Kant argues that there are synthetic judgments such as the connection of cause and effect (e.g., "... Every effect has a cause.") where no analysis of the subject will produce the predicate. Kant reasons that statements such as those found in geometry and Newtonian physics are synthetic judgments. Kant uses the classical example of 7 + 5 = 12. No amount of analysis will find 12 in either 7 or 5. Thus Kant arrives at the conclusion that all pure mathematics is synthetic though a priori; the number 7 is seven and the number 5 is five and the number 12 is twelve and the same principle applies to other numerals; in other words, they are universal and necessary. For Kant then, mathematics is synthetic judgment a priori. This conclusion led Kant into a new problem as he wanted to establish how this could be possible: How is pure mathematics possible? This also led him to inquire whether it could be possible to ground synthetic a priori knowledge for a study of metaphysics, because most of the principles of metaphysics from Plato through to Kant's immediate predecessors made assertions about the world or about God or about the soul that were not self-evident but which could not be derived from empirical observation (B18-24). For Kant, all post-Cartesian metaphysics is mistaken from its very beginning: the empiricists are mistaken because they assert that it is not possible to go beyond experience and the dogmatists are mistaken because they assert that it is possible to go beyond experience through theoretical reason.
Therefore, Kant proposes a new basis for a science of metaphysics, posing the question: how is a science of metaphysics possible, if at all? According to Kant, only practical reason, the faculty of moral consciousness, the moral law of which everyone is immediately aware, makes it possible to know things as they are. This led to his most influential contribution to metaphysics: the abandonment of the quest to try to know the world as it is "in itself" independent of sense experience. He demonstrated this with a thought experiment, showing that it is not possible to meaningfully conceive of an object that exists outside of time and has no spatial components and is not structured in accordance with the categories of the understanding, such as substance and causality. Although such an object cannot be conceived, Kant argues, there is no way of showing that such an object does not exist. Therefore, Kant says, the science of metaphysics must not attempt to reach beyond the limits of possible experience but must discuss only those limits, thus furthering the understanding of ourselves as thinking beings. The human mind is incapable of going beyond experience so as to obtain a knowledge of ultimate reality, because no direct advance can be made from pure ideas to objective existence.
Kant writes, "Since, then, the receptivity of the subject, its capacity to be affected by objects, must necessarily precede all intuitions of these objects, it can readily be understood how the form of all appearances can be given prior to all actual perceptions, and so exist in the mind a priori" (A26/B42). Appearance is then, via the faculty of transcendental imagination, grounded systematically in accordance with the categories of the understanding. Kant's metaphysical system, which focuses on the operations of cognitive faculties, places substantial limits on knowledge not founded in the forms of sensibility. Thus it sees the error of metaphysical systems prior to the Critique as failing to first take into consideration the limitations of the human capacity for knowledge. According to Heidegger, transcendental imagination is what Kant also refers to as the unknown common root uniting sense and understanding, the two component parts of experience. Transcendental imagination is described in the first edition of the Critique of Pure Reason but Kant omits it from the second edition of 1787.
It is because he takes into account the role of people's cognitive faculties in structuring the known and knowable world that in the second preface to the Critique of Pure Reason Kant compares his critical philosophy to Copernicus' revolution in astronomy. Kant writes: "Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our knowledge of objects by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge" (Bxvi). Just as Copernicus revolutionized astronomy by taking the position of the observer into account, Kant's critical philosophy takes into account the position of the knower of the world in general and reveals its impact on the structure of the known world. Kant's view is that in explaining the movement of celestial bodies Copernicus rejected the idea that the movement is in the stars and accepted it as a part of the spectator. Knowledge does not depend so much on the object of knowledge as on the capacity of the knower.
Kant's transcendental idealism should be distinguished from idealistic systems such as that of George Berkeley. While Kant claimed that phenomena depend upon the conditions of sensibility, space and time, and on the synthesizing activity of the mind manifested in the rule-based structuring of perceptions into a world of objects, this thesis is not equivalent to mind-dependence in the sense of Berkeley's idealism. Kant defines transcendental idealism:
- "I understand by the transcendental idealism of all appearances the doctrine that they are all together to be regarded as mere representations and not things in themselves, and accordingly that time and space are only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves. To this idealism is opposed transcendental realism, which regards space and time as something given in themselves (independent of our sensibility)." (CPR, A369)