41. Induction, Example, and Enthymeme in Reasoning

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Lecture Notes

Main Topics #

Forms of Argumentation Beyond the Syllogism #

Berquist distinguishes four main forms of argument:

• Syllogism: Uses universal premises; conclusion follows necessarily
• Induction: Argument from particulars (either singulars or less universal) to universal
• Example (Exemplum): Argument from one singular to another singular of the same kind
• Enthymeme: Argument from likelihood or signs; less universal than syllogism; based on what is true “for the most part” in human affairs

The Nature of Induction: Two Senses #

First Sense: Argument from many singulars to universal

• Strength depends on how representative the singulars are
• Reaches universal conclusion from particular cases
• Example: observing multiple cases of men and concluding “all men are mortal”
• Not necessarily conclusive; exceptions can occur (hence induction is not demonstrative)

Second Sense: Argument from less universal to more universal

• Much stronger when the lesser universals are exhaustive
• Example: Thomas Aquinas’s treatment of God’s simplicity in Summa Theologiae, Question 3
  • Articles 1-6 examine different kinds of composition in creatures
  • Article 7 concludes God is not composed in any way
  • This induction from six kinds of composition to universal non-composition is stronger because the kinds appear exhaustive

The Enthymeme and Its Characteristics #

• Defined as argument from likelihood (probabilis) or from signs
• Likelihood: what is true for the most part in human affairs (e.g., “boys will be boys”)
• Signs: things that strike the senses and bring something else to mind
• Most signs are not completely universal; they admit exceptions
• Example of sign argument: seeing someone leave a bar and inferring drunkenness (though exceptions exist—brain injury, age, etc.)
• Lacks complete universality of the syllogism but may be good “for the most part”

The Example and Its Function #

• Argument from one singular to another singular of the same kind
• Depends for its strength on how similar the two singulars are
• Illustrates a principle through a particular case (e.g., arguing from historical examples of city-states to modern states)
• Example from lecture: A landlady feared black men because she was beaten by black men; this is reasoning from one singular (those men) to a universal judgment unfairly

Proportional Relationship of Arguments #

Berquist clarifies the relationship: Enthymeme is to Example as Syllogism is to Induction

• Both enthymeme and syllogism argue toward conclusions
• Both example and induction deal with particulars
• Enthymeme and example lack the complete universality of demonstration

The Second Figure of the Syllogism #

Perfect vs. Imperfect Syllogisms

• Perfect (First Figure): The dictum de omne or dictum de nullo applies immediately; conclusion follows necessarily as stated
• Imperfect (Second Figure): The middle term is the predicate in both premises; must be converted to show necessity
  • Requires conversion of the universal negative (which converts simply, maintaining its force)
  • After conversion, the argument moves to the first figure
  • The universal affirmative cannot be syllogized in the second figure with two universal premises

Conversion Rules

• Universal negative: converts simply (maintains full force); No A is B ⟷ No B is A
• Universal affirmative: converts partially only; Every A is B converts to Some B is A, not Every B is A
• This asymmetry makes universal negatives more useful for syllogistic reasoning

Invalid Syllogisms with Two Negatives #

• Two universal negatives yield no necessary conclusion
• Can be shown invalid by finding examples where both premises are true but the conclusion varies (sometimes universal affirmative, sometimes universal negative)
• What is necessary cannot sometimes be so and sometimes not be so

Key Arguments #

The Strength of Induction in Theological Demonstration #

Thomas Aquinas uses induction in Article 7 of Question 3 (Summa Theologiae) to establish God’s absolute simplicity:

1. Articles 1-6 demonstrate that God lacks six specific kinds of composition found in creatures:
   • Composition of body and parts
   • Composition of body and soul
   • Composition of matter and form
   • Composition of substance and accident
   • Composition of subject and universal nature
   • Composition of nature and existence
2. Having exhausted the apparent kinds of composition, the inductive conclusion follows: God is not composed in any way
3. Berquist notes this is induction in the second sense—from less universal (particular kinds) to more universal (complete simplicity)
4. Thomas also includes a syllogistic argument in Article 7: God is pure actus (act); whatever is composed is a mixture of actus and potentia (potency); therefore God cannot be composed

