Observation supplies fact. Induction ascends from fact to law. Deduction, applying the pure logic of mathematics, reverses the process and descends from law to fact. The facts of observation are liable to the uncertainties and inaccuracies of the human senses; and the first inducation of law are rough approximations to the truth. The law is freed from the defects of observation and converted by the speculations of the geometer into exact form. But it has ceased to be be pure induction, and has become ideal hyptohesis. Deductions are made from its syllogistic precision, and consequent facts are logically evolved without immediate reference to the actual events of nature. If the results of computation coincide, not merely qualitatively but quantitatively, with observation, the law is established as a reality, and is restored to the domain of induction. (Benjamin Peirce, Ideality in the Physical Sciences 1881: 163-4)