47. Analysis of Complex Arguments: Syllogistic Structure and Forms

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Lecture Notes

Main Topics #

The Structure of Complex Arguments #

Complex philosophical and mathematical arguments typically contain multiple syllogisms working together:

• Main syllogism: Contains the chief or primary conclusion
• Back-up syllogisms: Support the premises of the main syllogism by proving them
• The relationship between main and supporting syllogisms mirrors the relationship between the natural road of human knowledge (from senses to reason) and the order of nature itself

Method of Analysis #

Berquist provides a systematic approach for analyzing complex arguments:

1. Start with the conclusion: Identify the main or chief conclusion first (often marked by words like “whence,” “hence,” or “therefore”)
2. Find the main syllogism: Determine what premises are immediate to this conclusion
3. Identify the middle term: The term that unites subject and predicate in the conclusion
4. Locate supporting arguments: Determine which syllogisms prove the major and minor premises
5. Classify the forms: Recognize whether categorical, if-then, or either-or syllogisms are being used

Key Arguments #

Thomas Aquinas on the Causes of Love (Summa, Question on Love) #

Main Syllogism:

• Major premise: “What is the object of love is properly the cause of love”
• Minor premise: “The good is the proper object of love”
• Middle term: “Object of love”
• Conclusion: “Therefore, the good is the proper cause of love”

Back-up for the Major Premise:

• Love pertains to the desiring ability (the heart)
• The desiring ability is an ability that is acted upon (passive power)
• What acts upon a passive power is the cause of its activity
• The object of love acts upon the heart, arousing its love
• Therefore, the object of love is the cause of love

Back-up for the Minor Premise:

• Love is nothing other than the agreement of the heart with its object
• What naturally fits or agrees with something is good for it
• The good is what fits you
• Therefore, the good is the proper object of love

Pedagogical Structure: Aquinas states his major premise at the end of the first paragraph (after providing reasons), then begins the second paragraph by stating the minor premise before giving its reason. This arrangement helps the student hold both premises together in mind before drawing the conclusion.

Euclid’s Proposition 6 (Equal Angles and Sides in Triangles) #

The Problem: Prove that in triangle ABC, if angles at B and C are equal, then sides AB and AC are equal.

Main Syllogism (Either-Or Form):

• Two straight lines are either equal or unequal
• AB and AC cannot be unequal (proven by contradiction)
• Therefore, AB and AC must be equal

Supporting If-Then Syllogism:

• If AB and AC were unequal, a part would equal the whole (absurd)
• Therefore, they cannot be unequal
• The reasoning: If AC is longer, cut off on AB a line BD equal to AC. Draw line DC. Triangles DBC and ACB would have equal angles and equal sides (by proposition 4), so they would be equal. But DBC is part of ABC, so the part would equal the whole—impossible.

Supporting Categorical Syllogism:

• Triangles having equal angles contained by equal sides are equal (proposition 4)
• Triangles DBC and ACB have equal angles contained by equal sides
• Therefore, DBC and ACB are equal (but this leads to contradiction)

Result: All three types of syllogisms are used in this elementary geometric demonstration.

Euclid’s Proposition 29 (Prime Numbers) #

The Problem: Prove that any prime number is prime to any number which it does not measure.

Main Syllogism (Either-Or Form):

• A and B are either prime to one another or not prime to one another
• They cannot fail to be prime to one another
• Therefore, A and B are prime to one another

Supporting Categorical Syllogism (Second Figure):

• Since C measures B and A does not measure B
• C is not the same as A
• This prevents C from being the common measure

Supporting If-Then Syllogism:

• If A and B are not prime to one another, something (C) measures both
• But A is prime; no prime can be measured by any number except itself
• C cannot equal A (because A doesn’t measure B)
• Therefore, C cannot measure A, contradicting the hypothesis

Result: All three syllogistic forms appear in this proposition, unlike proposition 1 (which uses only the first figure categorical form).

Important Definitions #

Continuous Syllogisms: Syllogisms linked together such that the conclusion of one becomes a premise of the next. Analogous to proportional relationships in mathematics (like 2:3 :: 4:6), where the end of one relationship is the beginning of the next.

Passive Power (or “ability that is acted upon”): A power where the object acts upon the power to produce its activity. Example: sensory powers (sight, hearing) are acted upon by their objects (light, sound). Contrasts with active powers where the power acts upon the object (e.g., digestion).

Middle Term: The term uniting the subject and predicate in a syllogism, functioning like a middle man in economics or a matchmaker—it “knows both” and brings them together.

Examples & Illustrations #

The Wounded Heart #

Berquist illustrates the passive nature of the desiring ability through common experience: “You make a big impression upon her” or “She made a big impression upon you.” The heart is said to be “wounded” by love. Even in the highest forms of mystical love, saints like Saint Thérèse of Lisieux describe receiving an increase of love under the likeness of being pierced with an arrow or lance—the image of the heart being acted upon.

Fear and Anger #

The object of fear causes fear (the object acts upon the heart). Similarly, if someone insults you, the object of your anger (the insult or the person) causes the anger. This demonstrates that in the desiring ability, the object is both the object of the act and the cause of the act.

The Shoe Analogy #

What is good for you must fit you. A shoe that is good for you has to fit you. Fitting is the connection between the good and what is the object of love.

Prime Numbers #

Three and five are prime numbers (measured only by one and themselves). Three and nine are not prime to one another because three measures both. Two numbers are prime to one another when no number measures both.

Notable Quotes #

“The chief or main conclusion, right? And then you figure out what are the premises that are immediate to that conclusion, right? And then everything else is either superfluous or it’s there to back up one or the other, or in some cases, both of those premises.”

“In the case of the other acts of the desiring ability, like fear or anger or something, right, huh? It’s the object that causes it… the object that arouses fear.”

“Notice grammatically, in the first paragraph, he gave the reason and then drew the conclusion. In the second paragraph, he states a conclusion and then gives a reason.”

“So there’s a structure, there’s a difference in the way the three syllogisms are worded, right? But nevertheless, there’s only one kind of argument being used in these.”

“Even in a very elementary theorem, like these two, it might require as many as all three kinds of syllogisms.”

Questions Addressed #

How do you analyze a complex philosophical argument? #

Start with the chief conclusion and work backward to identify the main syllogism and its premises. Then identify what back-up syllogisms prove each premise. This method reveals the logical structure underlying seemingly complex discourse.

Why does the order of stating and proving premises matter? #

It doesn’t matter logically, but pedagogically it matters greatly. By stating the minor premise first and then proving it, then the major premise appears immediately after, allowing the student to hold both premises together mentally before drawing the conclusion.

What is the relationship between the natural road of knowledge and the structure of arguments? #

The natural road of human knowledge is from senses to reason. This same ordering appears in how arguments are constructed: what is first in nature (the conclusion that expresses what something is) guides the structure of the argument that proves it.

Can elementary geometry require all three types of syllogisms? #

Yes. Euclid’s Proposition 6 demonstrates this—it uses either-or syllogisms (the main form), if-then syllogisms (supporting reductio ad absurdum), and categorical syllogisms (first figure, supporting the reduction). This shows that even seemingly simple demonstrations can involve all forms of syllogistic reasoning.