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 facts. 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)