Philosophy of Being and Knowledge

Logic (Philosophy of Thought)

Laws of Logic

Thought is composed of logical forms, as if from material. Alongside studying the forms of thought, which are the fundamental units with which thought operates, much attention in logical investigations is dedicated to the laws of logic. These laws form one of the core themes of logic, as they underlie and define the very nature of thinking. The laws of logic are the basic principles upon which thought is constructed. There are four principal logical laws:

• Law of Identity (lex identitatis): Every thought must be clear in scope, precise in content, and consistent throughout the course of reasoning.
• Law of Non-Contradiction (lex contradictionis): Two judgments, one of which affirms something and the other denies the same thing at the same time and in the same respect, cannot both be true simultaneously.
• Law of Excluded Middle (lex exclusi tertii sive medii inter duo contradictoria): Of two contradictory judgments, one must be true, and the other false—there is no third possibility.
• Law of Sufficient Reason (lex rationis determinantis sive sufficientis): A thought can only be considered true if its truth is grounded in sufficient evidence.

In addition to these, there are other laws of logic:

• Law of Double Negation: A double negation is equivalent to an affirmation.
• Law of Idempotence: Any repetition of the same judgment using the logical connectives of conjunction or disjunction is equivalent to that judgment itself.
• Law of Commutativity: Simple judgments connected by conjunction or disjunction can be swapped without changing their truth.
• Law of Contraposition: This allows the transformation of complex conditional judgments by switching the antecedent and consequent and altering their quality.
• Law of Associativity: It permits choosing any sequence of operations when using logical connectives in a complex judgment, provided the components are connected by a series of conjunctions or disjunctions.
• Law of Distributivity: This governs the transformation of complex judgments that combine conjunction and disjunction.
• De Morgan's Laws: These show the relationship between negation, conjunction, and disjunction, allowing the conversion of conjunction into disjunction using negation, and vice versa:

✵ First De Morgan's Law: The negation of a conjunction is equivalent to the disjunction of the negations.

✵ Second De Morgan's Law: The negation of a disjunction is equivalent to the conjunction of the negations.

The laws of logic operate in all areas of thought and knowledge and are universal across all people, nations, and cultures.