Logic: Laws and Forms of Correct Thinking

Fundamental Formal-Logical Laws

Human thought is not executed chaotically; it adheres to certain logical laws. The primary laws of formal logic include the law of identity, the law of excluded middle, the law of contradiction, and the law of sufficient reason.

These formal-logical laws serve the function of ensuring the correct construction and coherence of thought. They embody essential, universal, and indispensable properties of our reasoning, such as definiteness, non-contradiction, consistency, and justification. Violating the requirements of logical laws leads to human thought making errors and becoming illogical.

The law of identity is articulated as follows: any proposition in the course of a given reasoning (regardless of transformations) must retain the same content, meaning it must be identical to itself. One feature of natural language is its tendency to conflate different thoughts while failing to distinguish identical ones. These errors arise from the capacity of natural language to express the same idea through various linguistic forms, leading to a substitution of the original meaning of concepts and the replacement of one thought with another. In traditional logic, the law of identity is expressed as the formula: A is A.

We can specify the essence of the law of identity in the following requirements:

1. In the process of reasoning about a particular subject, one must think specifically of that subject and cannot substitute it with another object of thought.
2. In the course of reasoning, in arguments and discussions, concepts must be used with the same meaning.

The law of contradiction (also referred to as the law of non-contradiction) proclaims that two contradictory statements cannot both be true simultaneously; at least one of them must necessarily be false. In other words, two judgments cannot be simultaneously true if one asserts something about an object while the other denies the same about that very object at the same time and in the same respect. For instance: "I. Kant is the author of 'Critique of Pure Reason' and 'I. Kant is not the author of 'Critique of Pure Reason'." There is no contradiction if we speak of the same subject taken at different times or in different respects. Symbolically, the law of contradiction is represented as: it is not true that A and not-A. The law of contradiction does not negate real contradictions existing in the objective world; it merely prohibits logical contradictions that "contradict themselves."

The essence of the law of excluded middle is as follows: of two contradictory judgments about the same subject, at the same time, and in the same respect, one must necessarily be true, the other false, and there can be no third option. In other words, according to the law of excluded middle, the falsehood of one contradictory statement necessarily implies the truth of the other, and thus no third statement can be true apart from the two contradictory ones. For example: "All houses in this village are electrified" and "Some houses in this village are not electrified." According to this law, only one of the two contradictory statements can be true: either A or not-A; there is no third option.

The law of excluded middle and the law of contradiction are united in that they ensure the consistency and coherence of thought. However, while the law of contradiction states that two contradictory judgments cannot be simultaneously true and at least one must be false, the law of excluded middle indicates that two contradictory judgments cannot both be false. One of them is undoubtedly true.

The scope of the law of non-contradiction is broader (encompassing contradictory and opposing judgments) than the scope of the law of excluded middle (only contradictory judgments). In relation to opposing judgments (universal affirmative - universal negative), which cannot be simultaneously true but can be simultaneously false, only the law of non-contradiction applies. However, in relation to contradictory judgments (universal affirmative - particular negative, universal negative - particular affirmative), both the law of excluded middle and the law of non-contradiction apply. This will be further discussed in the section on "Judgments" within the subsection "Logical Square."

The most commonly used formulation of the law of sufficient reason is: every thought must have sufficient grounds. In other words, any thought can only be true if it is justified. The judgments provided to substantiate the truth of another judgment are referred to as logical grounds, while the judgment that follows from other judgments, as well as the grounds, is called the logical consequence. The law of sufficient reason reflects the necessary connection that exists between the objects and phenomena of the surrounding world, namely the reflection of causal relationships, genetic connections, and so forth.