Why Axioms Require Both Induction and Understanding #

• Axioms (statements known through themselves, e.g., “the whole is greater than the part”) are first known through induction
• However, once we grasp what “whole” and “part” mean, we understand by reason that the axiom must be true
• Not all conclusions can be reached by induction alone; some require syllogistic demonstration
• Example: The equality of the angles of a triangle to two right angles cannot be known from induction but requires syllogistic proof (Euclid, Elements, Book I, Proposition 32)

Important Definitions #

• Induction: Argument from particulars to universal; exists in two forms: (1) from many singulars to universal; (2) from less universal to more universal
• Example (Exemplum): Argument from one singular to another singular of the same kind; strength depends on similarity between the singulars
• Enthymeme: Argument from likelihood (probabilis) or from signs; true for the most part; lacks complete universality of the syllogism
• Sign (Signum): Something that strikes the senses and brings another thing to mind; most signs are not completely universal
• Likelihood: What is true for the most part in human affairs
• Perfect Syllogism: One in which the conclusion follows necessarily from the stated premises without conversion
• Imperfect Syllogism: One in which conversion of a premise is required to demonstrate necessity
• Conversion: Reversing the subject and predicate of a proposition while maintaining truth
  • Conversio simplex: maintains force (universal negative)
  • Conversio per accidens: loses force (universal affirmative converts to particular affirmative)

Examples & Illustrations #

Examples of Induction #

• Observing that people in a place where everyone is white might induce the false conclusion that all humans are white
• Historical argument from Greek city-states to modern states
• Thomas’s demonstration of God’s simplicity through exhaustion of six compositional forms

Examples of Enthymeme #

• “Boys will be boys” (likelihood in human affairs, though not always true)
• Seeing someone exit a bar and concluding they are drunk (a sign argument; admits exceptions like brain injury or age-related gait disturbance)

Examples of Example (Exemplum) #

• Brother Richard going to Mother Damien concerning a doctor; the landlady feared black men because she was beaten by black men—arguing from one incident to a general judgment about a class (an example of faulty reasoning)

Second Figure Syllogism and Conversion #

• No A is B; Every C is B → Convert to: No B is A; Every C is B → Therefore: No C is A (first figure)
• Cannot yield universal affirmative conclusions from two universal premises in the second figure

Notable Quotes #

“The strength of the example depends upon how much the two examples, singulars, are like each other.”

“Enthymeme is from likelihood or from signs, and most signs are not completely universal.”

“It’s appropriate that the wise men have a whole book where he distinguishes the words that are used most of all in wisdom.”

Questions Addressed #

What is the difference between induction and example? #

Answer: Induction argues from many particulars to a universal; example argues from one singular to another singular of the same kind. They differ in scope and force: induction reaches a universal claim, while example moves from particular to particular.

Why is the second figure called “imperfect”? #

Answer: Because the conclusion does not follow necessarily from the premises as stated. One must first convert a premise (typically the universal negative) to see that the argument has the necessary force. Once converted, it becomes a first-figure syllogism.

How does Thomas Aquinas use induction in proving God’s simplicity? #

Answer: He examines six different kinds of composition found in creatures (body/parts, body/soul, matter/form, substance/accident, subject/nature, nature/existence) and argues that God lacks each. Since these kinds appear to be exhaustive, the induction concludes that God is not composed in any way. This is stronger than argument from singulars because the lesser universals are complete.

Why does the universal negative convert more simply than the universal affirmative? #

Answer: The universal affirmative converts only partially because not everything that falls under the predicate necessarily falls under the subject (e.g., every dog is an animal, but not every animal is a dog). The universal negative, however, converts simply: if no A is B, then no B is A, because if even one B were an A, that would contradict the original statement.