1. Logos, the Three Acts of Reason, and the Division of Logic

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Lecture Notes

The Equivocal Nature of Logos #

Logos has three primary meanings:

1. Word (ὁ λόγος): Vocal sound signifying by convention
2. Thought (διάνοια): What the word signifies; the concept in the mind
3. Reason (λόγος): The faculty that produces and thinks thoughts

These are distinct but fundamentally connected: words signify thoughts, and thoughts proceed from reason knowing itself. In John’s Gospel, the Logos (the Second Person of the Trinity) is understood as the perfect thought of God knowing himself—the only thought that expresses God completely and is itself a person (the Son).

Why words precede thoughts in the order of knowledge: We name things as we know them. Words are sensible (heard and seen), while thoughts cannot be perceived by the senses, yet thought is more intimately connected to word because the word signifies the thought.

The Three Acts of Reason #

Thomas Aquinas identifies three fundamental acts of reason in the process of knowing:

1. Simple Understanding (Intelligere / Simplex Apprehensio) #

Direct grasping of what a thing is; understanding essences or natures.

• Examples: understanding what a square is, what a circle is, what an odd number is, what a dog is
• At this level, one apprehends the nature without making any judgment

2. Understanding of Truth or Falsehood (Compositio et Divisio) #

Combining or separating understood concepts to form judgments.

• Recognizing that “a square is not a circle” (true negative)
• Recognizing that “a square is a quadrilateral” (true affirmative)
• Recognizing that “a square is not a quadrilateral” (false negative)
• Prerequisite: Must first understand each term separately through the first act before combining them

3. Reasoning (Discursus) #

Proceeding from known statements to unknown conclusions through argumentation.

• Putting together two or more statements to derive another statement by argument
• The act of moving from what is known to what is unknown

The Division of Logic #

Thomas Aquinas’s Three-Part Division #

Logic should be divided into three parts, each corresponding to and directing one of the three acts of reason:

• Categoriae (Categories): Pertains to the first act of reason (simple understanding)
• Peri Hermeneus (De Interpretatione): Concerned with the second act (composition/division; truth and falsehood)
• Posterior Analytics, Topics, Sophistical Refutations, Rhetoric: Address the third act (reasoning and argumentation)

Thomas presents this division in his major proem (proemium) to the Posterior Analytics, which he wrote because the Posterior Analytics is “the greatest book of logic.” He also wrote a shorter proem to the Peri Hermeneus because a student requested him to explain that work.

Albert the Great’s Two-Part Division #

Albert divides logic into:

• Art of Defining: Addresses the simple unknown (What is a thing?) → answered by definition
• Art of Reasoning: Addresses the complex unknown (Is a statement true?) → answered by argument

Albert grounds this in the concept of discourse (discursus): coming to know what you don’t know through what you do know.

Reconciliation: Both divisions make sense. The two-part and three-part divisions are complementary and can be applied together as the “rule of two or three.”

Logic as the Art of Arts #

Definition: Logic is the art that directs reason itself and its acts of knowing.

Why it is supreme:

• All other arts direct some other faculty or part of human nature (using hands, feet, etc.) to create external things
• Logic alone directs reason’s own operations—the faculty that directs all other faculties
• Therefore, all other arts proceed from reason’s direction

Title: Logic is called the “art of arts” (ars artium), analogous to expressions like “king of kings.” This is not merely poetic; it demonstrates the foundational and supreme importance of logic to all other disciplines.

The Fundamental Distinction: Name and Speech #

Both name (nomen) and speech (oratio) are defined as vocal sounds (sonus vocalis) that signify by custom or convention (ex instituto/ex consensu), not by nature.

Name (Nomen) #

• Definition: A vocal sound having no part that signifies by itself
• Examples:
  • “Duane” - the syllables “Du” and “A” do not mean anything separately; only the whole signifies the person
  • “Bergquist” - originally from Swedish “Berg” (mountain) + “Quist” (branch), but as a name, the parts no longer signify separately
  • “Johnson” - etymologically means “son of John,” but when functioning as a proper name, it does not carry this meaning
• Key principle: Etymology is not the same as current meaning

Speech (Oratio) #

• Definition: A vocal sound having parts that signify by themselves
• Examples:
  • “You are a white man” - both “white” and “man” retain their individual meanings within the utterance
  • “Black man” - both parts carry independent significance

Significance for logic: This distinction is “very fundamental for logic” because all logical discourse ultimately resolves into names and speeches, and understanding their different structures is essential for understanding how definition, statement, and argument are constructed.

The Speech Perfecting Each Act #

Corresponding to each act of reason is a type of speech that perfects or completes it:

Definition (Definitio) #

• Perfects: The first act (understanding what something is)
• Composed of: Genus and difference (names)
• Example: “A perfect number is a number equal to the sum of all its divisors”
• Purpose: Renders understanding distinct and complete

Statement (Propositio) #

• Perfects: The second act (understanding truth or falsehood)
• Structure: Can be affirmative or negative
• Key relationship: If an affirmative statement is true, its opposed negative is false, and vice versa
• Purpose: Expresses judgments about whether things are or are not related

Argument/Syllogism (Syllogismus, Argumentum) #

• Perfects: The third act (reasoning)
• Composed of: Multiple statements in structured form
• Primary form: The demonstrative syllogism
• Purpose: Moves from known premises to unknown conclusions

Proportional relationship: Definition : First Act :: Statement : Second Act :: Argument : Third Act

