 A particularly intriguing aspect of Whewell’s philosophy of science is his claim that empirical science can reach necessary truths. Explaining this apparently contradictory claim was considered by Whewell to be the “ultimate problem” of philosophy (see the important paper by Morrison 1997). Whewell accounted for it by reference to his antithetical epistemology. Necessary truths are truths which can be known a priori; they can be known in this way because they are necessary consequences of ideas which are a priori. They are necessary consequences in the sense of being analytic consequences. Whewell explicitly rejected Kant’s claim that necessary truths are synthetic. Using the example “7 + 8 = 15,” Whewell claimed that “we refer to our conceptions of seven, of eight, and of addition, and as soon as we possess the conceptions distinctly, we see that the sum must be 15.” That is, merely by knowing the meanings of “seven,” and “eight,” and “addition,” we see that it follows necessarily that “7 + 8 = 15” (1848, 471).