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E pistemology, metaphysics For Kant , in order for quantitative experience to be possible, we must apply the categories of quantity, unity, plurality, and totality. We need rules to make these categories conform to the conditions of intuitions of objects. These rules for showing the objective validity of the categories of quantity are the axioms of intuitions. The leading principle for these axioms is that all intuitions are extensive magnitudes, meaning that they have magnitudes that are spatially or temporarily extended. This principle is purported to explain the application of geometry to empirical objects and to render possible the measurement of the experiential world. Kant did not, however, specify what these axioms are. This omission raises questions about the relations between the axioms of intuition and their leading principle and about the relation between the axioms of intuition and the categories of quantity. “Axioms of intuition. Their principle is: All intuitions are extensive magnitudes.” Kant, Critique of Pure Reason ... log in or subscribe to read full text