36. Definition, Statement, and the Structure of Reasoning

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Lecture Notes

Main Topics #

• Name vs. Speech (Nomen vs. Oratio): Both are vocal sounds produced by the vocal cords and signify by custom rather than by nature, but they differ fundamentally in structure
• Name (Nomen): A vocal sound with no parts that signify by themselves
• Speech (Oratio): A vocal sound with at least two parts that signify by themselves (e.g., “Johnson” as a name has no internal signifying parts, but “John-son” etymologically had two)
• Definition vs. Statement: Two species of speech distinguished by what they signify
• Simple Statements: The basic unit composed minimally of noun and verb
• Compound Statements: Disjunctive (either-or), conditional (if-then), and other complex forms
• The Role of the Verb: Unique in signifying with time, which poses philosophical challenges for transcending temporal categories

Key Arguments #

Definition as Speech Signifying What a Thing Is #

• A definition is speech that makes known distinctly what a thing is
• Example: The definition of a perfect number—a number equal to the sum of its proper divisors (6 = 1+2+3; 28 = 1+2+4+7+14)
• Definitions require more distinct understanding than mere naming
• We name things before we can define them (e.g., a child knows what “love” means but cannot define it)

Statement as Speech Signifying Truth and Falsity #

• A statement (or proposition, propositio) is speech signifying what is true or false
• Truth consists in saying what is, is and what is not, is not
• Falsity consists in saying what is not, is or what is, is not
• Examples:
  • “A square is a quadrilateral” (true)
  • “A square is not a circle” (true)
  • “A square is a circle” (false)
  • “A square is not a quadrilateral” (false)
• A single noun (like “dog”) cannot be true or false by itself—you must predicate something of it

Simple Statement Structure: Two-Part Division #

• Can be divided into noun and verb
• “Socrates sits,” “Socrates eats,” “Socrates thinks,” etc.
• Both noun and verb are names (nomina) in Greek/Latin, but English distinguishes them
• The verb adds something unique: it signifies with time (cum tempore)
• Grammatically, you cannot construct a statement without something like a noun and a verb

Simple Statement Structure: Three-Part Division #

• More natural division into subject, predicate, and copula
• Subject: that which is spoken of (the suppositum)
• Predicate: what is said or not said of the subject
• Copula: the sign of affirmation or negation (“is” or “is not”)
• This three-part structure is essential for understanding reasoning and the syllogism
• Based on principles like “if A is set of all B, then…” (nota omnium, nota nullius)

The Philosophical Problem of Temporal Signification #

• The verb’s essential connection to time reflects a deeper human limitation: we struggle to think beyond temporal categories
• Greeks believed “whatever is must be somewhere,” and by extension, must be in time
• This affects theological language: when Christ says “Before Abraham was, I am,” He transcends temporal predication to express divine eternity
• The eternal now is fundamentally different from temporal “before” and “after”

Compound Statements: The Conditional (If-Then) #

• If-then statement (conditional): Links two simple statements through logical dependence
• Form: “If A is so, then B is so”
• Critical logical point: An if-then statement does NOT assert that A or B are actually true in fact
• The if-then statement only asserts: if A is true, then B must also be true
• Example: “If I am a mother, then I am a woman” (true conditional, though I may not be a mother in fact)

The Four Possible Cases in Conditional Reasoning #

1. A true, B true: Necessarily follows from the if-then conditional ✓

   • “If I am a mother, then I am a woman. I am a mother. Therefore, I am a woman.”

2. A false, B unknown: Does NOT necessarily follow

   • “If I am a mother, then I am a woman. I am not a mother. Therefore…?” (I could still be a woman)
   • No valid conclusion: other causes might produce B

3. B true, A unknown: Does NOT necessarily follow (affirming the consequent fallacy)

   • “If Berkowitz dropped dead last night, then he is absent. Berkowitz is absent. Therefore he dropped dead” (false reasoning)
   • The effect B can result from other causes; from B alone you cannot infer A

4. B false, A necessarily false: Necessarily follows from the if-then conditional ✓

   • “If this is a dog, then it is an animal. This is not an animal. Therefore it is not a dog.”

