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Enthymemes:
Analyzing Enthymematic Arguments with Examples

Abstract: Enthymeme is defined with examples. Strategies for analyzing, completing, and evaluating enthymematic arguments are discussed.

  1. Definitions and Examples of Enthymemes

    A formal enthymeme is a syllogistic argument which has a statement omitted and is used to prove a conclusion.

    A rhetorical enthymeme is an informal, usually probabilistic, argument with a suppressed statement whose persuasive purpose influences an audience's values, beliefs, or attitudes.[1]


    Enthymematic arguments are formally discussed below in terms of traditional formal logic; only a few of their probabilistic or rhetorical uses are discussed.


    1. In ordinary language, nearly all syllogistic-type arguments are expressed as enthymemes. Usually, the missing proposition in such an argument is taken for granted for ease of expression and is evident to the reader.

      Often, if the missing statement were to be explicitly stated, the argument would lose rhetorical effectiveness and might be thought of as “stating the obvious.”


    2. The kinds of logical enthymemes are classified in order of their frequency of occurrence. Note that an enthymeme is always only a single inference.


      1. A first order enthymeme omits the major premise:

        “Balbus is avaricious, and therefore, he is unhappy.”

        [ . . . . . . . . . . . . . . . . ]

        Balbus is an avaricious person.

        Balbus is an unhappy person.

        Implicit Major Premise: “All avaricious persons are unhappy persons.”


      2. A second order omits the minor premise:

        “All avaricious persons are unhappy, and therefore, Balbus is unhappy.”

        All avaricious persons are unhappy persons

        [ . . . . . . . . . . . . . . . ]

        Balbus is an unhappy person.

        Implicit Minor Premise: Balbus is an avaricious person.


      3. A third-order omits the conclusion:

        “All avaricious persons are unhappy, and Balbus is avaricious.”

        All avaricious persons are unhappy persons.

        Balbus is an avaricious person.

        [ . . . . . . . . . . . . . . . ]

        Implicit Conclusion: Balbus is an unhappy person.


      4. Rhetorical enthymemes are classified in the same manner. Henry Aldrich explains this type of syllogism (when completed) with the following example:

        Most men who envy hate.

        This man envies.

        This man (probably) hates.

        The major premise is an almost universal statement; the minor premise is viewed as a singular sign of the conclusion. This syllogism is not intended to be deductive, for the major premise lacks universality, and the middle term is undistributed in both premises.[2]
  2. Stylistic reasons for the use of enthymematic arguments.

    1. In some cases, the missing proposition is not explicitly stated because the inference is only probable. In cases such as these, if the missing premise or conclusion were to be explicitly supplied, the argument would test out as formally invalid or unsound.[3] Fairly often enthymematic arguments seem sound but are invalid or are based on suppressed statements which are false or questionable.


      1. The following enthymematic example is often mistakenly attributed to Alexis de Tocqueville: [4]

        “America is great because she is good.”

        Implicitly, the conclusion “America is great” logically follows only if the doubtful assumed premise ”All good nations are great nations” is added to the given premise “She (i.e. America) is good.

        Thus, when the argument is explicitly reconstructed into standard form and order, 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 were necessarily restricted to a false major premise (i.e., the premise is false because some good nations are not great. Consequently, the argument is unsound.[5]


      2. Consider this second example:

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

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

        [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.


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


      3. In the third example, the following enthymeme leaves its conclusion unstated. If the argument were meant to be deductive and if it were explicitly stated, the reader might recognize that the argument is invalid.

        Nevertheless, it may well be that in an everyday context, the argument was never meant to be deductive; instead, it might have been intended to be an inductive, rhetorical enthymeme:

        “There is always some madness in love. But there is always, also some method in madness.”[6]

        The conclusion intuitively suggests itself as …
        “Therefore, there is some method in love.”
        So, the argument can be set up as something like …

        Some aspects of madness U are composites of love.

        Some methods are aspects of madness.U.

        [Some methods are composites of love.]


        As a deductive argument, the fallacy of the undistributed middle term occurs. However, as part of ordinary language, the argument is best rhetorically interpreted as intended to be persuasive or probable.


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

      “Mary does well because she pays attention.”

      Here, the suppressed premise necessary for validity would be “All attentive people are people who do well.” And so, the argument when stated explicitly becomes:

      [All attentive people are people who do well.]

      Mary is an attentive person.

      Mary is a person who does well.


      Since it seems reasonable to assume that not all attentive people do well, this reconstruction is unsound argument.

      However, if we adopt the principle of charity, the argument should be viewed as inductive or probable (rather than deductive and invalid) with the implicit major premise being:
      Many attentive people are people who do well.” rather than “All attentive people are people who do well. ”
      Even though the argument is logically unsound, it is rhetorically influential.