Important Definitions #

• Logos (λόγος): Word, thought, or the faculty of reason—an equivocal term with three principal meanings
• Simple Understanding (Intelligere): The direct apprehension of what a thing is; grasping an essence without judgment
• Composition and Division (Compositio et Divisio): Combining or separating concepts to form affirmative or negative judgments about truth or falsehood
• Reasoning (Discursus): The act of proceeding from known to unknown through argumentation and syllogistic reasoning
• Discourse: Coming to know what you don’t know through what you do know (Shakespeare’s definition)
• Name (Nomen): A vocal sound signifying by convention with no internally signifying parts
• Speech (Oratio): A vocal sound signifying by convention with parts that signify by themselves
• Definition: Speech that perfects understanding of what a thing is
• Statement (Propositio): Speech that perfects understanding of truth or falsehood; can be affirmative or negative
• Argument: Speech that perfects reasoning; the syllogism as its primary form
• Perfect Number: A number equal to the sum of all its proper divisors (e.g., 6 = 1+2+3; 28 = 1+2+4+7+14)

Examples & Illustrations #

Understanding What a Thing Is (First Act) #

• Understanding what a square is
• Understanding what a circle is
• Understanding what a triangle is
• Understanding what an odd or even number is
• Understanding what a dog or cat is (varying degrees of clarity)

Composition and Division (Second Act) #

• “A square is not a circle” (true negative)
• “A square is a quadrilateral” (true affirmative)
• “A square is not a quadrilateral” (false negative)
• “A square is a circle” (false affirmative)

The Relationship Between Etymology and Meaning #

• Philosophy: Etymologically means “love of wisdom” (φιλό- + σοφία), but Aristotle uses it to mean the knowledge that a lover of wisdom pursues, not the love itself
• Bergquist: Originally “Berg” (mountain) + “Quist” (branch) in Swedish, but no longer signifies “mountain-branch” when used as a name
• Johnson: Formerly meant “son of John,” but no longer carries this meaning as a proper name

Perfect Numbers #

• 6 (first perfect number): Divisors are 1, 2, 3; their sum = 6
• 28 (second perfect number): Divisors are 1, 2, 4, 7, 14; their sum = 28
• Berquist’s mnemonic: Thomas discusses perfection of God in chapter 28 of Summa Contra Gentiles, corresponding to 28 being the second perfect number
• Theological significance: St. Augustine and Thomas discussed the significance of the number six in relation to God and the universe

Iambic Pentameter (as Example of Understanding Names and Speech) #

• Iambic: Two syllables with accent on the second
• Pentameter: Five feet per line
• Example: “At the time of the year thou mayest in me behold”

Key Arguments #

Why Logic Has Three Parts #

Logic must have three parts because:

1. Reason has three distinct acts in the process of knowing
2. Each act requires a corresponding part of logic to direct it properly
3. This division is “very fundamental for logic”
4. The structure follows necessarily from the structure of reason’s operations

Why Logic Is the “Art of Arts” #

1. Logic directs the act of reason itself
2. All other arts direct some other faculty or part of human nature
3. All other arts proceed from reason’s direction
4. Therefore, logic is foundational to and supreme among all arts
5. The title “art of arts” (ἀρχή τῶν ἀρχῶν) emphasizes this foundational status

Why Words Precede Thoughts in the Order of Knowledge #

1. We name things as we know them
2. The order of names follows the order in our knowing
3. Words are sensible (can be heard and seen)
4. Thoughts cannot be perceived by the senses
5. Yet thought is more closely related to word because the word signifies thought
6. Therefore, in pedagogical order, we encounter words before we can reflect on the thoughts they express

Why Names and Speech Are Fundamentally Distinguished #

1. All logical discourse ultimately resolves into names and speeches
2. Names have no internally signifying parts; the whole signifies, not the parts
3. Speeches have parts that each signify independently
4. This distinction affects how each functions in definition, statement, and argument
5. Both signify by convention, not by nature, distinguishing them from natural signs (like a baby’s cry)

Questions Addressed #

What are the three meanings of logos? #

• Word (ὁ λόγος): Vocal sound that signifies by convention
• Thought (διάνοια): The concept in the mind; what the word signifies
• Reason (λόγος): The faculty that produces and thinks thoughts

How do the three acts of reason relate to the division of logic? #

Each act of reason requires a corresponding part of logic to direct it:

• Simple understanding → Categories (addressing essences)
• Composition/division → Peri Hermeneus (addressing truth and falsehood)
• Reasoning → Posterior Analytics and other works on argumentation

Why is logic called the “art of arts”? #

Because logic directs reason itself, whereas all other arts direct other faculties or parts of human nature. All other arts proceed from reason’s direction, making logic foundational and supreme.

What is the difference between a name and speech? #

• Name: A vocal sound with no internally signifying parts (e.g., “Duane”)
• Speech: A vocal sound with parts that signify by themselves (e.g., “white man”)
• Both signify by convention, not by nature

How do definition, statement, and argument relate to the three acts? #

• Definition perfects the first act (understanding what something is)
• Statement perfects the second act (understanding truth/falsehood)
• Argument perfects the third act (reasoning)

Why is etymology not the same as meaning? #

Because words often originally derived their names from meaningful parts (etymology), but as words are used conventionally over time, the current meaning may no longer reflect the original etymology. Example: “philosophy” etymologically means “love of wisdom” but is used to mean the knowledge a lover of wisdom pursues.

Can the two-part and three-part divisions of logic both be valid? #

Yes. Both divisions make sense and are complementary. Albert the Great’s two-part division (defining and reasoning) and Thomas Aquinas’s three-part division can both be applied, following what Berquist calls “the rule of two or three.”