Section 6.1

Structure of Arguments

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An argument in formal logic is a set of statements, where one statement (the conclusion) is claimed to logically follow from the others (the premises). Evaluating an argument requires dissecting its internal architecture, primarily through categorical propositions and syllogisms (Aristotle, trans. 1989).

1. Categorical Propositions

A categorical proposition affirms or denies a relationship between two categories or classes (a Subject and a Predicate). The standard form of a categorical proposition consists of four parts:

Quantifier + Subject Term + Copula + Predicate Term

Example: All (Quantifier) men (Subject) are (Copula) mortal (Predicate).

The Four Standard Forms (A, E, I, O)

  • A (Universal Affirmative): All S is P. (Distributes the Subject)
  • E (Universal Negative): No S is P. (Distributes both Subject and Predicate)
  • I (Particular Affirmative): Some S is P. (Distributes neither)
  • O (Particular Negative): Some S is not P. (Distributes the Predicate)

💡 Candidate Note

'Distribution' refers to whether a proposition makes a claim about every member of a class. A propositions only make a claim about every member of the Subject class, not the Predicate.

2. Mood and Figure

A standard-form categorical syllogism consists of three categorical propositions (two premises and one conclusion) containing exactly three terms (Major, Minor, and Middle term).

  • Mood: The sequence of the types of propositions (A, E, I, or O) comprising the syllogism. For example, a syllogism composed of three 'All S is P' statements has a Mood of AAA.
  • Figure: Determined by the position of the Middle Term (the term that appears in both premises but not the conclusion). There are four possible figures depending on whether the middle term is the subject or predicate in the major and minor premises.

3. Connotation and Denotation

Language functions structurally in two fundamental ways when defining terms:

  • Denotation (Extension): The literal, explicit class of objects to which a term refers. E.g., The denotation of 'planet' includes Jupiter, Mars, Earth, etc.
  • Connotation (Intension): The set of attributes, qualities, or characteristics implied by a term. E.g., The connotation of 'planet' is a celestial body moving in an elliptical orbit around a star.

Rule of Inverse Variation: Generally, as the intension (connotation) of a term increases, its extension (denotation) decreases, and vice versa. (E.g., adding attributes to 'vehicle' to make it 'red sports car' decreases the number of real-world objects it points to).

Academic References

  • Aristotle. (1989). Prior analytics (R. Smith, Trans.). Hackett Publishing Company.
  • Copi, I. M., Cohen, C., & McMahon, K. (2014). Introduction to logic (14th ed.). Pearson.