    3. “Portia” (from Merchant of Venice) 
painted by Fanny Bowers, Chromolithograph, 
P&P Online LC-USZC4-5219 Occasionally, a proposition is suppressed in an effort to conceal the unsoundness or the invalidity of the argument. E.g., in Shakespeare's The Merchant of Venice when the rich heiress Portia is asked how she likes one of her suitors who is a hard drinking young German, she responds:
      “Very vilely in the morning, when he is sober; and most vilely in the afternoon, when he is drunk … I will do anything … ere I'll be married to a sponge.[7]
      Since Shakespeare is using the metaphor “sponge” for someone who almost always drinks too much, the implicit enthymeme is as follows:
      [A sponge is someone who almost always drinks too much.]

      The young German is a person who almost always drinks too much.

      The young German is a sponge.

      This analysis assumes that some persons who occasionally drink too much are not sponges. Although the logic might appear good in the quotation, under examination, the fallacy of the undistributed middle terms is found.

      In sum, as John Neville Keynes points out:
      “[F]allacious arguments … are seldom completely stated, or their want of cogency would be more quickly recognised.[8]
      Keynes' observation applies to both logical and rhetorical enthymematic arguments.


    4. Note: Most sources define an enthymeme as an argument in which a premise is missing; nevertheless, some enthymemes omit the conclusion in order to tweak a rhetorical effect:

      “Self-absorbed people don't help charities and I know you're not 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 a formal conclusion being stated as “You are a person who helps charities.”)
      However, no conclusion validly follows from two negative premises.

      Possibly in this case, the conclusion was left unstated both to cover up the fact that the argument is invalid and for the supposed rhetorically persuasive effect of appealing to one's vanity in order to obtain help for a purported charity.

      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 statement is treated as an E-form statement.)

      [You are a person who helps charities.]

      (Note this statement is considered an A-form statement.]

      As mentioned above, this syllogism tests out invalid because of its exclusive premises. The argument also is fallacious because no valid syllogism can have an affirmative conclusion from a negative premise.


  3. How to Evaluate an Enthymeme

    In order to evaluate an enthymeme effectively, the argument needs to be explicitly stated in its reconstruction. To do so requires detective work based on a thorough understanding of …

    (1) the rules and the fallacies of standard form categorical syllogisms, and

    (2) how to translate ordinary language into standard form categorical statements, and

    (3) the distribution statuses of those statements.


    1. By the principle of charity, we should attempt to supply a missing statement completing the argument as valid if possible — unless the context of the passage explicitly prevents such an interpretation.


      1. To be able to supply the missing statement requires through knowledge of the fallacies and rules for syllogisms and an understanding of the intention of the individual advancing the argument.

      2. Reconstructing Formal (Deductive) Enthymemes: Initially, it might be necessary to check off each syllogistic rule systematically in order to deduce the appropriate missing proposition. Later, once the rules and fallacies become familiar, systematic checking will seldom be necessary for disclosing the intended missing proposition in formal arguments.

      3. Reconstructing Informal (Rhetorical) Enthymemes: When translating an enthymeme into a standard form syllogism, be careful not to supply a proposition which makes the argument invalid when such a proposition was not intended in the original context of the argument; otherwise, the straw man fallacy could occur.

        This advice is sometimes difficult to follow when working with inductive rhetorical enthymematic arguments. Michael Scriven has some helpful advice:
        “[P]roduce a set of premises which together convey the essential content of the assumptions underlying the argument. … First, the assumptions have to be strong enough to make the argument sound. Second, they should be no stronger than they have to be, since they might then be too strong to be true, and you would then have constructed a ‘straw-man’ version of the argument … Third … try to relate the assumptions as you formulate them to what the arguer would be likely to know or would believe to be true.[9]
        A straw man fallacy occurs whenever a proponent's argument is misrepresented by an opponent and then rejected as if the misrepresentation were the original argument at issue.

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


      1. Example 1:

        Some M is not P

        All MD is SU

        [. . . . . . . . . . .]


        We can systematically check each syllogistic fallacy and its corresponding rule in order to determine the structure of the statement form necessary for validity.[10]


        1. Four Term Fallacy: The syllogism must have exactly three terms. The argument form already has exactly three terms corresponding to S, P, and M. Since we are dealing with syllogistic forms and not actual statements this rule is inapplicable.

        2. Fallacy of the Undistributed Middle Term: The middle term must be distributed at least once in the premises. The middle term is distributed in the subject of the minor premise (as the subject of an A proposition), so this rule was not violated.

