The twelve a priori concepts (or categories) that Kant wishes to hold as objectively valid and a necessary condition of our synthetic experience of the world include: Unity, Plurality, and Totality (the Categories of Quantity); Reality, Negation, and Limitation (the Categories of Quality); Inherence and Subsistence, Causality and Dependence, and Community (the Categories of Relation), and Possibility-Impossibility, Existence-Nonexistence, Necessity-Contingency (the Categories of Modality).
In the preface to Critique of Pure Reason, Kant wrote: “I know of no investigations that would be more important for getting to the bottom of the faculty that we call understanding and at the same time for determining the rules and limits of its employment than those that I have undertaken in the second part of the Transcendental Analytic, under the title of the Deduction of the Pure Concepts of the Understanding; they have also cost me the most, but not, I hope, unrewarded effort.”
From the perspective of soundness, however, Kant’s transcendental arguments are an unrewarded effort. According to Paul Guyer, Kant’s arguments for Transcendental Deduction is formally unsound. But Guyer points out that despite the philosophical failure of Kant’s arguments, the Transcendental Deduction has played a pivotal role in effacing the influence of Cartesian rationalism and Lockean empiricism, and setting a new agenda for modern philosophy by enabling the development of philosophical movements like logical positivism and linguistic philosophy.
Here’s an excerpt from Guyer’s essay, “The Transcendental Deduction of the Categories,” (Chapter 4, The Cambridge Companion to Kant, Edited by Paul Guyer):
Formally speaking, the transcendental deduction is a failure, and at best sets the agenda for the detailed demonstration of the role of the categories in the determination of empirical relations in space and especially time in the following sections of the Critique of Pure Reason. Nevertheless, the transcendental deduction also completely transformed the agenda of modern philosophy. While he had difficulty initially spelling it out, Kant clearly perceived that there was some inescapable connection between self-knowledge and knowledge of objects, and this completely undermined the Cartesian assumptions that we could have a determinate knowledge of our inner states without any knowledge of the external world at all and that we had to discover some means of inferring from the former to the latter. And while Kant had difficultly in distinguishing between the categories as merely logical functions of judgement and as extra-logical constraints on judgement, he nevertheless clearly saw that both self-knowledge and knowledge of objects were intrinsically judgmental and necessarily involved logical structures as well as empirical inputs. This completely undermined the Lockean and Humean project of discovering the foundations of all knowledge and belief in the empirical input of sensation and reflection alone. Progress in philosophy is rarely dependent upon the formal soundness of an argument, but on the compelling force of the new vision, and from this point of the view the transcendental deduction was a total success, turning Cartesian rationalism and Lockean empiricism into mere history and setting new agendas for subsequent philosophical movements from German idealism to logical positivism and the linguistic philosophy of our own times.