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Click on the phrases to see them in context. The original texts by Immanuel Kant and David Hume are available from the Gutenberg Projet.
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But to determine a priori an intuition in space (its figure), to divide time into periods, or merely to cognize the quantity of an intuition in space and time, and to determine it by number--all this is an operation of reason by means of the construction of conceptions, and is called mathematical. If it is finite and limited, we have a right to ask; "What determines these limits?" Void space is not a self-subsistent correlate of things, and cannot be a final condition--and still less an empirical condition, forming a part of a possible experience. The categories are not based, as regards their origin, upon sensibility, like the forms of intuition, space, and time; they seem, therefore, to be capable of an application beyond the sphere of sensuous objects. If they adopt the second view of inherence, which is preferred by some metaphysical natural philosophers, and regard space and time as relations (contiguity in space or succession in time), abstracted from experience, though represented confusedly in this state of separation, they find themselves in that case necessitated to deny the validity of mathematical doctrines a priori in reference to real things (for example, in space)--at all events their apodeictic certainty. We have already traced to their sources the conceptions of space and time, by means of a transcendental deduction, and we have explained and determined their objective validity a priorI. Geometry, nevertheless, advances steadily and securely in the province of pure a priori cognitions, without needing to ask from philosophy any certificate as to the pure and legitimate origin of its fundamental conception of space. [*Footnote; Space is merely the form of external intuition (formal intuition), and not a real object which can be externally perceived. 4. Space is represented as an infinite given quantity.