The Fundamental Law of Thought: From Kant to Boole

In some matters, the philosophical significance of historical and logical research cannot be overestimated. First, because any significant philosophical system is based on a certain logic, rarely pronounced, and its explication helps to clarify the main points, reveal the genesis of this system and, possibly, avoid its frankly false interpretations. Immanuel Kant's doctoral thesis "A New Elucidation of the First Principles of Metaphysical Cognition (Principiorum primorum cognitionis metaphysicae nova dilucidatio)", presented at the Faculty of Philosophy at the University of Konigsberg in September 1755, can be considered his first serious work devoted to the actual problems of metaphysics. This treatise is remarkable, for, in it, Kant criticized two fundamental principles of the then dominant Leibniz-Wolff metaphysics, namely, the principles of contradiction and sufficient reason. He proposes to replace them with the principle of identity for the basis and criterion of all truths and the principle of the determining basis for finding the source of true knowledge. In his critical philosophy, Kant considers reason and mind as cognitive abilities that constitute rational thinking in general. Logic is the science of thinking, and general pure logic contains its basic and necessary, a priori principles. Any thinking, according to Kant, is based on the law of identity because no thinking about the world would be possible, firstly, if we could not perceive the identity of the objects of thinking in the process of perceiving the diverse in time and, secondly, without the identity of the perceiving subject. Thus, it must be admitted that the status of the law of identity has not changed much in Kant's critical philosophy, just like his idea of distinguishing between logical and real foundations of knowledge. Despite the fact that the origin of the first systems of symbolic logic is not associated with traditional metaphysics, it seems that it is not accidental; the course of George Boole's reasoning about the basic principle of logic surprisingly resembles that of early Kant. First, he formulates the fundamental law of thought, based on some version of the law of identity for classes and then deduces from it the law of contradiction. Then he turns to one of the most important tasks of Kant's critical philosophy to identify the elementary actions of thinking to create conditions for the construction of an adequate theory of consciousness. In his unpublished notes on the nature of logic, Boole writes that it is absolutely wrong to define logic as an art or a science of reasoning, since it is impossible to define the process of reasoning in any way without first analyzing the process of thinking, conceptualizing and judging. In addition, it is not enough just to recognize the existence of such processes and describe their objects. Their laws must be established. According to Boole, logic is the science of thought and its laws, expressed in operations on the concepts of judgments and reasoning and in language.

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