        3. Fallacies of Illicit Minor or Major Terms: If a term is undistributed in a premise 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 premise, the minor term S cannot be distributed in the conclusion or else the fallacy of illicit minor would occur.

        4. Fallacy of Exclusive Premises: At least one premise must be affirmative. This rule checks out OK since the minor premise is affirmative.

        5. Fallacy of an Affirmative Conclusion from a Negative Premise: If a premise is negative, the conclusion must also be negative. Since the major premise of the argument is negative, the missing conclusion must be negative or else the fallacy of Affirmative Conclusion for a Negative Premise would occur.

        6. Existential Fallacy: If both premises are universal the conclusion must be universal as well. Since the major premise of the argument form is particular, this rule does not apply.


        Thus, from our examination of the syllogistic rules, we conclude that the conclusion must meet the following requirements:

        * The conclusion must contain both the S and P terms (by terminological definition).

        * The conclusion must be negative with the minor term S undistributed.

        Hence, the conclusion must be the O statement:
        “Some SU is not PD

      2. Example 2:

        [. . . . . . . . . . .]

        Some S is MU

        Some S is not PD


        1. From our knowledge of the positions of terms in syllogistic forms, we know the missing major premise contains P, the major term, and M, the middle term (but we do not know, of course, their subject and predicate position yet.

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

        4. Thus, the missing major premise must have both terms distributed. So the major premise is an E statement:
          Either “No M is P” or
          “No P is M” fits the bill.
  4. Enthymeme Practice Exercises with Answers

    Try the following syllogisms on your own. Deduce the missing statement forms by referring to the syllogistic rules for valid arguments.





    1. All M is P

      [. . . . . . . . . ]

      All S is P

      Answer: The missing premise must be affirmative or else the fallacy of an affirmative conclusion from a negative premise would occur. It must also distribute the minor term S since the minor term is distributed in the conclusion or else the fallacy of illicit minor would occur. So the missing premise is:
      All S is M


    2. No P is M.

      [. . . . . . . . .]

      No S is P.

      The missing premise must be affirmative or else the fallacy of exclusive premises would occur, and the minor term must be distributed or else the fallacy of illicit minor would occur. Hence, the missing premise has to be:
      All S is M


    3. And finally a more difficult syllogistic form:

      [. . . . . . . . . . . . . .]

      Some M is not S

      Some S is not P


      To avoid the fallacy to two negative premises, the major premise must be affirmative.

      But the major term must be distributed since it is distributed in the conclusion (otherwise fallacy of illicit major would occur), and the middle term must also be distributed since it is undistributed in the minor premise (or the fallacy of the undistributed middle would occur).

      No affirmative statement has both terms distributed, so there is no solution of constructing this problem into a valid syllogistic form.

      Consequently, no supplied major premise would test valid in this syllogistic form.



    4. As a fairly difficult ordinary language problem, try to solve this example from an insurance company advertisement:

      State Mutual of America offered reduced rates of life insurance for nonsmokers.

      These are the reasons provided:

      “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.” Set up the enthymeme and find the missing concluding statement:

      All better risks are deservers of better rates.U

      All nonsmokers are better risks.

      [ . . . . . . . . . . . . . . . . . . . . . . . . . ]

      The missing conclusion must be universal to avoid the existential fallacy and must not distribute the major term in the conclusion in order to avoid the fallacy of the illicit minor term.

      Hence, the missing conclusion is an A type:

      All nonsmokers are deservers of better rates.U

Notes

(Most links are to page cited)

1. For an interesting historical summary of various uses of the term, see Thomas M. Conley, “The Enthymeme in Perspective,” Quarterly Journal of Speech 70 no. 2 (1984), 168-187.

The term “enthymeme” historically has several different uses. In one of Aristotle's uses of the word, he states:

“[A]n enthymeme (ενθυμημα) is a syllogism starting from probabilities or signs…”An. Pr. 2.27 70a9-11 (trans. A.J. Jenkinson)

… where, for him, a sign is a generally approved proposition which can be either necessary or not necessary). Aristotle provides the following example of the latter type of sign (where refutable probabilistic support moves from specific to general):

“The fact that Socrates was wise and just is a sign that the wise are just.” [Rh. 1.2 1357b12 (trans. W. Rhys Roberts)].

Aristotle says this argument is refutable because it does not form a (proper) syllogism, but he points out enthymemes such as these are useful even though they are not deductively valid. So with the rhetorical enthymeme the conclusion can follow either with necessity or follow for the most part. [Rh. 1.2 1356b.15 (trans. W. Rhys Roberts).]

One premise usually states a general probability which is almost universal and the other states a more or less fact or belief which indicates the conclusion. H.L. Mansel, “Appendix,” Artis Logicæ Rudimenta From the Text of Aldrich (Oxford: H. Hammans, 1862), 209.

