Kantian Journal

2017 Vol. 36. No. 3

Kant, Gödel, and the problem of synthetic a priori judgements

Abstract

Debates over Kant’s famous postulate about the existence of synthetic a priori judgements in mathematics, formulated in the Critique of Pure Reason, have been raging for over two centuries. On the one hand, it was fiercely criticised by neo-positivists in the early 20th century. On the other hand, Kant’s ideas on constructive nature of mathematics served as a philosophical framework for LEJ Brouwer’s programme of intuitionism in the foundations of mathematics. Of interest are the ideas of the great logician and mathematician Kurt Gödel about the analytical nature of mathematics, put forward in a number of his works on philosophy of mathematics. Although he never mentions synthetic a priori judgements, the course of his reasoning about analytical judgements is close to that employed by Kant. As early as the mid-20th century, Gödel’s incompleteness theorems and the works of Church and Turing constituted arguments in favour of the existence of synthetic a priori judgements. The American logician Irving Copi was the first to use Gödel’s first incompleteness theory to that end. While his small work went almost unnoticed, such ideas were expressed by at least two other mathematicians. In modern mathematics, particularly, Martin-Löf type theory, the existence of synthetic a priori truths, is considered justified. Although it is based on different grounds than those mentioned above, it is nevertheless compatible with Gödel’s results. Analysing proofs of existence of synthetic a priori judgements helps demonstrate that a solution to this problem is determined by the implicitly or explicitly accepted image of logic, whose key parameter is the object of logic or, in other worlds, the ideas about the nature of the logical and, therefore, the ideas about the boundaries of logic and mathematics.

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I. Kant’s and E. Husserl’s practical philosophy

Abstract

This article focuses on the problem of reconciling a priori and empirical dimensions of freedom, will, and action as the crucial point for understanding the relationship between theoretical and practical reason in Kant’s and Husserl’s practical philosophy. Relying on the explanation of the relationship between transcendental and practical freedom given in Kant's practical philosophy, the author problematizes Kant’s thesis about the primacy of practical reason. This is the starting point and leitmotif in analysing the nature of revision of Kant’s ideas, premises, and problems in the first draft of Husserl’s practical philosophy (scientific ethics). Comparative analysis reveals terminological and conceptual similarities and differences between Kant’s and Husserl’s practical philosophies. Another important result is identifying the principles and departure point ideas for both thinkers. These are a shared understanding of the relationship between theoretical and practical reason, the principle of the ‘purity’ of moral motives and compulsoriness of the a priori, the idea of parallelism between logic and ethics, the interaction between will and mind, and the determining role of the categorical imperative. The author stresses that an adequate understanding of the thinkers’ positions requires distinguishing between Kant’s transcendentalist perspective and Husserl’s phenomenological descriptive perspective, between the a priori of pure reason and the material a priori, between good will as a duty and the thetic acts of will, and between the absolute and relative compulsoriness of the categorical imperative. At the same time, the possibility of reconciling the obligatory and a priori greatest good with a concrete, practical situation of choice remains an open question.

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