      3. Rule 3: If a term is undistributed in a premiss it cannot be distributed in the conclusion. (Otherwise, we would be reasoning from only part of a class to a conclusion involving the entire class.) Since the minor term S is undistributed in its premiss, the minor term S cannot be distributed in the conclusion or else the fallacy of illicit minor would occur.

      4. Rule 4: At least one premiss must be affirmative. This rule checks out OK since the minor premiss is affirmative.

      5. Rule 5: If a premiss is negative, the conclusion must also be negative. Since the major premiss of the argument is negative, the missing conclusion must be negative or else the fallacy of Affirmative Conclusion for a Negative Premiss would occur.

      6. Rule 6: If both premisses are universal the conclusion must be universal as well. Since the major premiss of the argument form is particular, this rule does not apply.

      7. Thus, from our examination of the syllogistic rules, we conclude that the conclusion must contain both the S and P terms, and the conclusion must be negative with the minor term S, undistributed.

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

    1. Example 2:

        . . . . . . . . . . . .
        Some S is MD.
        Some S is not PD.

      1. From knowledge of the structure of syllogisms, we conclude the missing major premiss contains P, the major term, and M, the middle 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. So major premiss is an E statement: either "No M is P" or "No P is M" fits the bill.

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

        No P is M.
        . . . . . . . . . . .
        No S is P.


  5. Second, try to solve this ordinary language example from an old advertisement:

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

    2. “You see we're convinced that people who don't smoke cigaretttes 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.
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Suggested Readings:

The Body of Persuasion: A Theory of the Enthymeme” Jeffrey Walker questions how enthymemes are defined in many rhetoric and composition studies, develops a better characterization, and analyzes two readings first published in the journal College English.

Different Types of Enthymemes” Enthymemes are described in Christof Rapp's “Aristotle's Rhetoric” from the Stanford Encyclopedia of Philosophy.

Enthymeme” A concise, clear definition is stated from the classic 1911 Encyclopedia Britannica.

"Enthymeme," A short entry summary from Wikipedia.

Enthymemes,” “The Enthymeme: An Interdisciplinary Bibliography of Critical Studies” is prepared by Carol Poster, York University.

The Three Bases for the Enthymeme: A Dialogical Theory,” Douglas Walton develops a theory of enthymematic arguments in accordance with dialogical theory, illustrated with several examples first published in Journal of Applied Logic.


1. “Enthymeme” is not used in contemporary logic in the Aristotelian sense of the word. For example, Aristotle states “Now an enthymeme (ενθυμημα) is a syllogism starting from probabilities or signs…” where, for him, a sign is a generally approved demonstrative proposition) (The Basic Works of Aristotle, ed. Richard McKeon, Analytica Priora, trans. A.J. Jenkinson (New York: Random House: 1970) Bk. II, Ch. 26). Here is Aristotle's example of the former type of sign (where the logical support moves from specific to general):

“The fact that Socrates was wise and just is a sign that the wise are just”(Ibid, Rhetorica trans. W. Rhys Roberts, Bk. 1 Ch. 2, 1357b).

Aristotle says this argument is refutable because it does not form a syllogism. Rather than classifying this argument in accordance with Aristotle's concept of “enthymeme” contemporary usage would label the argument as an example of the informal fallacy of converse accident. Although enthymematic arguments are discussed here in terms of traditional formal logic, notice that these arguments can also be taken in the rhetorical sense of being probable, as is often done so in English rhetoric and composition studies.

2. See John J. Pitney, Jr., “The Tocqueville Fraud,"" The Weekly Standard (November 13, 1995), (accessed February 5, 2015).

3. These rules and fallacies presented here are from I.M. Copi and Carl Cohen, Introduction to Logic (Pearson, 2010). Rules in various textbooks differ according to author, but the main procedure outlined here would, of course, work systematically to discover the missing propositions with those rules and fallacies as well.

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