30. Truth and Falsity in Simple Statements

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Lecture Notes

Main Topics #

• Truth as Conformity with Reality: Truth in simple statements means the mind is in agreement with things—saying what is, is, OR saying what is not, is not
• Two Modes of Falsity: Falsity occurs in precisely two ways: by addition (asserting what does not exist) or by subtraction (denying what does exist)
• Truth as a Mean: Truth occupies a modest mean between two extremes, unlike virtue which is a mean in the sense of proportion
• Contradictory Statements: Simple statements with identical subject and predicate, one affirmative and one negative, such that one must be true and one must be false
• How We Know Truth: Logic alone cannot determine which contradictory is true; we require senses, definition/understanding, or reasoning

Key Arguments #

The Definition of Truth and Falsity #

• Truth in affirmative statements: Saying what is, is (e.g., “Berquist is standing now” when he is standing)
• Truth in negative statements: Saying what is not, is not (e.g., “Berquist is not sitting now” when he is not sitting)
• Falsity by addition: Saying what is not, is (e.g., “Berquist is sitting now” when he is standing)
• Falsity by subtraction: Saying what is, is not (e.g., “Berquist is not standing now” when he is standing)
• Both modes of falsity are equally opposed to truth; one adds to reality, the other subtracts from it

The Courtroom Oath as Revealing the Two Modes of Falsity #

• The oath “I swear to tell the truth, the whole truth, and nothing but the truth” is not merely repetitive emphasis
• “The whole truth” opposes falsity by subtraction (what is, is not)
• “Nothing but the truth” opposes falsity by addition (what is not, is)
• Example: A bartender testifying that John, Thomas, and Paul were at the bar (when only John and Thomas were there) adds to the truth; testifying only John was there subtracts from it

Truth as a Mean Between Extremes #

• Truth is “modest truth”—neither more nor less than what is
• This differs from the mean in moral virtues (which is a proportion), as truth is an absolute mean
• Both extremes (addition and subtraction) equally depart from truth
• In theological mysteries, truth often lies between two heresies that each grasp part of the truth

Contradictory Statements #

• Definition: Two simple statements with the same subject and predicate, one affirmative and one negative
• Logical properties: Both cannot be true; both cannot be false; one must be true and one must be false
• What logic tells us: Logic knows that one must be true and the other false, but cannot determine which without additional information
• How we determine truth value: By senses (observation), by understanding what the terms mean (definition), or by reasoning from other known truths

Important Definitions #

• Truth (veritas): The conformity or equality of the mind with things; saying what is, is, and what is not, is not
• Falsity: Either saying what is, is not (subtraction) or saying what is not, is (addition)
• Simple statement: A statement composed of subject and predicate that affirms or denies one thing of another
• Contradictory statements: Two simple statements identical in subject and predicate, differing only in that one affirms and the other denies
• Conformity of mind with things: The fundamental nature of truth as the mind’s agreement with the way things actually are

Examples & Illustrations #

Truth and Falsity Examples #

• “Berquist is standing now” (true when he stands—says what is, is)
• “Berquist is not sitting now” (true when he stands—says what is not, is not)
• “Berquist is not standing now” (false when he stands—says what is, is not)
• “Berquist is sitting now” (false when he stands—says what is not, is)

Courtroom Testimony Example #

• Fact: John and Thomas were at the bar between 9-10 PM; no one else was present
• Testimony adding to truth: “John, Thomas, and Paul were there” (introduces what is not)
• Testimony subtracting from truth: “Only John was there” (denies what is)
• Complete truthful testimony: “John and Thomas were there”

Contradictory Statements #

• “President Bush is sitting now” vs. “President Bush is not sitting now”—one must be true, one false
• “No odd number is even” vs. “Some odd number is even”—determined by understanding what odd and even mean
• “No circle is a square” vs. “Some circle is a square”—determined by understanding definitions of circle and square

Theological Examples #

• Trinity (one nature, three persons):

  • Error by addition (Arianism-like): Three natures and three persons—says what is not, is
  • Error by subtraction (Sabellianism-like): One nature and one person—says what is, is not
  • Truth: One nature and three persons—the modest mean

• Incarnation (one person, two natures):

  • Error by addition (Nestorianism-like): Two persons and two natures—says what is not, is
  • Error by subtraction (Monophysitism-like): One person and one nature—says what is, is not
  • Truth: One person and two natures—the modest mean

Notable Quotes #

“Truth means saying what is, that it is. Or it says what is not, that what is not, in things, is not.”

“I swear to tell the truth, the whole truth, and nothing but the truth.” (Courtroom oath—analyzed to reveal the two modes of falsity)

“All my reports go with the modest truth, nor more, nor clipped, but so.” (Shakespeare, King Lear, Kent’s statement illustrating truth as a mean)

“Truth is the conformity of the mind with things.”

“The mind is in agreement with things, saying what is, is, and what is not, is not.”

Questions Addressed #

How do we know which of two contradictory statements is true? #

• By the senses: Direct observation (e.g., observing whether Berquist is standing)
• By definition and understanding: Knowing what the terms mean makes their relationship clear (e.g., odd and even cannot both apply to the same number)
• By reasoning: Deducing from other known truths (e.g., using geometry to prove a property must hold)
• Logic alone cannot tell us which is true; it only guarantees that one must be true and one must be false

Why does the courtroom oath use three phrases instead of just “tell the truth”? #

The three phrases reveal that there are exactly two ways to depart from truthful testimony—by addition and by subtraction—showing that truth is a mean between these extremes.

How can both contradictory statements be false if they exhaust the possibilities? #

They cannot both be false. The law of non-contradiction guarantees that if one contradictory is true, the other must be false. This follows from the definitions of truth and falsity themselves.