All human knowledge begins with intuitions, proceeds from thence to concepts, and ends with ideas.

As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method.

First of all, we ought to observe, that mathematical propositions, properly so called, are always judgments a priori, and not empirical, because they carry along with them necessity, which can never be deduced from experience. If people should object to this, I am quite willing to confine my statements to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure knowledge a priori.

I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially [science] of nature, requires a pure portion, lying at the foundation of the empirical, and based upon a priori knowledge of natural things. … To the possibility of a determinate natural thing, and therefore to cognise it à priori, is further requisite that the intuition corresponding à priori to the conception should be given; in other words, that the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.

In scientific matters ... the greatest discoverer differs from the most arduous imitator and apprentice only in degree, whereas he differs in kind from someone whom nature has endowed for fine art. But saying this does not disparage those great men to whom the human race owes so much in contrast to those whom nature has endowed for fine art. For the scientists' talent lies in continuing to increase the perfection of our cognitions and on all the dependent benefits, as well as in imparting that same knowledge to others; and in these respects they are far superior to those who merit the honour of being called geniuses. For the latter's art stops at some point, because a boundary is set for it beyond which it cannot go and which has probably long since been reached and cannot be extended further.

Our knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (receptivity for impressions), the second is the power of knowing an object through these representations (spontaneity [in the production] of concepts).

Philosophy stands in need of a science which shall determine the possibility, principles, and extent of human knowledge à priori.

Science is organized knowledge. Wisdom is organized life.
[Author Will Durant’s summary of Kant’s ideas; not a direct translation of Kant’s own words.]

Thoughts without content are empty, intuitions without concepts are blind... The understanding can intuit nothing, the senses can think nothing. Only through their union can knowledge arise.