Application: The Weakness in Confirmatory Reasoning in Experimental Science #

• A scientist proposes a hypothesis: “If my hypothesis is correct, then the eclipse will occur at 10:06 AM tomorrow”
• The eclipse does occur at exactly 10:06 AM
• The scientist concludes: “My hypothesis is confirmed!”
• Logical error: This commits the fallacy of affirming the consequent
• Just because B occurred does not prove A is true—the eclipse could be explained by other astronomical factors
• The hypothesis does not cause the eclipse; correct prediction does not prove correctness of the hypothesis
• Understanding the logical form prevents this inference error

Compound Statements: The Disjunctive (Either-Or) #

• Either-or statement: Presents alternatives that exhaust the possibilities
• Form: “Either A or B” (or both in some formulations)
• Example: “Either a number is odd or a number is even”
• Requirement: The disjunction must exhaust logical possibilities
• Challenge: As with Aristotelian virtues (natural understanding, episteme, reason, knowledge, or wisdom), it can be difficult to verify exhaustiveness

Important Definitions #

Definition (Definitio): Speech signifying what a thing is; specifically, speech that makes known distinctly the essence or nature of a thing. Distinguished from mere naming by its capacity to articulate the constitutive parts (genus and differences) that constitute a thing’s essence.

Statement or Proposition (Propositio): Speech signifying the true or the false. A statement necessarily involves predication of something concerning a subject, making it capable of truth-value. The term propositio derives from pro bono (before) because one states beforehand (propone) what one proposes to prove or investigate.

Simple Statement (Enuntiatio simplex): A statement composed of at least a noun and verb, affirming or denying one thing of another. The subject (what is spoken of) and predicate (what is said of it) with a copula connecting them.

Compound Statement: A statement formed by combining simple statements through logical connectives (disjunction, conditionality, conjunction).

Conditional Statement (If-Then): A compound statement of the form “If A, then B” that asserts a logical dependence between antecedent and consequent without asserting the factual truth of either component.

Name (Nomen): A vocal sound with no parts that signify by themselves; signifies by custom or convention.

Speech (Oratio): A vocal sound with at least two parts that signify by themselves; likewise signifies by custom or convention.

Verb: A name that adds to ordinary signification the feature of signifying with time (cum tempore).

Examples & Illustrations #

The Name “Johnson” #

• Etymologically composed of “John” (a name) and “son” (signifying a male child)
• When “Johnson” functions as a family name for a female, it no longer signifies “daughter of John”
• As a name, Johnson signifies the whole sound and nothing internal to it
• This illustrates the distinction between etymology (historical derivation) and meaning (current signification)

Berquist’s Own Name: Bergkriston #

• Original Swedish name: Bergkriston (“Berg” = mountain; “krist” = branch)
• His father removed the “G”: Berkriston
• His mother’s maiden name was Berk, which he incorporated
• His son’s nickname at West Point became “B-Q” (phonetic abbreviation)
• Illustrates how names, though compositionally analyzable etymologically, function as simple wholes signifying their bearers

The Baby’s Cry #

• A baby cries with various acoustic results
• The cry naturally signifies bodily need (hunger, pain from a pin)
• Parent recognizes this natural signification and responds
• Contrasts with arbitrary names/speeches that signify only by custom or convention
• Shows that signification can be either natural (as in the baby’s cry) or conventional (as in human language proper)

Simple Statements About Shapes #

• “A square is a quadrilateral” (TRUE: what is, is)
• “A square is not a circle” (TRUE: what is not, is not)
• “A square is a circle” (FALSE: what is not, is)
• “A square is not a quadrilateral” (FALSE: what is, is not)

Conditional Statements with Varying Truth Conditions #

Case 1 - Valid inference (affirming antecedent):

• “If I am a mother, then I am a woman”
• “I am a mother”
• “Therefore, I am a woman” ✓

Case 2 - Invalid inference (denying antecedent):

• “If I am a mother, then I am a woman”
• “I am not a mother”
• “Therefore, I am not a woman” ✗
• (I could be a woman without being a mother)

