Claim. Symbolic logic develops formal logic by using mathematical symbols to express precisely the connections between propositions, through five basic forms: negation, disjunction, conjunction, implication, and equivalence.
Elaboration. Sang Hun Lee distinguishes symbolic logic’s focus from classical formal logic’s (D. Symbolic Logic). Where formal logic studies the relationship of implications between terms (subject and predicate within a proposition), symbolic logic studies the connection between propositions using mathematical symbols, treating these connections as the subject matter of the laws of thought.
The five basic connectives between propositions p and q:
- Negation — ‘not-p’ (~p)
- Disjunction — ‘p or q’ (p ∨ q)
- Conjunction — ‘p and q’ (p ∧ q)
- Implication — ‘if p then q’ (p ⊃ q)
- Equivalence — ‘p equals q’ (p ≡ q)
Any complex deductive inference can be accurately expressed by combining these. The classical laws of formal logic — identity, contradiction, excluded middle — can themselves be symbolized in this notation.
Lee gives a motivating rationale: ‘philosophers often proposed extensive thought systems, but the question is whether or not their logical constructions are correct.’ To ascertain logical correctness, mathematical symbols and calculations are needed. Symbolic logic arose from this verificationist impulse.
The Unification Thought appraisal (in Section III) will be sympathetic but qualified: pursuing rigor in thinking is valuable, but mathematical strictness alone cannot fully grasp human thinking. Because in the Original Image the Inner Hyungsang contains laws and mathematical principles, Logos naturally contains mathematical structure — which is why nature is amenable to mathematical study. But Heart stands higher than reason and mathematics in the formation of Logos. So while symbolic logic captures a real feature of thought (its mathematical scaffolding), the human being is fundamentally a being of emotion as well as logos, and meaning can be conveyed without mathematical accuracy when love or emotion is present.
See also. formal-logic-four-laws-of-thought, logic-is-laws-and-forms-of-thinking, inference-deduction-induction-analogy