So for Aristotle, a rhetorical syllogism is characterized as informally offering a reason or an apparent reason for that which is stated.

Thomas Hobbes expresses a notion of both the logical and rhetorical syllogisms as follows:

“[A] sentence, if the reason be rendered, becomes a Conclusion, and both together make an Enthymeme.” [Thomas Hobbes, The Whole Art of Rhetoric in The English Works of Thomas Hobbes of Malmesbury ed. Molesworth (London: John Bohn, 1840), 475.]

Hobbes' definition does not distinguish deductive (or apodictic) enthymemes from rhetorical (or probabilistic) enthymemes and is a useful overall view of the various historical definitions proposed.

2. Mansel, “Appendix,” 210. In standard form and order the syllogism is something like:

Some [persons who envy] U are [persons who hate].
All [persons who are this person] are [persons who envy]U.
All [persons who are this person] are [persons who hate].

The minor premise and conclusion of this syllogism are A form statements.

3. See the discussion on this point by the first modern logician Richard Whately, Elements of Logic (London: Mawman, 1826), 201-202.

4. John J. Pitney, Jr., “The Tocqueville FraudThe Weekly Standard (November 13, 1995) (accessed February 5, 2015).

5. Denial of the falsity of the major premise, implying the persuasive definition that a “great” nation is one that is good, leads to a viciously circular argument.

“A ‘persuasive definition” is one which gives a new conceptual meaning to a familiar word without substantially changing its emotive meaning, and which is used with the conscious or unconscious purpose of changing, by this means, the direction of people's interests.”

Charles L Stevenson. Facts and Values. New Haven: Yale Univ. Press, 1963. 32.

6. Friederich Nietzsche, Thus Spake Zarathustra trans. Thomas Common (New York: Boni and Liveright, 1921), 44.

7. Shakespeare, MV, 1.ii 91-93,104-105.

8. John Neville Keynes, Studies and Exercises in Formal Logic 4th ed. (London: Macmillan, 1906), 368.

9. Michael Scriven, Reasoning (New York: McGraw-Hill, 1976), 85.

10. The rules and fallacies presented here (and explained here) are from I.M. Copi and Carl Cohen, Introduction to Logic (Pearson, 2010). Rules in some other textbooks might differ somewhat but the main procedure outlined here would, of course, work with those rules and fallacies as well.



Suggested Readings

Thomas M. Conley, “The Enthymeme in Perspective,” Quarterly Journal of Speech 70 no. 2 (1984), 168-187. doi: 10.1080/00335638409383687 A study of the different meanings of ”enthymeme“ with an emphasis on the rhetorical enthymeme.

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

Sir William Hamilton, Discussions on Philosophy and Literature (New York: Harper & Brothers, 1860), 153-157. Hamilton discusses historical interpretations of Aristotle on enthymemes and outlines four categories of meaning for the term.

Michael D. Hood, “The Enthymeme: A Brief Bibliography of Modern Sources,” Rhetoric Society Quarterly 14 no. 3/4 (Summer-Autumn, 1984), 159-162.

H.W.B. Joseph, An Introduction to Logic 2nd ed. (Oxford: Clarendon Press, 1916), 350-353. Joseph reviews Mandel's commentary on Aldrich and provides examples from the history of logic and relates the enthymeme to prosyllogism, episyllogism, and epicheirema.

Carol Poster, “The Enthymeme: An Interdisciplinary Bibliography Journal for the Study of the Rhetoric of the New Testament (from off-line e-journal, July, 2022). An extensive bibliography.

Christof Rapp, “Different Types of Enthymemes” in “Aristotle's Rhetoric” from the Stanford Encyclopedia of Philosophy (Spring, 2010).

Jeffrey Walker, “The Body of Persuasion: A Theory of the EnthymemeCollege English 56 no. 1 (January, 1994), 46-65. doi: 10.2307/378216 [Preview; to read use alternative access with free registration.] 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.

Douglas Walton, “The Three Bases for the Enthymeme: A Dialogical Theory,” Journal of Applied Logic 6 no. 3 (September, 2008), 361-379. doi: 10.1016/j.jal.2007.06.002 Douglas Walton develops a theory of enthymematic arguments in accordance with dialogical argumentation, illustrated with several examples.

Douglas Walton and Christopher A. Reed, “Argumentation Schemes and EnthymemesSynthese 145 no. 3 (July, 2005), 339-370. Also here. doi: 10.1007/s11229-005-6198-x An examination of ten case studies of enthymematic reconstruction in light of the principle of charity and the avoidance of the straw man fallacy.
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