C. S. Peirce: Belief, Truth, and Going from the Known to the Unknown

Abstract

The third philosophical stratagem for cutting off inquiry consists in maintaining that this, that, or the other element of science is basic, ultimate, independent of aught else and utterly inexplicable— not so much from any defect in our knowing as because there is nothing beneath it to know. The only type of reasoning by which such a conclusion could be reached is retroduction. Now nothing justifies a retroductive inference except its affording an explanation of the farts. It is, however, no explanation at all of a fact to pronounce it inexplicable. That, therefore, is a conclusion which no reasoning can ever justify or excuse. (Peirce, Collected Papers 1.139)

Abduction consists in studying facts and devising a theory to explain them. Its only justification is that, if we are ever to understand things at all, it must be in that way. (Peirce, Collected Papers, 5.145)

[Scientific procedure] will at times find a high probability established by a single confirmatory instance, while at others it will dismiss a thousand as almost worthless. (Frege, Foundations of Arithmetic (1884), p. 16)