Logic: From Kant to Frege

Logic: From Kant to Frege

The field of logic, like any other field of sciences, mathematics, or even social sciences has undoubtedly withstood countless reforms, agreements, disagreements, deconstructions, and has most importantly managed to advance. Two of logic's most decorated contributors include Frege and Kant, who had diverging views on the conception of logic. In this paper I will show that Frege holds that logic, as it concerns numbers and arithmetic, is of an analytic nature. This will be done firstly by briefly expounding on Kant's conception of logic followed by a detailed explanation of Frege's critical stance against Kant's theory of logic as found in Frege's 1893 work The Foundations of Arithmetic. It will be shown how Frege disagrees with Kant's view on whether numerical formulas are provable, followed by an explication of the nature of the laws of arithmetic, namely whether they are synthetic a priori as Kant alludes to, or analytic as Frege alludes to. However, it is firstly necessary to understand Kant's conception of logic.

For Kant, understanding and reason are both capacities of the human mind and work in accordance with governing rules. The rules can act as contingent or necessary depending on the object at hand. This is to say that it is possible for understanding to work differently when used for mathematics, metaphysics, ethics or epistemology. Kant differentiates between two types of logic, general logic and special logic. Kant refers to general logic as a logic where the rules used are necessary for understanding, and in absence of these rules, no understanding would be possible to take place. On the other hand, special logics are those which use special employments of understanding, (Linnebo, p. 2). Kant also proposes a pure logic, which is deductive in nature derived from our empirical understanding. Kant's idea of pure logic seems to be what Frege takes aim at in The Foundations of Arithmetic. Kant defines pure logic as " the science of the necessary laws of the understanding and reason in general," (Kant, p. 17). Kant appeals to the formality of rules to explain how the necessary rules for understanding hold for all types of understanding, (Linnebo, p. 2). This is to say that Kant views the rules as they relate to the form of the object and not the matter present in the object. Kant also argues against a psychological approach to logic by arguing that, "an investigation of logic can proceed entirely a priori, without any need for empirical study of actual human thought," (Linnebo p. 3). Kant's second idea deals with constitutivity, where logic is said to dictate how to properly use our understanding in order to claim knowledge. This is to say that without logic, thought is not possible. Now that we have a clear understanding of Kant's conception of logic, a detailed look at Frege's notion