Philosophy of Being and Knowledge

Logic (Philosophy of Thought)

Complex Judgments

In addition to simple judgments, complex judgments frequently occur in thought processes. Complex judgments are formed by combining multiple simple judgments using logical connectives.

• When a connective of conjunction is used in a complex judgment, it is called a conjunctive judgment. Conjunction is a logical connective that unites two simple judgments and corresponds to the conjunction "and" in everyday language (e.g., "It is raining and the sun is shining"). It is symbolically denoted by the sign "∧". Consequently, the formula for a complex conjunctive judgment is "A ∧ B", where A and B are simple judgments. A conjunctive judgment is true only when all the simple judgments that comprise it are true.
• When a connective of disjunction is used in a complex judgment, it is called a disjunctive judgment. Disjunction is a logical connective that joins two simple judgments and corresponds to the conjunction "or" in everyday language (e.g., "It is raining or the sun is shining"). It is symbolically represented by the sign "∨". Thus, the formula for a complex disjunctive judgment is "A ∨ B", where A and B are simple judgments. A disjunctive judgment is true if at least one of the simple judgments within it is true.
• An implicative judgment refers to a complex judgment in which one simple judgment is a condition for the other (e.g., "If it is raining, then the road is wet"). In an implicative judgment, simple judgments are connected by the logical connective of implication, symbolized by "→" and read as "if..., then...". The first simple judgment, which serves as the condition, is called the antecedent or premise, and the second is called the consequent or result. An implicative judgment is false only when the antecedent is true and the consequent is false; in all other cases, it is true.
• An equivalency judgment is a complex judgment consisting of two simple judgments where each is a condition for the other (e.g., "A number is divisible by three if and only if it is divisible by three"). This type of judgment uses the logical connective of equivalence, symbolized by "↔" and read as "if and only if". An equivalency judgment is false when one of its components is false while the other is true; it is true if both components have the same truth value, meaning both are true or both are false.
• Negations are judgments that deny a simple judgment (e.g., "The table is not wooden" is a negation of the judgment "The table is wooden"). Negation is symbolized by "¬". The formula "¬A" is read as "not A".