Case 3 - Invalid inference (affirming consequent):

• “If Berkowitz dropped dead last night, then Berkowitz is absent from class”
• “Berkowitz is absent from class”
• “Therefore, Berkowitz dropped dead last night” ✗

Case 4 - Valid inference (denying consequent):

• “If Berkowitz dropped dead last night, then Berkowitz is absent from class”
• “Berkowitz is not absent from class”
• “Therefore, Berkowitz did not drop dead last night” ✓

Scientific Hypothesis Confirmation #

• Hypothesis: “If my astronomical model is correct, then the solar eclipse will occur at precisely 10:06 AM tomorrow”
• Observation: The eclipse occurs at exactly 10:06 AM
• Scientist’s erroneous conclusion: “My hypothesis is confirmed!”
• Logical analysis: This is affirming the consequent
• The eclipse’s occurrence does not prove the hypothesis because the eclipse would occur regardless (it is caused by celestial mechanics, not by the hypothesis being true)
• The form of reasoning is invalid: “If A, then B. B is true. Therefore A is true” ✗

Questions Addressed #

Why distinguish between name and speech if both are vocal sounds? #

Both are vocal sounds signifying by convention, but they differ structurally:

• Names have no parts that signify by themselves
• Speeches have at least two parts that each signify by themselves
• This structural difference enables different logical functions: names identify things, speeches make claims about things

Why is a single noun (like “dog”) neither true nor false? #

Because truth and falsity require predication—claiming that something is or is not the case. A bare noun makes no such claim. To get truth or falsity, you must construct a statement: “A dog is an animal” (true) or “A dog is a cat” (false).

What is peculiar about the verb’s relationship to time? #

The verb essentially signifies with time (cum tempore), whereas a noun signifies without temporal reference. This reflects a deep human limitation: we naturally think things must exist somewhere (in space) and somewhen (in time). This makes it philosophically difficult to express truths about eternal beings or God, who transcends temporal categories entirely.

How can an if-then statement be true even if both components are false? #

Because the if-then statement does not assert that either component is true in fact. It asserts only a logical dependence: if the antecedent were true, then the consequent would necessarily be true. “If I am a mother, then I am a woman” is a true conditional even though I (Berquist) am neither a mother nor a woman.

What follows logically from affirming the antecedent in a conditional? #

If “If A, then B” is true AND A is true, then necessarily B must be true. This is the only valid forward inference from a conditional. Example: “If this is a dog, then it is an animal. This is a dog. Therefore, it is an animal.”

What does NOT follow when the antecedent is false? #

Nothing necessarily follows about B. B could be true or false. Example: “If I am a mother, then I am a woman. I am not a mother. Therefore…?” — I could still be a woman for other reasons. Multiple possible causes can produce the same effect.

Why is affirming the consequent a logical fallacy? #

Because B (the consequent) can result from multiple causes, not only from A (the antecedent). Observing that B is true does not prove A caused it or that A is true. The effect does not determine its cause uniquely. Example: “If Berkowitz dropped dead, he’d be absent. Berkowitz is absent. Therefore he dropped dead.” — But he could be absent for many reasons.

How does this explain the weakness in experimental confirmation? #

Scientists often reason: “If my hypothesis is correct, then phenomenon B will occur. B occurred. Therefore my hypothesis is correct.” This commits the affirming-the-consequent fallacy. The phenomenon B might be caused by completely different factors. The hypothesis doesn’t cause the eclipse; correct prediction doesn’t prove the hypothesis true. The logical form is invalid regardless of how well predictions match observations.

Notable Quotes #

“When you say that what is, is, you’re being true. And when you say what is not, is not, you’re being true. And you’re being false when you say that what is not, is, or what is, is not.”

— Berquist, articulating the classical definition of truth in statements

“Before Abraham was, I am.”

— Jesus (cited by Berquist as an example of transcending temporal language to express God’s eternity)

“It’s very hard for us to escape from time. Though our knowledge and our meaning starts from the continuous, a place and time, which are species of the continuous.”

— Berquist, on humanity’s inherent temporal perspective and its philosophical implications